Abstract
We verify the self-duality of Green-Schwarz supercoset sigma models on AdS d × S d backgrounds (d = 2, 3, 5) under combined bosonic and fermionic T-dualities without gauge fixing kappa symmetry. We also prove this property for superstrings on AdS d × S d × S d (d = 2, 3) described by supercoset sigma models with the isometries governed by the exceptional Lie supergroups D(2, 1; α) (d = 2) and D(2, 1; α) × D(2, 1; α) (d = 3), which requires an additional T-dualisation along one of the spheres. Then, by taking into account the contribution of non-supercoset fermionic modes (up to the second order), we provide evidence for the T-self-duality of the complete type IIA and IIB Green-Schwarz superstring theory on AdS d × S d × T 10−2d (d = 2, 3) backgrounds with Ramond-Ramond fluxes. Finally, applying the Buscher-like rules to T-dualising supergravity fields, we prove the T-self-duality of the whole class of the AdS d × S d × M 10−2d superbackgrounds with Ramond-Ramond fluxes in the context of supergravity.
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O. Aharony, S.S. Gubser, J.M. Maldacena, H. Ooguri and Y. Oz, Large-N field theories, string theory and gravity, Phys. Rept. 323 (2000) 183 [hep-th/9905111] [INSPIRE].
J.M. Maldacena, TASI 2003 lectures on AdS/CFT, hep-th/0309246 [INSPIRE].
H. Nastase, Introduction to AdS-CFT, arXiv:0712.0689 [INSPIRE].
N. Beisert et al., Review of AdS/CFT Integrability: An Overview, Lett. Math. Phys. 99 (2012) 3 [arXiv:1012.3982] [INSPIRE].
G. ’t Hooft, A Planar Diagram Theory for Strong Interactions, Nucl. Phys. B 72 (1974) 461 [INSPIRE].
J.M. Maldacena, The large-N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 [hep-th/9711200] [INSPIRE].
J.A. Minahan and K. Zarembo, The Bethe ansatz for \( \mathcal{N}=4 \) super Yang-Mills, JHEP 03 (2003) 013 [hep-th/0212208] [INSPIRE].
I. Bena, J. Polchinski and R. Roiban, Hidden symmetries of the AdS 5 × S 5 superstring, Phys. Rev. D 69 (2004) 046002 [hep-th/0305116] [INSPIRE].
N. Berkovits and J. Maldacena, Fermionic T-duality, Dual Superconformal Symmetry and the Amplitude/Wilson Loop Connection, JHEP 09 (2008) 062 [arXiv:0807.3196] [INSPIRE].
N. Beisert, R. Ricci, A.A. Tseytlin and M. Wolf, Dual Superconformal Symmetry from AdS 5 × S 5 Superstring Integrability, Phys. Rev. D 78 (2008) 126004 [arXiv:0807.3228] [INSPIRE].
R. Ricci, A.A. Tseytlin and M. Wolf, On T-duality and Integrability for Strings on AdS Backgrounds, JHEP 12 (2007) 082 [arXiv:0711.0707] [INSPIRE].
E. O Colgain, Fermionic T-duality: A snapshot review, Int. J. Mod. Phys. A 27 (2012) 1230032 [arXiv:1210.5588] [INSPIRE].
A. Babichenko, B. Stefanski, Jr. and K. Zarembo, Integrability and the AdS 3 /CFT 2 correspondence, JHEP 03 (2010) 058 [arXiv:0912.1723] [INSPIRE].
D. Sorokin and L. Wulff, Evidence for the classical integrability of the complete \( Ad{S}_4\times \mathrm{\mathbb{C}}{P}^3 \) superstring, JHEP 11 (2010) 143 [arXiv:1009.3498] [INSPIRE].
D. Sorokin, A. Tseytlin, L. Wulff and K. Zarembo, Superstrings in AdS 2 × S 2 × T 6, J. Phys. A 44 (2011) 275401 [arXiv:1104.1793] [INSPIRE].
A. Cagnazzo, D. Sorokin and L. Wulff, More on integrable structures of superstrings in \( Ad{S}_4\times \mathrm{\mathbb{C}}{P}^3 \) and AdS 2 × S 2 × T 6 superbackgrounds, JHEP 01 (2012) 004 [arXiv:1111.4197] [INSPIRE].
P. Sundin and L. Wulff, Classical integrability and quantum aspects of the AdS 3 × S 3 × S 3 × S 1 superstring, JHEP 10 (2012) 109 [arXiv:1207.5531] [INSPIRE].
L. Wulff, Superisometries and integrability of superstrings, JHEP 05 (2014) 115 [arXiv:1402.3122] [INSPIRE].
L. Wulff, On integrability of strings on symmetric spaces, JHEP 09 (2015) 115 [arXiv:1505.03525] [INSPIRE].
I. Adam, A. Dekel and Y. Oz, On Integrable Backgrounds Self-dual under Fermionic T-duality, JHEP 04 (2009) 120 [arXiv:0902.3805] [INSPIRE].
P.A. Grassi, D. Sorokin and L. Wulff, Simplifying superstring and D-brane actions in \( Ad{S}_4\times \mathrm{\mathbb{C}}{P}^3 \) superbackground, JHEP 08 (2009) 060 [arXiv:0903.5407] [INSPIRE].
I. Bakhmatov and D.S. Berman, Exploring Fermionic T-duality, Nucl. Phys. B 832 (2010) 89 [arXiv:0912.3657] [INSPIRE].
H. Godazgar and M.J. Perry, Real fermionic symmetry in type-II supergravity, JHEP 01 (2011) 032 [arXiv:1008.3128] [INSPIRE].
I. Bakhmatov, On \( Ad{S}_4\times \mathrm{\mathbb{C}}{P}^3 \) T-duality, Nucl. Phys. B 847 (2011) 38 [arXiv:1011.0985] [INSPIRE].
Y.-t. Huang and A.E. Lipstein, Dual Superconformal Symmetry of \( \mathcal{N}=6 \) Chern-Simons Theory, JHEP 11 (2010) 076 [arXiv:1008.0041] [INSPIRE].
D. Gang, Y.-t. Huang, E. Koh, S. Lee and A.E. Lipstein, Tree-level Recursion Relation and Dual Superconformal Symmetry of the ABJM Theory, JHEP 03 (2011) 116 [arXiv:1012.5032] [INSPIRE].
W.-M. Chen and Y.-t. Huang, Dualities for Loop Amplitudes of \( \mathcal{N}=6 \) Chern-Simons Matter Theory, JHEP 11 (2011) 057 [arXiv:1107.2710] [INSPIRE].
M.S. Bianchi, M. Leoni, A. Mauri, S. Penati and A. Santambrogio, Scattering in ABJ theories, JHEP 12 (2011) 073 [arXiv:1110.0738] [INSPIRE].
T. Bargheer, F. Loebbert and C. Meneghelli, Symmetries of Tree-level Scattering Amplitudes in \( \mathcal{N}=6 \) Superconformal Chern-Simons Theory, Phys. Rev. D 82 (2010) 045016 [arXiv:1003.6120] [INSPIRE].
M.S. Bianchi, M. Leoni, A. Mauri, S. Penati, C. Ratti and A. Santambrogio, From Correlators to Wilson Loops in Chern-Simons Matter Theories, JHEP 06 (2011) 118 [arXiv:1103.3675] [INSPIRE].
M.S. Bianchi, M. Leoni, A. Mauri, S. Penati and A. Santambrogio, Scattering Amplitudes/Wilson Loop Duality In ABJM Theory, JHEP 01 (2012) 056 [arXiv:1107.3139] [INSPIRE].
J. Gomis, D. Sorokin and L. Wulff, The Complete \( Ad{S}_4\times \mathrm{\mathbb{C}}{P}^3 \) superspace for the type IIA superstring and D-branes, JHEP 03 (2009) 015 [arXiv:0811.1566] [INSPIRE].
I. Adam, A. Dekel and Y. Oz, On the fermionic T-duality of the AdS 4 × CP 3 σ-model, JHEP 10 (2010) 110 [arXiv:1008.0649] [INSPIRE].
I. Oda and M. Tonin, On the Berkovits covariant quantization of GS superstring, Phys. Lett. B 520 (2001) 398 [hep-th/0109051] [INSPIRE].
N. Rughoonauth, P. Sundin and L. Wulff, Near BMN dynamics of the AdS 3 × S 3 × S 3 × S 1 superstring, JHEP 07 (2012) 159 [arXiv:1204.4742] [INSPIRE].
E. O Colgain, Self-duality of the D1-D5 near-horizon, JHEP 04 (2012) 047 [arXiv:1202.3416] [INSPIRE].
T.H. Buscher, A Symmetry of the String Background Field Equations, Phys. Lett. B 194 (1987) 59 [INSPIRE].
T.H. Buscher, Path Integral Derivation of Quantum Duality in Nonlinear σ-models, Phys. Lett. B 201 (1988) 466 [INSPIRE].
J. Simon, T duality and effective D-brane actions, Phys. Rev. D 61 (2000) 047702 [hep-th/9812095] [INSPIRE].
M.T. Grisaru, P.S. Howe, L. Mezincescu, B. Nilsson and P.K. Townsend, \( \mathcal{N}=2 \) Superstrings in a Supergravity Background, Phys. Lett. B 162 (1985) 116 [INSPIRE].
L. Wulff, The type-II superstring to order θ 4, JHEP 07 (2013) 123 [arXiv:1304.6422] [INSPIRE].
V.V. Serganova, Classification of real simple Lie superalgebras and symmetric superspaces, Funct. Anal. Appl. 17 (1983) 200 [INSPIRE].
L. Frappat, P. Sorba and A. Sciarrino, Dictionary on Lie superalgebras, hep-th/9607161 [INSPIRE].
R.R. Metsaev and A.A. Tseytlin, Type IIB superstring action in AdS 5 × S 5 background, Nucl. Phys. B 533 (1998) 109 [hep-th/9805028] [INSPIRE].
J. Rahmfeld and A. Rajaraman, The GS string action on AdS 3 × S 3 with Ramond-Ramond charge, Phys. Rev. D 60 (1999) 064014 [hep-th/9809164] [INSPIRE].
J.-G. Zhou, Super 0-brane and GS superstring actions on AdS 2 × S 2, Nucl. Phys. B 559 (1999) 92 [hep-th/9906013] [INSPIRE].
N. Berkovits, M. Bershadsky, T. Hauer, S. Zhukov and B. Zwiebach, Superstring theory on AdS 2 × S 2 as a coset supermanifold, Nucl. Phys. B 567 (2000) 61 [hep-th/9907200] [INSPIRE].
G. Arutyunov and S. Frolov, Superstrings on \( Ad{S}_4\times \mathrm{\mathbb{C}}{P}^3 \) as a Coset σ-model, JHEP 09 (2008) 129 [arXiv:0806.4940] [INSPIRE].
B. Stefanski, jr, Green-Schwarz action for Type IIA strings on \( Ad{S}_4\times \mathrm{\mathbb{C}}{P}^3 \), Nucl. Phys. B 808 (2009) 80 [arXiv:0806.4948] [INSPIRE].
K. Zarembo, Strings on Semisymmetric Superspaces, JHEP 05 (2010) 002 [arXiv:1003.0465] [INSPIRE].
A. Dekel and Y. Oz, Self-Duality of Green-Schwarz σ-models, JHEP 03 (2011) 117 [arXiv:1101.0400] [INSPIRE].
A.S. Schwarz and A.A. Tseytlin, Dilaton shift under duality and torsion of elliptic complex, Nucl. Phys. B 399 (1993) 691 [hep-th/9210015] [INSPIRE].
P. Claus, R. Kallosh, J. Kumar, P.K. Townsend and A. Van Proeyen, Conformal theory of M2, D3, M5 and D1-branes + D5-branes, JHEP 06 (1998) 004 [hep-th/9801206] [INSPIRE].
A.A. Tseytlin, Harmonic superpositions of M-branes, Nucl. Phys. B 475 (1996) 149 [hep-th/9604035] [INSPIRE].
I.R. Klebanov and A.A. Tseytlin, Intersecting M-branes as four-dimensional black holes, Nucl. Phys. B 475 (1996) 179 [hep-th/9604166] [INSPIRE].
J.P. Gauntlett, D.A. Kastor and J.H. Traschen, Overlapping branes in M-theory, Nucl. Phys. B 478 (1996) 544 [hep-th/9604179] [INSPIRE].
M.J. Duff, H. Lü and C.N. Pope, AdS 5 × S 5 untwisted, Nucl. Phys. B 532 (1998) 181 [hep-th/9803061] [INSPIRE].
H.J. Boonstra, B. Peeters and K. Skenderis, Brane intersections, anti-de Sitter space-times and dual superconformal theories, Nucl. Phys. B 533 (1998) 127 [hep-th/9803231] [INSPIRE].
J. Lee and S. Lee, Mass spectrum of D = 11 supergravity on AdS 2 × S 2 × T 7, Nucl. Phys. B 563 (1999) 125 [hep-th/9906105] [INSPIRE].
P.M. Cowdall and P.K. Townsend, Gauged supergravity vacua from intersecting branes, Phys. Lett. B 429 (1998) 281 [Erratum ibid. B 434 (1998) 458] [hep-th/9801165] [INSPIRE].
J.P. Gauntlett, R.C. Myers and P.K. Townsend, Supersymmetry of rotating branes, Phys. Rev. D 59 (1998) 025001 [hep-th/9809065] [INSPIRE].
J. de Boer, A. Pasquinucci and K. Skenderis, AdS/CFT dualities involving large 2-D \( \mathcal{N}=4 \) superconformal symmetry, Adv. Theor. Math. Phys. 3 (1999) 577 [hep-th/9904073] [INSPIRE].
S. Gukov, E. Martinec, G.W. Moore and A. Strominger, The Search for a holographic dual to AdS 3 × S 3 × S 3 × S 1, Adv. Theor. Math. Phys. 9 (2005) 435 [hep-th/0403090] [INSPIRE].
E. Ivanov, S. Sidorov and F. Toppan, Superconformal mechanics in SU(2|1) superspace, Phys. Rev. D 91 (2015) 085032 [arXiv:1501.05622] [INSPIRE].
I.A. Bandos, E. Ivanov, J. Lukierski and D. Sorokin, On the superconformal flatness of AdS superspaces, JHEP 06 (2002) 040 [hep-th/0205104] [INSPIRE].
D. Butter, G. Inverso and I. Lodato, Rigid 4D \( \mathcal{N}=2 \) supersymmetric backgrounds and actions, JHEP 09 (2015) 088 [arXiv:1505.03500] [INSPIRE].
I.A. Bandos and B. Julia, Superfield T duality rules, JHEP 08 (2003) 032 [hep-th/0303075] [INSPIRE].
V. Forini, V.G.M. Puletti and O. Ohlsson Sax, The generalized cusp in \( Ad{S}_4\times \mathrm{\mathbb{C}}{P}^3 \) and more one-loop results from semiclassical strings, J. Phys. A 46 (2013) 115402 [arXiv:1204.3302] [INSPIRE].
E. Alvarez, L. Álvarez-Gaumé and Y. Lozano, An Introduction to T duality in string theory, Nucl. Phys. Proc. Suppl. 41 (1995) 1 [hep-th/9410237] [INSPIRE].
M. Fukuma, T. Oota and H. Tanaka, Comments on T dualities of Ramond-Ramond potentials on tori, Prog. Theor. Phys. 103 (2000) 425 [hep-th/9907132] [INSPIRE].
S.F. Hassan, T duality, space-time spinors and RR fields in curved backgrounds, Nucl. Phys. B 568 (2000) 145 [hep-th/9907152] [INSPIRE].
C.M. Hull, Timelike T duality, de Sitter space, large-N gauge theories and topological field theory, JHEP 07 (1998) 021 [hep-th/9806146] [INSPIRE].
A. Cagnazzo, D. Sorokin, A.A. Tseytlin and L. Wulff, Semiclassical equivalence of Green-Schwarz and Pure-Spinor/Hybrid formulations of superstrings in AdS 5 × S 5 and AdS 2 × S 2 × T 6, J. Phys. A 46 (2013) 065401 [arXiv:1211.1554] [INSPIRE].
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Abbott, M.C., Murugan, J., Penati, S. et al. T-duality of Green-Schwarz superstrings on AdS d × S d × M 10−2d . J. High Energ. Phys. 2015, 1–52 (2015). https://doi.org/10.1007/JHEP12(2015)104
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DOI: https://doi.org/10.1007/JHEP12(2015)104