Abstract
We carry out a general analysis of the representations of the superconformal algebras SU(2, 2/N), OSp(8/4, ∝), and OSp(8*/2N) and give their realization in superspace. We present a construction of their UIRs by multiplication of the different types of massless superfields (“supersingletons”). Particular attention is paid to the so-called “short multiplets.” Representations undergoing shortening have “protected dimension” and may correspond to BPS states in the dual supergravity theory in anti-de Sitter space. These results are relevant for the classification of multitrace operators in boundary conformally invariant theories as well as for the classification of AdS black holes preserving different fractions of supersymmetry.
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REFERENCES
Aharony, O., Berkooz, M., and Seiberg, N. (1998). Advances in Theoretical and Mathematical Physics 2, 119, hep-th/9712117.
Aharony, O., Gubser, S. S., Maldacena, J., Hirosi Ooguri, and Yaron Oz (2000). Physics Reports 323, 183, hep-th/9905111.
Aharony, O., Oz, Y., and Yin, Z. (1998). Physics Letters B 430, 87, hep-th/9803051.
Andrianopoli, L. and Ferrara, S. (1998a). Physics Letters B 430, 248, hep-th/9803171.
Andrianopoli, L. and Ferrara, S. (1998b). Letters in Mathematical Physics 46, 265, hep-th/9807150.
Andrianopoli, L. and Ferrara, S. (1999). Letters in Mathematical Physics 48, 145, hep-th/9812067.
Andrianopoli, L., Ferrara, S., Sokatchev, E., and Zupnik, B. Shortening of primary operators in Nextended SCFT 4 and harmonic-superspace analyticity, hep-th/9912007.
Angelopoulos, E. and Laoues, M. (1998). Reviews of Mathematical Physics 10, 271.
Bandos, I. (1988). Theoretical and Mathematical Physics 76, 783.
Bars, I. and Günaydin, M. (1983). Communications in Mathematical Physics 91, 31.
Behrndt, K., Cvetic, M., and Sabra, W. hep-th/9810227.
Bergshoeff, E., Sezgin, E., and Van Proeyen, A. (1986). Nuclear Physics B 264, 653.
Bianchi, M. and Kovacs, S. (1999). Physics Letters B 468, 102, hep-th/9910016.
Bianchi, M., Kovacs, S., Rossi, G. C., and Stanev, Ya. S. (1999). Journal of High Energy Physics 08, 020, hep-th/9906188.
Binegar, B. (1986). Physical Review D 34, 525.
Binegar, B., Fronsdal, C., and Heidenreich, W. (1983). Journal of Mathematical Physics 24, 2828.
Chalmers, G. and Schalm, K. “Holographic normal ordering and multiparticle states in the AdS/CFT correspondence,” hep-th/9901144.
Chamblin, A., Emparan, R., Johnson, C. V., and Myers, R. C. hep-th/9902170.
Claus, P., Kallosh, R., and Van Proeyen, A. (1998). Nuclear Physics B 518, 117.
Cremmer, E. and Julia, B. (1979). Nuclear Physics B 159, 141.
D'Hoker, E., Mathur, S. D., Matusis, A., and Rastelli, L. “The Operator Product Expansion of N = 4 SYM and the 4-point Functions of Supergravity,” hep-th/9911222.
D'Hoker, E., Freedman, D. Z., Mathur, S. D., Matusis, A., and Rastelli, L. “Extremal correlators in the AdS/CFT correspondence,” hep-th/9908160.
Dobrev, V. K. and Petkova, V. B. (1985). Physics Letters B 162 127.
Dobrev, V. K. and Petkova, V. B. (1987). Fortschritte der Physik 35, 7, 537.
Duff, M. J. (1987). In 4th Quantum Gravity Seminar, Moscow, 1987 (0325, QC178:S4).
Duff, M. J. (1988). Classical and Quantum Gravity 5, 189.
Duff, M. (1999). International Journal of Modern Physics A 14, 815.
Duff, M. J. and Liu, J. T. (1999). Nuclear Physics B 554, 237.
Duff, M. J. and Liu, J. T. hep-th/9901149.
Fabbri, D., Fré, P., Gualtieri, L., and Termonia, P. (2000). Classical and Quantum Gravity 17, 55.
Ferrara, S. and Fronsdal, C. Conformal fields in higher dimensions, hep-th/0006009.
Ferrara, S. and Günaydin, M. (1998). International Journal of Modern Physics A 13, 2075.
Ferrara, S., Iliopoulos, J., and Zumino, B. (1974). Nuclear Physics B 77, 413.
Ferrara, S., Kehagias, A., Partouche, H., and Zaffaroni, A. (1998). Physics Letters B 431, 42.
Ferrara, S. and Maldacena, J. (1998). Classical and Quantum Gravity 15, 749.
Ferrara, S. and Sokatchev, E. Short representations of SU(2, 2/N) and harmonic superspace analyticity, hep-th/9912168.
Ferrara, S. and Sokatchev, E. Conformal primaries of OSp(8/4, ℝ) and BPS states in AdS 4, hepth/0003051.
Ferrara, S. and Sokatchev, E. Representations of (1, 0) and (2, 0) superconformal algebras in six dimensions: Massless and short superfields, hep-th/0001178.
Ferrara, S., Wess, J., and Zumino, B. (1974). Physics Letters B 51, 239.
Ferrara, S. and Zaffaroni, A. Superconformal field theories, multiplet shortening, and the AdS(5)/SCFT(4) correspondence, hep-th/9908163.
Flato, M. and Fronsdal, C. (1978). Letters in Mathematical Physics 2, 421.
Flato, M. and Fronsdal, C. (1980). Physics Letters 97B, 236.
Flato, M. and Fronsdal, C. (1981). Journal of Mathematical Physics 22, 1100.
Flato, M. and Fronsdal, C. (1986). Physics Letters B 172, 412.
Frappat, L., Sciarrino, A., and Sorba, P. (2000). Sorba: Command not found. In Dictionary on Lie Algebras and Superalgebras, Academic Press, New York.
Fré, P., Gualtieri, L., and Termonia, P. (1999). Physics Letters B 471, 27.
Fronsdal, C. (1982). Physical Review D 26, 1988.
Galperin, A., Howe, P. S., and Stelle, K. S. (1992). Nuclear Physics B 368, 248.
Galperin, A., Ivanov, E., Kalitzin, S., Ogievetsky, V., and Sokatchev, E. (1984). Classical and Quantum Gravity 1, 469.
Galperin, A., Ivanov, E., Kalitzin, S., Ogievetsky, V., and Sokatchev, E. (1985). Classical and Quantum Gravity 2, 155.
Galperin, A., Ivanov, E., and Ogievetsky, V. I. (1981). JETP Lett. 33, 168.
Galperin, A., Ivanov, E., and Ogievetsky, V. (1987). Soviet Journal of Nuclear Physics 46, 543.
Gubser, S. S., Klebanov, I. R., and Polyakov, A. M. (1998). Physics Letters B 428, 105, hep-th/9802109.
Günaydin, M. (1982). Oscillator like unitary representations of noncompact groups and supergroups and extended supergravity theories, Extended version presented at 11th Int. Colloq. on Group Theoretical Methods in Physics, Istanbul, Turkey, Aug 23–28, 1982; Istanbul Group Theoretical Methods, 192.
Günaydin, M. and Hyun, S. J. (1988). Journal of Mathematical Physics 29, 2367.
Günaydin, M. and Marcus, N. (1985). Classical and Quantum Gravity 2, L11, L19.
Günaydin, M., Minic, D., and Zagermann, M. (1998). Nuclear Physics B 534, 96, hep-th/9806042.
Günaydin, M., Minic, D., and Zagermann, M. (1999). Nuclear Physics B 544, 737, hep-th/9810226.
Günaydin, M., Nilsson, B., Sierra, G., and Townsend, P. (1986). Physics Letters B 176, 45.
Günaydin, M. and Saclioglu, C. (1982a). Communications in Mathematical Physics 87, 159.
Günaydin, M. and Saclioglu, C. (1982b). Physics Letters B 108, 180.
Günaydin, M. and Takemae, S. Unitary supermultiplets of OSp(8/4) and the AdS7/CFT6 duality, hep-th/9910110.
Günaydin, M. and Warner, N. (1985). Nuclear Physics B 272, 99.
Halyo, E. (1998). JHEP 04 011, hep-th/9803077.
Hartwell, G. G. and Howe, P. S. (1995a). International Journal of Modern Physics A 10, 3901, hepth/ 9412147.
Hartwell, G. G. and Howe, P. S. (1995b). Classical and Quantum Gravity 12, 1823.
Hawking, S. W., Hunter, C. J., and Taylor-Robinson, M. M. (1999). Physical Review D 59, 064005.
Heslop, P. and Howe, P. S. On harmonic superspaces and superconformal fields in four dimensions, hep-th/0005135.
Howe, P. S. (1999). Supersymmetries and quantum symmetries. In Lecture Notes in Physics, Wess, J. and Ivanov, E. A. eds., Springer, Berlin, pp. 68–78.
Howe, P. S. and Leeming, M. I. (1994). Classical and Quantum Gravity 11, 2843.
Howe, P. S., Sierra, G., and Townsend, P. K. (1983). Nuclear Physics B 221, 331.
Howe, P. S., Stelle, K. S., and Townsend, P. K. (1981). Nuclear Physics B 191, 445.
Howe, P. S., Stelle, K. S., and Townsend, P. K. (1981). Nuclear Physics B 192, 332.
Howe, P. S., Stelle, K., and West, P. (1985). Classical and Quantum Gravity 2, 815–821.
Howe, P. S. and West, P. C. (1999). International Journal of Modern Physics A 14, 2659 hep-th/9509140.
Howe, P. S. and West, P. C. (1996). Physics Letters B 389, 273.
Howe, P. S. and West, P. C. (1997). Physics Letters B 400, 307.
Hull, C. BPS supermultiplets in five dimensions, hep-th/0004086.
Hull, C. Strongly coupled gravity and duality, hep-th/0004195.
Iliopoulos, J. and Zumino, B. (1974). Nuclear Physics B 76, 310.
Ivanov, E., Kalitsyn, S., Nguyen Ai Viet, and Ogievetsky, V. (1985). Journal of Physics A 18, 3433.
Ivanov, E. A. and Sorin, A. (1980). Journal Physics A 13, 1159.
Kallosh, R. (1985). Pis'ma ZHETF, 41, 172.
Knapp, A. W. (1977). Encyclopedic Dictionary of Mathematics, MIT Press, Cambridge, MA.
Knapp, A. W. (1986). Representation Theory of Semisimple Groups, Princeton University Press, Princeton, NJ.
Leigh, K. G. and Rozsli, M. (1998). Physics Letters B 431, 311, hep-th/9803068.
Maldacena, J. M. (1998). Advances in Theoretical and Mathematical Physics 2, 231.
Maldacena, J. M. (1999). International Journal of Theoretical Physics 38, 1113.
Minwalla, S. (1998). Advances in Theoretical and Mathematical Physics 2, 781.
Minwalla, S. (1998). JHEP 10, 002, hep-th/9803053.
Morel, B., Sciarrino, A., and Sorba, P. (1986). Physics Letters B 166, 69; erratum B 167, (1986) 486.
Nicolai, H. (1984). Representations Of Supersymmetry In Anti-De Sitter Space, Trieste School, p. 368.
Nicolai, H. and Sezgin, E. (1984). Physics Letters B 143, 389.
Park, J.-H. (1999). Nuclear Physics B 539, 599.
Park, J.-H. Superconformal symmetry in three dimensions, hep-th/9910199.
Rosly, A. A. (1983). Constraints in supersymmetric Yang-Mills theory as integrability conditions. In Theoretical Group Methods in Physics, Markov, M. and Man'ko, V., eds., Nauka, Moskwa, p. 263.
Rosly, A. A. (1985). Classical and Quantum Gravity 2, 693.
Rosly, A. A. and Schwarz, A. S. (1986). Communications in Mathematical Physics 105, 645.
Salam, A. and Strathdee, J. (1974). Nuclear Physics B 76, 477.
Siegel, W. (1981). Nuclear Physics B 177, 325.
Siegel, W. (1989). International Journal of Modern Physics A 4, 2015.
Skiba, W. (1999). Physical Review D 60, 105038, hep-th/9907088.
Sohnius, M. F. (1978). Nuclear Physics B 138, 109.
Sohnius, M. F. (1978). Nuclear Physics B 136, 461.
Wess, J. and Zumino, B. (1974). Physics Letters B 49, 52.
Wess, J. and Zumino, B. (1974b). Nuclear Physics B 70, 39.
Witten, E. (1998). Advances in Theoretical and Mathematical Physics 2, 253, hep-th/9802150.
Witten, E. (1998). Advances in Theoretical and Mathematical Physics 2, 505.
Zupnik, B. M. (1986a). Soviet Journal of Nuclear Physics 44, 512.
Zupnik, B. M. (1986b). Theoretical-group methods in physics, In Proceedings of the 1985 Yurmala Conference, Nauka, Moscow, Vol. 1, pp. 52–59.
Zupnik, B. M. and Khetselius, D. V. (1988). Soviet Journal of Nuclear Physics 47, 730.
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Ferrara, S., Sokatchev, E. Superconformal Interpretation of BPS States in AdS Geometries. International Journal of Theoretical Physics 40, 935–984 (2001). https://doi.org/10.1023/A:1004183023962
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DOI: https://doi.org/10.1023/A:1004183023962