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Three-point correlators of stress tensors in maximally-supersymmetric conformal theories in \(d=3\) and \(d=6\). (English) Zbl 0976.81112

Summary: We consider free superconformal theories of a \(N=8\) scalar multiplet in \(d=3\) and a \((2,0)\) tensor multiplet in \(d=6\) and compute 2-point and 3-point correlators of their stress tensors. The results for the 2-point and the 3-point correlators for a single \(d=3\) and \(d=6\) multiplet differ from the “strong-coupling” \(\text{AdS}_4\) and \(\text{AdS}_7\) supergravity predictions by the factors \(4\sqrt{2}/3\pi N^{3/2}\) and \(4N^3\), respectively. These are the same factors as found earlier in the comparison of the brane free field theory and the \(d=11\) supergravity predictions for the absorption cross sections of longitudinally polarized gravitons by \(N\) M2 and M5 branes. While the correspondence of the results for the cross sections and 2-point functions was expected on the basis of unitarity, the fact that the same coefficients appear in the ratio of the free-theory and supergravity 3-point functions is nontrivial. Thus, like in the \(d=4\) SYM case, in both \(d=3\) and \(d=6\) theories the ratio of the 3-point and 2-point correlators \(\langle TTT\rangle/\langle TT\rangle\) is exactly the same in the free field theory and in the interacting CFT as described (to leading order in large \(N\)) by the 11-dimensional supergravity on \(\text{AdS}_{d+1}\times S^{10-d}\).

MSC:

81T60 Supersymmetric field theories in quantum mechanics
81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
83E50 Supergravity
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References:

[1] Aharony, O.; Gubser, S. S.; Maldacena, J.; Ooguri, H.; Oz, Y., Large \(N\) field theories, string theory and gravity · Zbl 1368.81009
[2] Seiberg, N., Nucl. Phys. Proc. Suppl., Vol. 67, 158 (1998)
[3] Strominger, A., Phys. Lett. B, Vol. 383, 44 (1996)
[4] Witten, E., Some comments on string dynamics · Zbl 1003.81535
[5] Seiberg, N.; Witten, E., Nucl. Phys. B, Vol. 471, 121 (1996)
[6] Aharony, O.; Berkooz, M.; Kachru, S.; Seiberg, N.; Silverstein, E., Adv. Theor. Math. Phys., Vol. 1, 148 (1998)
[7] Aharony, O.; Berkooz, M.; Seiberg, N., Adv. Theor. Math. Phys., Vol. 2, 119 (1998)
[8] Ganor, O.; Motl, L., J. High Energy Phys., Vol. 05, 009 (1998)
[9] Ganor, O. J., Nucl. Phys. B, Vol. 489, 95 (1997)
[10] Duff, M. J.; Stelle, K. S., Phys. Lett. B, Vol. 253, 113 (1991)
[11] Güven, R., Phys. Lett. B, Vol. 276, 49 (1992)
[12] Bergshoeff, E.; Sezgin, E.; Townsend, P. K., Phys. Lett. B, Vol. 189, 75 (1987)
[13] Gibbons, G. W.; Townsend, P. K., Phys. Rev. Lett., Vol. 71, 3754 (1993)
[14] Kaplan, D. M.; Michelson, J., Phys. Rev. D, Vol. 53, 3474 (1996)
[15] Gubser, S. S.; Klebanov, I. R.; Peet, A. W., Phys. Rev. D, Vol. 54, 3915 (1996)
[16] Klebanov, I. R.; Tseytlin, A. A., Nucl. Phys. B, Vol. 475, 164 (1996)
[17] Gubser, S. S.; Klebanov, I. R.; Tseytlin, A. A., Nucl. Phys. B, Vol. 534, 202 (1998)
[18] Klebanov, I. R., Nucl. Phys. B, Vol. 496, 231 (1997)
[19] Gubser, S. S.; Klebanov, I. R.; Tseytlin, A. A., Nucl. Phys. B, Vol. 499, 217 (1997)
[20] Emparan, R., Nucl. Phys. B, Vol. 516, 297 (1998)
[21] Gubser, S. S.; Klebanov, I. R., Phys. Lett. B, Vol. 413, 41 (1997)
[22] Gubser, S. S.; Klebanov, I. R.; Polyakov, A. M., Phys. Lett. B, Vol. 428, 105 (1998)
[23] Maldacena, J., Adv. Theor. Math. Phys., Vol. 2, 231 (1998)
[24] Witten, E., Adv. Theor. Math. Phys., Vol. 2, 253 (1998)
[25] Aharony, O.; Oz, Y.; Yin, Z., Phys. Lett. B, Vol. 430, 87 (1998)
[26] Minwalla, S., J. High Energy Phys., Vol. 10, 002 (1998)
[27] Leigh, R. G.; Rozali, M., Phys. Lett. B, Vol. 431, 311 (1998)
[28] Halyo, E., J. High Energy Phys., Vol. 04, 011 (1998)
[29] Henningson, M.; Skenderis, K., J. High Energy Phys., Vol. 07, 023 (1998)
[30] Harvey, J. A.; Minasian, R.; Moore, G., J. High Energy Phys., Vol. 09, 004 (1998)
[31] Awata, H.; Hirano, S., Adv. Theor. Math. Phys., Vol. 3, 147 (1999)
[32] Graham, C. R.; Witten, E., Nucl. Phys. B, Vol. 546, 52 (1999)
[33] Henningson, M.; Skenderis, K., J. High Energy Phys., Vol. 06, 012 (1999)
[34] Corrado, R.; Florea, B.; McNees, R., Phys. Rev. D, Vol. 60, 085011 (1999)
[35] Nastase, H.; Vaman, D.; van Nieuwenhuizen, P., Consistent nonlinear KK reduction of 11d supergravity on \(AdS(7)×S(4)\) and selfduality in odd dimensions · Zbl 0987.81570
[36] Bastianelli, F.; Zucchini, R., Three-Point Functions of Chiral Primary Operators in \(d=3 , N=8\) and \(d=6 , N=(2,0)\) SCFT at Large \(N\) · Zbl 0987.81600
[37] Bastianelli, F.; Zucchini, R., Three point functions for a class of chiral operators in maximally supersymmetric CFT at large \(N\) · Zbl 1056.81560
[38] Nishimura, M.; Tanii, Y., Local symmetries in the AdS(7)/CFT(6) correspondence
[39] Liu, H.; Tseytlin, A. A., Nucl. Phys. B, Vol. 533, 88 (1998)
[40] Park, J., Nucl. Phys. B, Vol. 539, 599 (1999)
[41] Park, J., Superconformal symmetry and correlation functions · Zbl 0957.81055
[42] Park, J., Superconformal symmetry in three-dimensions · Zbl 0974.58003
[43] Arutyunov, G.; Frolov, S., Phys. Rev. D, Vol. 60, 026004 (1999)
[44] Banks, T.; Green, M. B., J. High Energy Phys., Vol. 05, 002 (1998)
[45] Klebanov, I. R.; Tseytlin, A. A., Nucl. Phys. B, Vol. 475, 179 (1996)
[46] Bekaert, X.; Henneaux, M.; Sevrin, A., Deformations of chiral two-forms in six dimensions · Zbl 0987.81566
[47] Bekaert, X., Interactions of chiral two-forms · Zbl 1273.81179
[48] Osborn, H.; Petkou, A. C., Ann. Phys., Vol. 231, 311 (1994)
[49] Alvarez-Gaume, L.; Witten, E., Nucl. Phys. B, Vol. 234, 269 (1984)
[50] Henneaux, M.; Teitelboim, C., Phys. Lett. B, Vol. 206, 650 (1988)
[51] Pasti, P.; Sorokin, D.; Tonin, M., Phys. Rev. D, Vol. 55, 6292 (1997)
[52] Bastianelli, F.; van Nieuwenhuizen, P., Phys. Rev. Lett., Vol. 63, 728 (1989)
[53] Lechner, K., Nucl. Phys. B, Vol. 537, 361 (1999)
[54] Van Den Broeck, C.; Van Hoof, K., Batalin-Vilkovisky gauge-fixing of a chiral two-form in six dimensions · Zbl 0939.83049
[55] Lee, S.; Minwalla, S.; Rangamani, M.; Seiberg, N., Adv. Theor. Math. Phys., Vol. 2, 697 (1998)
[56] Anselmi, D., Higher-spin current multiplets in operator-product expansions · Zbl 0968.81024
[57] Erdmenger, J.; Osborn, H., Nucl. Phys. B, Vol. 483, 431 (1997)
[58] Bergshoeff, E.; Sezgin, E.; Van Proeyen, A., \(( 2,0\) ) Tensor Multiplets and Conformal Supergravity in \(D=6\) · Zbl 0935.83042
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