Skip to main content Accessibility help
×
  • Cited by 23
  • Sergio Cecotti, Scuola Internazionale Superiore di Studi Avanzati, Trieste
Publisher:
Cambridge University Press
Online publication date:
January 2015
Print publication year:
2015
Online ISBN:
9781107284203

Book description

Adopting an elegant geometrical approach, this advanced pedagogical text describes deep and intuitive methods for understanding the subtle logic of supersymmetry while avoiding lengthy computations. The book describes how complex results and formulae obtained using other approaches can be significantly simplified when translated to a geometric setting. Introductory chapters describe geometric structures in field theory in the general case, while detailed later chapters address specific structures such as parallel tensor fields, G-structures, and isometry groups. The relationship between structures in supergravity and periodic maps of algebraic manifolds, Kodaira–Spencer theory, modularity, and the arithmetic properties of supergravity are also addressed. Relevant geometric concepts are introduced and described in detail, providing a self-contained toolkit of useful techniques, formulae and constructions. Covering all the material necessary for the application of supersymmetric field theories to fundamental physical questions, this is an outstanding resource for graduate students and researchers in theoretical physics.

Refine List

Actions for selected content:

Select all | Deselect all
  • View selected items
  • Export citations
  • Download PDF (zip)
  • Save to Kindle
  • Save to Dropbox
  • Save to Google Drive

Save Search

You can save your searches here and later view and run them again in "My saved searches".

Please provide a title, maximum of 40 characters.
×

Contents

References
[1] Abbott, L.F., and Deser, S. 1982. Stability of gravity with a cosmological constant. Nucl. Phys., B195, 76.
[2] Adams, J. F. 1996. Lectures on Exceptional Lie Groups. University of Chicago Press.
[3] Aharony, O., Bergman, O., Jafferis, D.L., and Maldacena, J. 2008. N = 6 superconformal Chern–Simons–matter theories, M2-branes and their gravity duals. JHEP, 0810, 091.
[4] Akhiezer, D. N. 1990. Homogeneous complex manifolds. Pages 148–244. of: Several Complex Variables IV. (Encyclopaedia of Mathematical Sciences, vol. 10). Springer.
[5] Alekseeskii, D. V. 1975. Classification of quaternionic spaces with transitive solvable group of motion. Ozv. Akad. Nauk. SSSR Ser. Math., 39, 315–362.
[6] Alekseev, A., Malkin, A., and Meinjrenken, E. 1998. Lie group valued momentum maps. J. Differential Geom., 48, 445–195.
[7] Alvarez-Gaumé, L. 1983. Supersymmetry and the Atiyah–Singer index theorem. Commun. Math. Phys., 90, 161–173.
[8] Alvarez-Gaumé, L., and Freedman, D. 1983. Potentials for the supersymmetric non–linear σ-models. Commun. Math. Phys., 91, 87.
[9] Alvarez-Gaumé, L., and Freedman, D. Z. 1980. Kähler geometry and the renormalization of supersymmetric sigma models. Phys. Rev., D22, 846.
[10] Alvarez-Gaumé, L., and Freedman, D. Z. 1981. Geometrical structure and ultraviolet finiteness in the supersymmetric sigma model. Commun. Math. Phys., 80, 443.
[11] Alvarez-Gaumé, L., and Witten, E. 1983. Gravitational anomalies. Nucl. Phys., B234, 269–330.
[12] Alvarez-Gaumé, L., Freedman, D. Z., and Mukhi, S. 1981. The background field method and the ultraviolet structure of the supersymmetric nonlinear sigma model. Ann. Phys., 134, 85.
[13] Ambrose, W., and Singer, I. M. 1953. A theorem on holonomy. Trans. Amer. Math. Soc., 79, 428–443.
[14] Andrianopoli, L., Bertolini, M., Ceresole, A., D'Auria, R., Ferrara, S., Fré, P., and Magri, T. 1997. N =2 supergravity and N = 2 superYang–Mills theory on general scalar manifolds: symplectic covariance, gaugings and the momentum map. J. Geom. Phys., 23, 111–189.
[15] Andrianopoli, L., Cordaro, F., Fré, P., and Gualtieri, L. 2001. Nonsemisimple gaugings of D = 5 N = 8 supergravity and FDA.s. Class. Quant. Grav., 18, 395–414.
[16] Andrianopoli, L., D'Auria, R., Ferrara, S., and Lledo, M. A. 2002a. Duality and spontaneously broken supergravity in flat backgrounds. Nucl. Phys., B640, 63–77.
[17] Andrianopoli, L., D'Auria, R., Ferrara, S., and Lledo, M. A. 2002b. Gauging of flat groups in four-dimensional supergravity. JHEP, 0207, 010.
[18] Arnold, V. I. 1989. Mathematical Methods of Classical Mechanics. (Graduate Texts in Mathematics, vol. 60). Springer.
[19] Arnold, V. I., and Givental, A. B. 2001. Symplectic geometry. In: Dynamical Systems. IV. (Encyclopaedia of Mathematical Sciences, vol. 4). Springer.
[20] Atiyah, M. 1988a. Collected Works. Vol. 3. Index Theory. Oxford Science Publications; Oxford University Press.
[21] Atiyah, M. 1988b. Collected Works. Vol. 4. Index Theory: 2. Oxford Science Publications; Oxford University Press.
[22] Atiyah, M. F. 1984. The momentum map in symplectic geometry. Pages 43–51. of: Durham Symposium on Global Riemannian Geometry. Ellis Horwood Ltd.
[23] Atiyah, M. F., and Bott, R. 1966. A Lefschetz fixed point formula for elliptic differential operators. Bull. Amer. Math. Soc., 12, 245.
[24] Atiyah, M. F., and Bott, R. 1982. Yang–Mills equations over Riemann surfaces. Phil. Trans. R. Soc. Lond., A308, 523–615.
[25] Atiyah, M. F., and Bott, R. 1984. The momentum map and equivariant cohomology. Topology, 23, 1–28.
[26] Atiyah, M. F., Bott, R., and Shapiro, A. 1964. Clifford modules. Topology, 3, 3–38.
[27] Awada, M., and Townsend, P. K. 1986. Gauged N = 4, d = 6 Maxwell–Einstein supergravity and “antisymmetric-tensor Chern–Simons” forms. Phys. Rev., D33(Mar), 1557–1562.
[28] Baez, J. C. 2002. The octonions. Bull. Amer. Math. Soc., 39, 145–205.
[29] Bagger, J., and Lambert, N. 2007. Modeling Multiple M2's. Phys. Rev., D75, 045020.
[30] Bagger, J., and Lambert, N. 2008. Gauge symmetry and supersymmetry of multiple M2-branes. Phys. Rev., D77, 065008.
[31] Bagger, J., and Witten, E. 1983. Matter couplings in N = 2 supergravity. Nucl. Phys., B222, 1.
[32] Banks, T., and Seiberg, N. 2011. Symmetries and strings in field theory and gravity. Phys. Rev., D83, 084019.
[33] Bar, Ch. 1993. Real Killing spinors and holonomy. Commun. Math. Phys., 154, 509–521.
[34] Baum, H. 2002. Conformal Killing spinors and special geometric structures in Lorentzian geometry – a survey. arXiv:math/0202008 [math.DG].
[35] Baum, H. 2008. Conformal Killing spinors and the holonomy problem in Lorentzian geometry – A survey of new results. In: Symmetries and Overdetermined Systems of Partial Differential Equations. Springer.
[36] Baum, H. 2011. Holonomy groups of Lorentzian manifolds – a status report. Available at the author's webpage: http://www.mathematik.hu-berlin.de/baum/publikationen-fr/Publikationen-ps-dvi/Baum-Holono-my-report-final.pdf. Accessed August 13, 2014.
[37] Baum, H., and Kath, I. 1999. Parallel spinors and holonomy groups on pseudo'Riemannian spin manifolds. Ann. Global Anal. Geom., 17, 1–17.
[38] Baum, H., Friedrich, T., Grunewald, R., and Kath, I. 1991. Twistor and Killing Spinors on Riemannian Manifolds. (Teubner–Texte zur Mathematik, vol. 124). Teubner-Verlag.
[39] Berard-Bergery, L., and Ikenakhen, A. 1993. On the holonomy of Lorentzian manifolds. In: Differential Geometry: Geometry in Mathematical Physics and Related Topics. American Mathematical Society.
[40] Berg, M., Haak, M., and Samtleben, H. 2003. Calabi–Yau fourfolds with flux and supersymmetry breaking. JHEP, 04, 3–38.
[41] Berger, M. 1955. Sur les groupes d'holonomie des variétés à connexion affine et des variétés riemanniennes. Bull. Soc. Math. France., 83, 279–330.
[42] Berger, M. 2000. A Panoramic View of Riemannian Geometry. Springer.
[43] Berger, M., Gauduchon, P., and Mazet, E. 1971. Le spectre d'une varieté riemannienne. (Lectures Notes in Mathematics, vol. 194). Springer.
[44] Bergman, S. 1950. The Kernel Function and Conformal Mapping. (Mathematical Surveys and Monographs, vol. 5). America Mathematical Society.
[45] Bergshoeff, E., Koh, I. G., and Sezgin, E. 1985. Coupling YangéMills to N = 4 d = 4 supergravity. Phys. Lett., B155, 71–75.
[46] Bergshoeff, E., Cecotti, S., Samtleben, H., and Sezgin, E. 2010. Superconformal sigma models in three dimensions. Nucl. Phys., B838, 266–297.
[47] Bergshoeff, E. A., de Roo, M., and Hohm, O. 2008a. Multiple M2-branes and the embedding tensor. Class. Quant. Grav., 25, 142001.
[48] Bergshoeff, E. A., Hohm, O., Roest, D., Samtleben, H., and Sezgin, E. 2008b. The superconformal gaugings in three dimensions. JHEP, 0809, 101.
[49] Berndt, R. 2001. An Introduction to Symplectic Geometry. (Graduate Studies in Mathematics, vol. 26). American Mathematical Society.
[50] Bershadsky, M., Cecotti, S., Ooguri, H., and Vafa, C. 1994. Kodaira–Spencer theory of gravity and exact results for quantum string amplitudes. Commun. Math. Phys., 165, 311–428.
[51] Besse, A. L. 1987. Einstein Manifolds. Springer.
[52] Birmingham, D., Blau, M., Rakowski, M., and Thompson, G. 1991. Topological field theory. Phys. Rep., 209, 129–340.
[53] Blau, M., and Thompson, G. 1995. Localization and diagonalization: a review of functional integral techniques for low-dimensional gauge theories and topological field theories. J. Math. Phys., 36, 2192–2236.
[54] Blencowe, M. P., and Duff, M. J. 1988. Supermembranes and the signature of space-time. Nucl. Phys., B310, 387–404.
[55] Borel, A. 1949. Some remarks about Lie groups transitive on spheres and tori. Bull. Amer. Math. Soc., 55, 580–587.
[56] Borel, A. 1950. Le plan projectif des octaves et les sphéres comme espaces homogènes. C. R. Acad. Sci. Paris, 230, 1378–1380.
[57] Borel, A. 1960. On the curvature tensor of Hermitian symmetric manifolds. Ann. Math., 71, 508–521.
[58] Born, M., and Infeld, L. 1934. Foundations of the new field theory. Proc. R. Soc., A144, 425–451.
[59] Bott, R. 1957. Homogeneous vector bundles. Ann. Math., 66, 203–248.
[60] Bott, R., and Wu, L. W. 1982. Differential Forms in Algebraic Topology. (Graduate Texts in Mathematics, vol. 82). Springer.
[61] Bourbaki, N. 1989. Elements of Mathematics. Lie Groups and Lie Algebras. Chapt. 1–3. Springer.
[62] Boyer, C., and Galicki, K. 2008. Sasakian Geometry. (Oxford Mathematical Monographs). Oxford University Press.
[63] Boyer, C. P., and Galicki, K. 1999. 3–Sasakian manifolds. Surveys Diff. Geom., 7, 123.
[64] Boyer, C. P., Galicki, K., and Mann, B. M. 1993. Quaternionic reduction and Einstein manifolds. Commun. Anal. Geom., 1, 229–279.
[65] Bröker, T., and tom Dieck, T. 1985. Representations of Compact Lie Groups. (Graduate Texts in Mathematics vol. 98). Springer.
[66] Bryant, R., and Griffiths, P. 1983. Some observations on the infinitesimal period relations for regular threefolds with trivial canonical bundle. Pages 77–102. of: Artin, M. and Tate, J. (eds.), Arithmetic and Geometry. Papers dedicated to I.R. Shafarevich. Vol. II. Birkhäuser.
[67] Bryant, R. L., Chern, S. S., Gardner, R. B., Goldschmidt, H. L., and Griffiths, P. A. 1991. Exterior Differential Systems. (Mathematical Sciences Research Institute Publications, vol. 18). Springer.
[68] Bump, D. 1997. Automorphic Forms and Representations. (Studies in Advanced Mathematics, vol. 55). Cambridge University Press.
[69] Bump, D. 2000. Lie Groups. (Graduate Texts in Mathematics, vol. 225). Springer.
[70] Cahen, M., and Wallach, N. 1970. Lorentzian symmetric spaces. Bull. AMS, 76, 585–591.
[71] Calabi, E., and Vesentini, E. 1960. On compact, locally symmetric Kahler manifolds. Ann. Math., 71, 472–507.
[72] Campbell, L. C., and West, P. C. 1984. N =2, d = 2 nonchiral supergravity and its spontaneous compactification. Nucl. Phys., B243, 112–124.
[73] Candelas, P. 1988. Yukawa couplings between (2,1) forms. Nucl. Phys., B298, 458.
[74] Candelas, P., Horowitz, G. T., Strominger, A., and Witten, E. 1985. Vacuum configurations for superstrings. Nucl. Phys., B 258, 46–74.
[75] Candelas, P., De La Ossa, X. C., Green, P. S., and Parkes, L. 1991. A pair of Calabi–Yau manifolds as an exactly soluble superconformal theory. Nucl. Phys., B 359, 21–74.
[76] Cannas da Silva, A. 2008. Lectures on Symplectic Geometry. (Lecture Notes in Mathematics, vol. 1764). Springer.
[77] Carlson, J., Müller-Stach, S., and Peters, C. 2003. Period Mappings and Period Domains. (Cambridge Studies in Advanced Mathematics, vol. 85). Cambridge University Press.
[78] Cartan, E. 1935. Sur les domaines bornés homogènes de l'espace de n variables complexes. Abh. Math. Semin. Univ. Hamb., 11, 116–162.
[79] Castellani, L., Ceresole, A., D'Auria, R., Ferrara, S., Fre, P., and Maina, E. 1985. σ Models, duality transformations and scalar potentials in extended supergravities. Phys. Lett., B161, 91.
[80] Castellani, L., Ceresole, A., D'Auria, R., Ferrara, S., Fré, P., and Maina, E. 1986a. The complete N = 3 matter coupled supergravity. Nucl. Phys., B268, 376–382.
[81] Castellani, L., Ceresole, A., Ferrara, S., D'Auria, R., Fré, P., and Maina, E. 1986b. The complete N = 3 matter coupled supergravity. Nucl. Phys., B268, 317.
[82] Castellani, L., D'Auria, R., and Fré, P. 1991. Supergravity and Superstrings: A Geometrical Perspective, vols. 1, 2 … 3. World Scientific.
[83] Cecotti, S. 1988. Homogeneous Kähler manifolds and flat potential N = 1 supergravities. Phys. Lett., B215, 489–490.
[84] Cecotti, S. 1989. Homogeneous Kähler manifolds and T algebras in N = 2 super-gravity and superstrings. Commun. Math. Phys., 124, 23–55.
[85] Cecotti, S. 1991. Geometry of N = 2 Landau–Ginzburg families. Nucl. Phys., B 355, 755–776.
[86] Cecotti, S., and Girardello, L. 1982. Functional measure, topology and dynamical supersymmetry breaking. Phys. Lett., B110, 39.
[87] Cecotti, S., and Vafa, C. 1991. Topological antitopological fusion. Nucl. Phys., B367, 359–461.
[88] L., Lusanna (ed.). 1985. John Hopkins workshop on current problems in particle theory 9: new trends in particle theory. Singapore: World Scientific.
[89] Cecotti, S., Girardello, L., and Porrati, M. 1986. Constraints on partial superHiggs. Nucl. Phys., B268, 295–316.
[90] Cecotti, S., Ferrara, S., and Girardello, L. 1988. Hidden noncompact symmetries in string theories. Nucl. Phys., B308, 436.
[91] Cecotti, S., Ferrara, S., and Girardello, L. 1989. Geometry of type II superstrings and the moduli of superconformal field theories. Int. J. Mod. Phys., A4, 2475.
[92] Chapline, G., and Manton, N. S. 1983. Unification of Yang–Mills theory and super-gravity in ten dimensions. Phys. Lett., B120, 124–134.
[93] Chern, S. S. 1943. On the Curvatura Integra in a Riemannian manifold. Ann. Math., 46, 674–684.
[94] Chern, S. S. 1979. Complex Manifolds without Potential Theory (with an Appendix in the Geometry of Characteristic Classes). Springer.
[95] Chow, B., Chu, S.-C., Glickestein, D.Guenther, C., Isenberg, J., Ivey, T., Knopf, D., Lu, P., Luo, F., and Ni, L. 2007. The Ricci Flow: Techniques and Applications. Part I: Geometric Aspects. (Mathematical Surveys and Monographs vol. 135). American Mathematical Society.
[96] Coleman, S., and Mandula, J. 1967. All possible symmetries of the S-matrix. Phys. Rev., 159, 1251.
[97] Cordaro, F., Fré, P., Gualtieri, L., Termonia, P., and Trigiante, M. 1998. N = 8 gaugings revisited: an exhaustive classification. Nucl. Phys., B532, 245–279.
[98] Cremmer, E., and Julia, B. 1979. The SO(8) supergravity. Nucl. Phys., B159, 141–212.
[99] Cremmer, E., and Van Proeyen, A. 1985. Classification of Kähler manifolds in N = 2 vector multiplet supergravity couplings. Class. Quant. Grav., 2, 445.
[100] Cremmer, E., Julia, B., Scherk, J., Ferrara, S., Girardello, L., and van Nieuwen-huizen, P. 1979. Spontaneous symmetry breaking and Higgs effect in supergravity without cosmological constant. Nucl. Phys., B147, 105.
[101] Cremmer, E., Ferrara, S., Kounas, C., and Nanopoulos, D. V. 1983a. Naturally vanishing cosmological constant in N = 1 supergravity. Phys. Lett., B133, 61.
[102] Cremmer, E., Ferrara, S., Girardello, L., and Van Proeyen, A. 1983b. Yang-Mills theories with local supersymmetry: Lagrangian, transformation laws and super-Higgs effect. Nucl. Phys., B212, 413.
[103] de Boer, J., Manshot, J., Papadodimas, K., and Verlinde, E. 2009. The chiral ring of AdS3/CFT and the atractor mechanism. JHEP, 0903, 030.
[104] de Roo, M. 1985. Matter coupling in N = 4 supergravity. Nucl. Phys., B255, 515–531.
[105] de Roo, M., van Holten, J. W., de Wit, B., and Van Proeyen, A. 1980. Chiral super-fields in N = 2 supergravity. Nucl. Phys., B173, 175.
[106] de Wit, B. 1979. Properties of SO(8) extended supergravity. Nucl. Phys., B158, 189–212.
[107] de Wit, B. 1982. Conformal invariance in extended supergravity. Pages 267–312. of: Supergravity 1981. Cambridge University Press.
[108] de Wit, B. 2002. Supergravity. Lectures at the 2001 Le Houches Summer School. arXiv:hep-th/0212245.
[109] de Wit, B., and Freedman, D. Z. 1977. On SO(8) extended supergravity. Nucl. Phys., B130, 105–113.
[110] de Wit, B., and Nicolai, H. 1982. N = 8 supergravity. Nucl. Phys., B208, 323–364.
[111] de Wit, B., and Samtleben, H. 2005. Gauged maximal supergravities and hierarchies of nonabelian vector—tensor systems. Fortsch. Phys., 53, 442–449.
[112] de Wit, B., and Samtleben, H. 2008. The end of the p-form hierarchy. JHEP, 0808, 015.
[113] de Wit, B., and van Nieuwenhizen, P. 1989. Rigidly and locally supersymmetric two-dimensional non-linear σ-models with torsion. Nucl. Phys., B2, 58–94.
[114] de Wit, B., and Van Proeyen, A. 1984. Potentials and symmetries of general gauged N = 2 supergravity–Yang–Mills models. Nucl. Phys., B245, 89–117.
[115] de Wit, B., and Van Proeyen, A. 1992. Special geometry, cubic polynomials and homogeneous quaternionic spaces. Commun. Math. Phys., 149, 307–334.
[116] de Wit, B., van Holten, J. W., and van Proeyen, A. 1981. Structure of N =2 super-gravity. Nucl. Phys., B184, 77.
[117] de Wit, B., Lauwers, P. G., Philippe, R., Su, S. Q., and Van Proeyen, A. 1984. Gauge and matter fields coupled to N = 2 supergravity. Phys. Lett., B134, 37.
[118] de Wit, B., Lauwers, P. G., and Van Proeyen, A. 1985. Lagrangians of N = 2 super-gravity – matter systems. Nucl. Phys., B255, 569.
[119] de Wit, B., Tollsten, A. K., and Nicolai, H. 1993. Locally supersymmetric D = 3 nonlinear sigma models. Nucl. Phys., B 392, 3–38.
[120] de Wit, B., Herger, I., and Samtleben, H. 2003a. Gauged locally supersymmetric D = 3 nonlinear sigma models. Nucl. Phys., B671, 175–216.
[121] de Wit, B., Samtleben, H., and Trigiante, M. 2003b. On Lagrangians and gaugings of maximal supergravities. Nucl. Phys., B655, 93–126.
[122] de Wit, B., Samtleben, H., and Trigiante, M. 2004. Gauging maximal supergravities. Fortsch. Phys., 52, 489–496.
[123] de Wit, B., Nicolai, H., and Samtleben, H. 2008. Gauged supergravities, tensor hierarchies, and M-theory. JHEP, 0802, 044.
[124] Denef, F. 2008. Les Houches Lectures on Constructing String Vacua. e-print arXiv:0803.1194.
[125] Deser, S., and Zumino, B. 1976. Consistent supergravity. Phys. Lett., 62B, 335–337.
[126] Deser, S., Jackiw, R., and Templeton, S. 1982. Topologically massive gauge theories. Ann. Phys., 140, 373–411.
[127] Dieudonné, J. 1975. Eléments d'Analyse. Tome 5. Gauthier—Villars.
[128] Dirac, P.A.M. 1931. Quantised singularities in the electromagnetic field. Proc. R. Soc., A133, 60–73.
[129] Donagi, R., and Witten, E. 1996. Supersymmetric Yang–Mills theory and integrable systems. Nucl. Phys., B460, 299–334.
[130] Donagi, R.Y., and Wendland, K (eds.). 2008. From Hodge Theory to Integrability and TQFT: tt*-geometry. American Mathematical Society.
[131] Duistermaat, J. J., and Heckman, G. J. 1982. On the variation in the cohomology in the symplectic form of the reduced phase space. Invent. Math., 69, 259–268.
[132] Dumitrescu, T. T., and Seiberg, N. 2011. Supercurrents and brane currents in diverse dimensions. JHEP, 1107, 095.
[133] Dumitrescu, T. T., Festuccia, G., and Seiberg, N. 2012. Exploring curved superspace. JHEP, 1208, 141.
[134] Eisenhart, L. P. 1997. Riemannian Geometry. Princeton University Press.
[135] Faddeev, L. D., and Reshetikhin, N. Yu. 1986. Integrability of the principal chiral field model in (1+1)-dimension. Ann. Phys., 167, 227.
[136] Farkas, H. M., and Kra, I. 1992. Riemann Surfaces. (Graduate Texts in Mathematics, vol. 71). Springer.
[137] Feger, R., and Kephart, T. W. 2012. LieART – A Mathematical application for Lie algebras and Representation Theory. arXiv:1206.6379 [math-ph].
[138] Ferrara, S., and Sabharwal, S. 1990. Quaternionic manifolds for type II superstring vacua of Calabi–Yau spaces. Nucl. Phys., B 332, 317–332.
[139] Ferrara, S., and Savoy, C. A. 1982. Representations of extended supersymmetry on one and two-particle states. Pages 47–84.of: Supergravity 1981. Cambridge University Press.
[140] Ferrara, S., and Van Proeyen, A. 1989. A theorem on N = 2 special Kahler product manifolds. Class. Quant. Grav., 6, L243.
[141] Figueroa-O'Farrill, J. M., Kohl, C., and Spence, B. J. 1997. Supersymmetry and the cohomology of (hyper) Kahler manifolds. Nucl. Phys., B503, 614–626.
[142] Fischbacher, T., Nicolai, H., and Samtleben, H. 2004. Nonsemisimple and complex gaugings of N = 16 supergravity. Commun. Math. Phys., 249, 475–496.
[143] Fomenko, A. T. 1995. Symplectic Geometry. 2nd ed. (Advanced Studies in Contemporary Mathematics, vol. 5). Gordon and Breach.
[144] Fré, P. 2013. Gravity, a Geometrical Course. Vol 2. Springer.
[145] Freed, D. S. 1999. Special Kähler manifolds. Commun. Math. Phys., 203, 31–52.
[146] Freedman, D. Z., and van Proeyen, A. 2012. Supergravity. Cambridge University Press.
[147] Freedman, D. Z., van Nieuwenhuizen, P., and Ferrara, S. 1976. Progress toward a theory of supergravity. Phys. Rev., D13, 3214–3218.
[148] Freund, P.G.O. 1988. Introduction to Supersymmetry. Cambridge Monographs on Mathematical Physics. Cambridge University Press.
[149] Fritzsche, K., and Grauert, H. 2002. From holomorphic functions to complex manifolds. Graduate Texts in Mathematics, vol. 213. Springer.
[150] Gaillard, M. K., and Zumino, B. 1981. Duality rotations for interacting fields. Nucl. Phys., B193, 221–244.
[151] Gaiotto, D., and Witten, E. 2010. Janus configurations, Chern-Simons couplings, and the theta-angle in N=4 Super Yang-Mills Theory. JHEP, 1006, 097.
[152] Gaiotto, D., and Yin, X. 2007. Notes on superconformal Chern-Simons-Matter theories. JHEP, 0708, 056.
[153] Galaev, A. 2006. Isometry groups of Lobachewskian spaces, similarity transformation groups of Euclidean spaces and Lorentzian holonomy groups. Rend. Circ. Mat. Palermo, 79, 87–97.
[154] Galicki, K. and Lawson, H. B. 1988. Quaternionic reduction and quaternionic orbifolds. Math. Ann., 282, 1–21.
[155] Galicki, K. 1987. A generalization of the momentum mapping construction for quaternionic Kahler manifolds. Commun. Math. Phys., 108, 117–138.
[156] Garrett, P.Volume of SL(n, ℤ)\SL(n,ℝ) and Spn(ℤ)\Spn(ℝ). Available at http://www.users.math.umn.edu/∼garrett/m/v/volumes.pdf. Accessed August 13, 2014.
[157] Gates, S. J., Grisaru, M. T., Rocek, M., and Siegel, W. 2001. Superspace, or One Thousand and One Lessons in Supersymmetry. Free electronic version of the 1983 book (with corrections). Availableas arXiv:hep-th/0108200.
[158] Giani, F., and Pernici, M. 1984. N = 2 supergravity in ten dimensions. Phys. Rev., D30, 325–333.
[159] Gibbons, G. W., and Hull, C. M. 1982. A Bogomolny bound for general relativity and solitons in N = 2 supergravity. Phys. Lett., B 109, 190.
[160] Gibbons, G. W., Hull, C. M., and Warner, N. P. 1983. The stability of gauged super-gravity. Nucl. Phys., B218, 173.
[161] Gindikin, S. G., Pjateckii-Sapiro, I.I. and Vinberg, E. B. 1965. Classification and canonical realization of complex bounded homogeneous domains. Pages 404–437. of: Transactions of the Moscow Mathematical Society for the Year 1963. American Mathematical Society.
[162] Giveon, A., Porrati, M., and Rabinovici, E. 1994. Target space duality in string theory. Phys. Rep., 244, 77–202.
[163] Goldberg, S. I. 1982. Curvature and Homology. Dover.
[164] Goldberg, S. I. 1960. Conformal transformations of Kahler manifolds. Bull. Amer. Math. Soc., 66, 54–58.
[165] Goldfeld, D. 2006. Automorphic Forms and L-functions for the Group GL(n, ℝ). (Cambridge Studies in Advanced Mathematics, vol. 99). Cambridge University Press.
[166] Gomis, J., Milanesi, G., and Russo, J. G. 2008. Bagger–Lambert Theory for general Lie algebras. JHEP, 0806, 075.
[167] Gorbatsevich, V. V., Onishchik, . L., and Vinberg, E. B. 1994. Structure of Lie groups and Lie algebras. In: Lie Groups and Lie Algebras III. (Encyclopaedia of Mathematical Sciencesm, vol. 41). Springer.
[168] Grauert, H., and Remmert, R. 1979. Theory of Stein Spaces. Springer.
[169] Green, M. B., Schwarz, J. H., and West, P. C. 1985. Anomaly free chiral theories in six-dimensions. Nucl. Phys., B254, 327.
[170] Green, M. B., Schwarz, J. H., and Witten, E. 2012. Superstring Theory. (Cambridge Monographs on Mathematical Physics). Cambridge University Press (2 volumes).
[171] Griffiths, P., and Harris, J. 1978. Principles of Algebraic Geometry. Wiley Interscience.
[172] Griffiths, P., and Schmid, W. 1969. Locally homogeneous complex manifolds. Acta Math., 123, 145–166.
[173] Griffiths, P. A. 1984. Topics in Transcendental Algebraic Geometry. (Annals of Mathematical Studies.) Princeton University Press.
[174] Gross, D. J., Harvey, J. A., Martinec, E. J., and Rohm, R. 1985. Heterotic string theory. 1. The free heterotic string. Nucl. Phys., B256, 253.
[175] Gross, D. J., Harvey, J. A., Martinec, E. J., and Rohm, R. 1986. Heterotic string theory. 2. The interacting heterotic string. Nucl. Phys., B267, 75.
[176] Gross, M., Huybrechts, D., and Joyce, D. 2003. Calabi–Yau Manifolds and Related Geometries. (Universitext). Springer.
[177] Guillemin, V., and Sternberg, S.. 1990. Symplectic Techniques in Physics. Cambridge University Press.
[178] Guillemin, V. W., and Sternberg, S. 1999. Supersymmetry and Equivariant de Rham Theory. Springer.
[179] Gunaydin, M., Sierra, G., and Townsend, P. K. 1983. Exceptional supergravity theories and the MAGIC square. Phys. Lett., B133, 72.
[180] Gunaydin, M., Romans, L. J., and Warner, N. P. 1986. Compact and noncompact gauged supergravity theories in five dimensions. Nucl. Phys., B272, 598.
[181] Gunning, R. C., and Rossi, H. 1965. Analytic Functions of Several Complex Variables. Prentice-Hall.
[182] Haag, R., Lopuszanski, J. T., and Sohnius, M. 1975. All possible generators of supersymmetries of the S-matrix. Nucl. Phys., B88, 257.
[183] Hawking, S. W. 1983. The boundary conditions for gauged supergravity. Phys. Lett., B126, 175–177.
[184] Helgason, S. 2001. Differential Geometry, Lie Groups, and Symmetric Spaces. (Graduate Studies in Mathematics, vol. 34). American Mathematical Society.
[185] Hirsch, M. W. 1976. Differential Topology. (Graduate Texts in Mathematics, vol. 33). Springer.
[186] Hirzebruch, F. 1995. New Topological Methods in Algebraic Geometry. (Classics in Mathematics). Springer.
[187] Hiwaniec, H., and Kowalski, E. 2004. Analytic Number Theory. (Colloquium Publications, vol. 53). American Mathematical Society.
[188] Hori, K., Katz, S., Klemm, A., Pandharipande, R., Thomas, R., Vafa, C., Vakil, R., and Zaslov, E. 2003. Mirror Symmetry. (Clay Mathematics Monographs, vol. 1). American Mathematical Society.
[189] Hosomichi, K., Lee, K.-M., Lee, S., Lee, S., and Park, J. 2008a. N = 4 superconformal Chern–Simons theories with hyper and twisted hyper multiplets. JHEP, 0807, 091.
[190] Hosomichi, K., Lee, K.-M., Lee, S., Lee, S., and Park, J. 2008b. N = 5,6 superconformal Chern–Simons theories and M2-branes on orbifolds. JHEP, 0809, 002.
[191] Howe, P. and West, P. C. 1984. The complete N = 2, d = 10 supergravity. Nucl. Phys., B238, 181–219.
[192] Hull, C. M. 1983. The positivity of gravitational energy and global supersymmetry. Commun. Math. Phys., 90, 545.
[193] Hull, C. M. 1984a. A new gauging of N = 8 supergravity. Phys. Rev., D30, 760.
[194] Hull, C. M. 1984b. More gaugings of N = 8 supergravity. Phys. Lett., B148, 297–300.
[195] Hull, C. M. 1984c. Noncompact gaugings of N = 8 supergravity. Phys. Lett., B142, 39.
[196] Hull, C. M. 1984d. The spontaneous breaking of supersymmetry in curved space-time. Nucl. Phys., B239, 541.
[197] Hull, C. M. 1985. The minimal couplings and scalar potentials of the gauged N = 8 supergravities. Class. Quant. Grav., 2, 343.
[198] Hull, C. M. 2003. New gauged N = 8, D = 4 supergravities. Class. Quant. Grav., 20, 5407–5424.
[199] Hull, C. M., and Townsend, P. K. 1995. Unity of superstring dualities. Nucl. Phys., B438, 109–137.
[200] Hull, C. M., and Witten, E. 1985. Supersymmetric sigma models and the heterotic string. Phys. Lett., 160 B, 398–402.
[201] Husemöller, D. 1994. Fibre Bundles. (Graduate Texts in Mathematics, vol. 20). American Mathematical Society.
[202] Husemoaller, D. 2004. Elliptic Curves. 2nd ed. (Graduate Texts in Mathematics, vol. 111). Springer.
[203] Huybrechts, D. 2005. Complex Geometry. An Introduction. (Universitext). Springer.
[204] Intriligator, K., and Seiberg, N. 2013. Aspects of 3d N = 2 Chern–Simons–matter theories. JHEP, 1307, 079.
[205] Israel, W., and Nester, J. M. 1981. Positivity of the Bondi gravitational mass. Phys. Lett., A85, 259–260.
[206] Jeffrey, L. C., and Kirwan, F. C. 1993. Localization for non-Abelian gauge actions. arXiv:alg-geom/9307001 [math.AG].
[207] Ji, L. 2005. Lectures on locally symmetric spaces and arithmetic groups. Pages 87–146 of: Lie Groups andAutomorphic Forms. American Mathematical Society.
[208] Joyce, D. D. 2000. Compact Manifolds with Special Holonomy. (Oxford Mathematical Monographs). Oxford University Press.
[209] Joyce, D. D. 2007. Riemannian Holonomy Groups and Calibrated Geometry. (Oxford Graduate Texts in Mathematics, vol. 12). Oxford University Press.
[210] Julia, B. 1981. Group disintegration. In: Hawking, S. W., and Rocek, M. (eds.). Superspace and Supergravity. Cambridge University Press.
[211] Kac, V.G. 1977. Lie superalgebras. Adv. Math., 26, 8.
[212] Kao, H. C., and Lee, K. M. 1992. Self—dual Chern—Simons systems with N = 3 extended supersymmetry. Phys. Rev., D46, 4691–4697.
[213] Katz, S. 2006. Enumerative Geometry and String Theory. (Student Mathematical Library, vol. 32). American Mathematical Society.
[214] Kobayashi, S. 1995. Transformation Groups in Differential Geometry. (Classics in Mathematics). Springer.
[215] Kobayashi, S., and Nomizu, K. 1963. Foundations of Differential Geometry. Vol. 1. Wiley.
[216] Kodaira, K. 1954. On Käahler varieties of the restricted type (an intrinsic characterization of algebraic varieties). Ann. Math., 60, 28–48.
[217] Kodaira, K. 1986. Complex Manifolds and Deformation of Complex Structures. (Comprehensive Studies in Mathematics, vol. 283). Springer.
[218] Kodaira, K., and Spencer, D. C. 1958. On deformations of complex analytic structures, I–II. Ann. Math., 67, 328–466.
[219] Kostant, B. 1955. Holonomy and the Lie algebra of infinitesimal motions of a Riemannian manifold. Trans. Amer. Math. Soc., 80, 528–542.
[220] Kugo, T., and Townsend, P. K. 1983. Supersymmetry and the division algebras. Nucl. Phys., B221, 357–380.
[221] Kumar, V., Morrison, D. R., and Taylor, W. 2010. Global aspects of the space of 6D N = 1 supergravities. JHEP, 1011, 118.
[222] Labastida, J.M.F., and Llatas, P. M. 1991. Potentials for topological sigma models. Phys. Lett., B271, 101–108.
[223] Lahanas, A., and Nanopoulos, D. V. 1987. The road to no–scale supergravity. Phys. Rep., 145, 1.
[224] Lang, S. 1995. Differential and Riemannian Manifolds. (Graduate Texts in Mathematics, vol. 160). Springer.
[225] Lang, S. 1999. Fundamentals of Differential Geometry. Graduate Texts in Mathematics, vol. 191). Springer.
[226] Langlands, R. P. 1966. Volume of the fundamental domain for some arithmetical subgroup of Chevalley groups. Pages 235–257. of: Algebraic Groups and Discontinuous Subgroups. Proc. Symp. Pure Math. Vol. IX. American Mathematical Society.
[227] Leistner, T. 2007a. Towards a classification of Lorentzian holonomy groups. J. Differential Geom., 76, 423–484.
[228] Leistner, T. 2007b. Towards a classification of Lorentzian holonomy groups. Part II: Semisimple, non-simple weak-Berger algebras. J. Differential Geom., 76, 423–484.
[229] Libermann, P., and Marle, C. M. 1987. Symplectic Geometry and Analytical Mechanics. Reider.
[230] Margulis, G. A. 1991. Discrete Subgroups of Semisimple Lie Groups. Springer.
[231] Mariño, M. 2005. Chern–Simons Theory, Matrix Models, and Topological Strings. (International Series of Monographs on Physics, vol. 131). Oxford University Press.
[232] McLenaghan, R. G. 1974. On the validity of Huygens' principle for second order partial differential equations with four independent variables. Part I: Derivation of necessary conditions. Ann. Inst. H. Poincari, A20, 153–188.
[233] Merkulov, S., and Schwachhöfer. 1999. Classification of irreducible holonomies of torsion–free affine connections. Ann. Math., 150, 77–150.
[234] Meyers, S. B., and Steenrod, N. 1939. The group of isometries of a Riemannian manifold. Ann. Math., 40, 400–416.
[235] Milnor, J., and Stasheff, J. 1974. Characteristic Classes. (Annals of Mathematical Studies, vol. 76). Princeton University Press.
[236] Mohaupt, T. 2001. Black hole entropy, special geometry and strings. Fortsch. Phys., 49, 3–161.
[237] Montgomery, D., and Samelson, H. 1943. Transformations groups on spheres. Ann. Math., 44, 454–470.
[238] Moore, G. W. 2011. A Minicourse on Generalized Abelian Gauge Theory, Self–Dual Theories, and Differential Cohomology. Available at the author's webpage: http://www.physics.rutgers.edu/gmoore/SCGP-Minicourse.pdf. Accessed August 13, 2014.
[239] Morgan, J., and Tian, G. 2007. Ricci Flow and the Poincare Conjecture. (Clay Mathematics Monographs, vol. 3). American Mathematical Society.
[240] Morozov, A. 1994. Integrability and matrix models. Phys. Usp., 37, 1–55.
[241] Morris, D.W. 2001. Introduction to Arithmetic Groups. Available as arXiv:math/0106063.
[242] Morse, M. 1934. The Calculus of Variations in the Large. (Colloquium Publications, vol. 18). American Mathematical Society (10th printing 2001).
[243] Narain, K. S. 1986. New heterotic string theories in uncompactified dimension < 10. Phys. Lett., B169, 41.
[244] Narain, K. S., Sarmadi, M. H., and Witten, E. 1987. A note on toroidal compactification of heterotic string theory. Nucl. Phys., B279, 369.
[245] Nester, J. A. 1981a. A new gravitational energy expression with a simple positivity proof. Phys. Lett., A83, 241–242.
[246] Nester, J. A. 1981b. Positivity of the Bondi gravitational mass. Phys. Lett., A85, 259–260.
[247] Nester, J. M. 1981c. A new gravitational energy expression with a simple positivity proof. Phys. Lett., A83, 241–242.
[248] Nicolai, H., and Samtleben, H. 2001a. Compact and noncompact gauged maximal supergravities in three-dimensions. JHEP, 0104, 022.
[249] Nicolai, H., and Samtleben, H. 2001b. Maximal gauged supergravity in three dimensions. Phys. Rev. Lett., 86, 1686–1689.
[250] Nicolai, H., and Samtleben, H. 2003. Chern–Simons versus Yang–Mills gaugings in three dimensions. Nucl. Phys., B668, 167–178.
[251] Nijenhuis, A. 1953. On the holonomy group of linear connections. Indag. Math., 15, 233–249.
[252] Nishino, H., and Sezgin, E. 1984. Matter and gauge couplings of N = 2 supergravity in six dimensions. Phys. Lett., B144, 187–192.
[253] Novikov, S., Munakov, S. V., Pitaevsky, L. P., and Zakharov, V. E. 1984. Theory of Solitons: The Inverse Scattering Method. (Contemporary Soviet Mathematics). Plenum.
[254] Olmos, C. 2005. A geometric proof of the Berger holonomy theorem. Ann. Math., 161, 579–588.
[255] Ooguri, H., and Vafa, C. 2007. On the geometry of the string landscape and the swampland. Nucl. Phys., B766, 21–33.
[256] Pernici, M., Pilch, K., and van Nieuwenhuizen, P. 1984. Gauged maximally extended supergravity in seven dimensions. Phys. Lett., B143, 103.
[257] Petrov, V. I. 1969. Einstein Spaces. Princeton University Press.
[258] Polchinski, J. 1998. String Theory. (Cambridge Monographs on Mathematical Physics). Cambridge University Press (2 volumes).
[259] Poletskiǐ, E.A., and Shabat, B. V. 1989. Invariant metrics. In: Several Complex Variables, III. (Encyclopaedia of Mathematical Sciences, vol. 9). Springer.
[260] Polyakov, A. M. 1981. Quantum geometry of fermionic strings. Phys. Lett., B103, 211–213.
[261] Polyakov, A.M., and Wiegmann, P. B. 1983. Theory of nonabelian Goldstone bosons. Phys. Lett., B131, 121–126.
[262] Postnikov, M. M. 1994. Lectures in Geometry: Lie Groups and Lie Algebras. Editorial URSS.
[263] Postnikov, M. M. 2001. Geometry VI. Riemannian Geometry. (Encyclopaedia of Mathematical Sciences, vol. 91). Springer.
[264] Pyatetskiǐ-Shapiro, I. I. 1960. Automorphic Functions and the Geometry of Classical Domains. Gordon and Breach.
[265] Romans, L. J. 1986. Self–duality for interacting fields: covariant field equations for six-dimensional chiral supergravities. Nucl. Phys., B276, 71–92.
[266] Salam, A., and Sezgin, E. 1989. Supergravity in Diverse Dimensions, vols. 1 & 2. World Scientific.
[267] Salamon, S. 1989. Riemannian Geometry and Holonomy Groups. Longman Scientific and Technical.
[268] Schoen, R., and Yau, S.-T. 1979a. Positivity of the total mass of a general space-time. Phys.Rev. Lett., 43, 1457–1459.
[269] Schoen, R., and Yau, S.-T. 1981. Proof of the positive mass theorem. 2. Commun. Math. Phys., 79, 231–260.
[270] Schoen, R., and Yau, S. T. 1979b. On the proof of the positive mass conjecture in General Relativity. Commun. Math. Phys., 65, 45–76.
[271] Schoen, R. M., and Yau, S.-T. 1979c. Proof of the positive action conjecture in quantum gravity. Phys. Rev. Lett., 42, 547–548.
[272] Seiberg, N., and Taylor, W. 2011. Charge lattices and consistency of 6D supergravity. JHEP, 1106, 001.
[273] Seiberg, N., and Witten, E. 1994a. Electric–magnetic duality, monopole condensation, and confinement in N = 2 supersymmetric Yang–Mills theory. Nucl. Phys., B426, 19–52.
[274] Seiberg, N., and Witten, E. 1994b. Monopoles, duality and chiral symmetry breaking in N = 2 supersymmetric QCD. Nucl. Phys., B431, 484–550.
[275] Seiberg, N., and Witten, E. 1996. Comments on string dynamics in six-dimensions. Nucl. Phys., B471, 121–134.
[276] Serre, J. P. 1973. A Course in Arithmetic. (Graduate Texts in Mathematics, vol. 7). Springer.
[277] Sezgin, E., and Tanii, Y. 1995. Superconformal sigma models in higher than two dimensions. Nucl. Phys., B443, 70–84.
[278] Simons, J. 1962. On transitivity of holonomy systems. Ann. Math., 76, 213–234.
[279] Slansky, R. 1981. Group theory for unified model building. Phys. Rep., 79C, 1–118.
[280] Sternberg, S. 1983. Lectures on Differential Geometry. Chelsea Pub. Co.
[281] Strathdee, J. 1987. Extended Poincare supersymmetry. Int. J. Mod. Phys., A2, 273–300.
[282] Swann, A. F. 1991. Hyperkähler and quaternionic Kähler geometry. Math. Ann., 289, 421–450.
[283] Tanii, Y. 1984. N = 8 supergravity in six dimensions. Phys. Lett., B147, 47–51.
[284] Terras, A. 1988. Harmonic Analysis on Symmetric Spaces and Applications. II. Springer.
[285] Tian, G. 1987. Smoothness of the universal deformation space of compact Calabi–Yau manifolds and its Petersson–Weil metric. Pages 629–645. of: Yau, S. T. (ed.), Mathematical Aspects of String Theory. World Scientific.
[286] Townsend, P. K. 1984. A new anomaly free chiral supergravity from compactification on K3. Phys. Lett., B139, 283–287.
[287] Vafa, C. 2005. The String Landscape and the Swampland. e-print arXix:hep-th/0509212.
[288] van Leeuwen, M.A.A., Cohen, A.M., and Lisser, B. 1992. LiE, A Package for Lie Group Computations. Computer Algebra Nederland.
[289] Van Nieuwenhuizen, P. 1981. Supergravity. Phys. Rep., 68, 189–398.
[290] van Proeyen, A. 1999. Tools for Supersymmetry. (Lectures at the Spring School in Calimananesti, Romania). arXiv:hep-th/9910033.
[291] van Proyen, A. 1983. Superconformal tensor calculus in N = 1 and N = 2 super-gravity. In: Supersymmetry and Supergravity 1983. World Scientific.
[292] Vinberg, E. B. 1965. The theory of convex homogeneous cones. Pages 340–403. of: Transactions of the Moscow Mathematical Society for the Year 1963. American Mathematical Society.
[293] Voisin, C. 2007a. Hodge Theory and Complex Algebraic Geometry I. (Cambridge Studies in Advanced Mathematics, vol. 76). Cambridge University Press.
[294] Voisin, C. 2007b. Hodge Theory and Complex Algebraic Geometry II. (Cambridge Studies in Advanced Mathematics, vol. 77). Cambridge University Press.
[295] Wang, M. Y. 1989. Parallel spinors and parallel forms. Ann. Global Anal. Geom., 7, 59–68.
[296] Weinberg, S. 1972. Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity. Wiley.
[297] Wess, J., and Bagger, J. 1992. Supersymmetry and Supergravity (Revised edn.). (Princeton Series in Physics). Princeton University Press.
[298] West, P. 1990. Introduction to Supersymmetry and Supergravity. (Revised and extended second edn.). World Scientific.
[299] Witten, E. 1979. Dyons of charge eθ/2π. Phys. Lett., B86, 283–287.
[300] Witten, E. 1981. A new proof of the positive energy theorem. Commun. Math. Phys., 80, 381–402.
[301] Witten, E. 1982a. Constraints on supersymmetry breaking. Nucl. Phys., B202, 253.
[302] Witten, E. 1982b. Supersymmetry and Morse theory. J. Differential Geom., 17, 661–692.
[303] Witten, E. 1983a. Current algebra, baryons, and quark confinement. Nucl. Phys., B223, 433–444.
[304] Witten, E. 1983b. Global aspects of current algebra. Nucl. Phys., B223, 422–432.
[305] Witten, E. 1983c. Some inequalities among hadron masses. Phys. Rev. Lett., 31, 2351–2354.
[306] Witten, E. 1986. New issues in manifolds of SU(3) holonomy. Nucl. Phys., B283, 79.
[307] Witten, E. 1987. Elliptic genera and quantum field theory. Commun. Math. Phys., 109, 525–536.
[308] Witten, E. 1988a. 2+1 dimensional supergravity as an exactly soluble system. Nucl. Phys., B 311, 46–78.
[309] Witten, E. 1988b. Topological quantum field theory. Commun. Math. Phys., 117, 411–449.
[310] Witten, E. 1988c. Topological σ-models. Commun. Math. Phys., 118, 411.
[311] Witten, E. 1989. Quantum field theory and the Jones polynomial. Commun. Math. Phys., 121, 351.
[312] Witten, E. 1992. Two–dimensional gauge theories revisited. J. Geom. Phys., 9, 303–368.
[313] Witten, E. 1995a. On S-duality in Abelian gauge theory. Selecta Math., 1, 383.
[314] Witten, E. 1995b. Some Comments on String Dynamics. e-preprint arXiv:hep-th/9507121.
[315] Witten, E. 1996. talk given at the Newton Institute for Mathematical Sciences, Cambridge.
[316] Witten, E. 1998. New ‘gauge’ theories in six dimensions. JHEP, 9801, 001.
[317] Witten, E. 2005. Non—Abelian localization for Chern—Simons theory. J. Geom. Phys., 70, 183–323.
[318] Witten, E., and Bagger, J. 1982. Quantization of Newton's constant in certain super-gravity theories. Phys. Lett., B 115, 202.
[319] Wolf, J. A. 1962. Discrete groups, symmetric spaces, and global holonomy. Amer. J. Math., 84, 527–542.
[320] Wolf, J. A. 1965. Complex homogeneous contact manifolds and quaternionic symmetric spaces. J. Math. Mech., 14, 1033–1047.
[321] Wu, H. 1964. On the de Rham decomposition theorem. Ill. J. Math., 8, 291–310.
[322] Wu, H. 1967. Holonomy groups of indefinite metrics. Pac. J. Math., 20, 351–392.
[323] Xu, Y. 2000. Theory of Complex Homogenous Bounded Domains. Science Press/Kluwer Academic Publishers.
[324] Yano, K. 1952. On harmonic and Killing vector fields. Ann. Math., 55, 38–45.
[325] Yano, K. 2011. The Theory of Lie Derivatives and its Applications. Nabu Press.
[326] Yau, S. T. 1978. On the Ricci curvature of a compact Kahler manifold and the complex Monge—Ampere equation. I. Commun. Pure Appl. Math., 31, 339–411.
[327] Zamolodchikov, A. B. 1986. Irreversibility of the flux of the renormalization group in a 2D field theory. JETP Lett., 43, 730–732.

Metrics

Altmetric attention score

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Book summary page views

Total views: 0 *
Loading metrics...

* Views captured on Cambridge Core between #date#. This data will be updated every 24 hours.

Usage data cannot currently be displayed.