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Perturbative and instanton corrections to the OPE of CPOs in \(N=4\) SYM\(_4\). (English) Zbl 1097.81567

Summary: We study perturbative and instanton corrections to the Operator Product Expansion of the lowest weight Chiral Primary Operators of \(N=4\) SYM\(_4\). We confirm the recently observed non-renormalization of various operators (notably of the double-trace operator with dimension 4 in the 20 irrep of SU(4)), that appear to be unprotected by unitarity restrictions. We demonstrate the splitting of the free-field theory stress tensor and \(R\)-symmetry current in supermultiplets acquiring different anomalous dimensions in perturbation theory and argue that certain double-trace operators also undergo a perturbative splitting into operators dual to string and two-particle gravity states, respectively. The instanton contributions affect only those double-trace operators that acquire finite anomalous dimensions at strong coupling. For the leading operators of this kind, we show that the ratio of their anomalous dimensions at strong coupling to the anomalous dimensions due to instantons is the same number.

MSC:

81T13 Yang-Mills and other gauge theories in quantum field theory
81T60 Supersymmetric field theories in quantum mechanics
81R05 Finite-dimensional groups and algebras motivated by physics and their representations
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[1] Maldacena, J., The large \(N\) limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys., 2, 231 (1998) · Zbl 0914.53047
[2] Gubser, G. G.; Klebanov, I. R.; Polyakov, A. M., Gauge theory correlators from noncritical string theory, Phys. Lett. B, 428, 105 (1998) · Zbl 1355.81126
[3] Witten, E., Anti-de Sitter space and holography, Adv. Theor. Math. Phys., 2, 253 (1998) · Zbl 0914.53048
[4] Banks, T.; Green, M. B., Non-perturbative effects in AdS(5)×\(S^5\) string theory and \(d=4\) SUSY Yang-Mills, JHEP, 9805, 002 (1998)
[5] Lee, S.; Minwalla, S.; Rangamani, M.; Seiberg, N., Three-point functions of chiral operators in \(D=4, N=4\) SYM at large \(N\), Adv. Theor. Math. Phys., 2, 697 (1998) · Zbl 0923.53033
[6] D’Hoker, E.; Freedman, D. Z.; Skiba, W., Field theory tests for correlators in the AdS/CFT correspondence, Phys. Rev. D, 59, 045008 (1999)
[7] Skiba, W., Correlators of short multi-trace operators in \(N=4\) supersymmetric Yang-Mills, Phys. Rev. D, 60, 105038 (1999)
[8] Gonzalez-Rey, F.; Kulik, B.; Park, I. Y., Non-renormalization of two point and three point correlators of \(N=4\) SYM in \(N=1\) superspace, Phys. Lett. B, 455, 164 (1999) · Zbl 1058.81707
[9] Petkou, A. C.; Skenderis, K., A non-renormalization theorem for conformal anomalies, Nucl. Phys. B, 561, 100 (1999) · Zbl 0958.81161
[10] Penati, S.; Santambrogio, A.; Zanon, D., Two-point functions of chiral operators in \(N=4\) SYM at order \(g^4\), JHEP, 9912, 006 (1999)
[11] Penati, S.; Santambrogio, A.; Zanon, D., More on correlators and contact terms in \(N=4\) SYM at order \(g^4\) · Zbl 0971.81520
[12] Howe, P. S.; Sokatchev, E.; West, P. C., 3-point functions in \(N=4\) Yang-Mills, Phys. Lett. B, 444, 341 (1998)
[13] Arutyunov, G.; Frolov, S., Scalar quartic couplings in type IIB supergravity on \(AdS_5×S^5\), Nucl. Phys. B, 579, 117 (2000) · Zbl 0992.83085
[14] Arutyunov, G.; Frolov, S., Four-point functions of lowest weight CPOs in \(N=4 SYM_4\) in supergravity approximation, Phys. Rev. D, 62, 064016 (2000)
[15] Arutyunov, G.; Frolov, S.; Petkou, A. C., Operator product expansion of the lowest weight CPOs in \(N=4 SYM_4\) at strong coupling, Nucl. Phys. B, 586, 547 (2000) · Zbl 1043.81709
[16] Liu, H.; Tseytlin, A. A., On four-point functions in the CFT/AdS correspondence, Phys. Rev. D, 59, 086002 (1999)
[17] Freedman, D.; Mathur, S. D.; Matusis, A.; Rastelli, L., Comments on 4-point functions in the CFT/AdS correspondence, Phys. Lett. B, 452, 61 (1999) · Zbl 1058.81704
[18] Chalmers, G.; Schalm, K., The large \(N_c\) limit of four-point functions in \(N=4\) super Yang-Mills theory from anti-de Sitter supergravity, Nucl. Phys. B, 554, 215 (1999) · Zbl 0958.81133
[19] D’Hoker, E.; Freedman, D., Gauge boson exchange in \(AdS_{d+1} \), Nucl. Phys. B, 544, 612 (1999) · Zbl 0944.81026
[20] Brodie, J. H.; Gutperle, M., String corrections to 4-point functions in the AdS/CFT correspondence, Phys. Lett. B, 445, 296 (1999) · Zbl 1059.81586
[21] Liu, H., Scattering in anti-de Sitter space and operator product expansion, Phys. Rev. D, 60, 106005 (1999)
[22] D’Hoker, E.; Freedman, D., General scalar exchange in \(AdS_{d+1} \), Nucl. Phys. B, 550, 612 (1999)
[23] D’Hoker, E.; Freedman, D.; Mathur, S.; Matusis, A.; Rastelli, L., Graviton exchange and complete 4-point functions in the AdS/CFT correspondence, Nucl. Phys. B, 562, 353 (1999) · Zbl 0958.81147
[24] D’Hoker, E.; Freedman, D.; Rastelli, L., AdS/CFT 4-point functions: how to succeed at \(z\)-integrals without really trying, Nucl. Phys. B, 562, 395 (1999) · Zbl 0958.81143
[25] Sanjay, On direct and crossed channel asymptotics of four-point functions in AdS/CFT correspondence, Mod. Phys. Lett. A, 14, 1413 (1999)
[26] D’Hoker, E.; Mathur, S. D.; Matusis, A.; Rastelli, L., The operator product expansion of \(N=4\) SYM and the 4-point functions of supergravity · Zbl 1060.81600
[27] Hoffmann, L.; Petkou, A. C.; Rühl, W., A note on the analyticity of AdS scalar exchange graphs in the crossed channel, Phys. Lett. B, 478, 320 (2000) · Zbl 1050.81647
[28] Herzog, C. P., OPEs and 4-point functions in AdS/CFT correspondence
[29] Hoffmann, L.; Petkou, A. C.; Rühl, W., Aspects of the conformal operator product expansion in AdS/CFT correspondence · Zbl 1018.81047
[30] Hoffmann, L.; Mesref, L.; Ruhl, W., AdS box graphs, unitarity and operator product expansions · Zbl 1060.81562
[31] Ferrara, S.; Zaffaroni, A., Superconformal field theories, multiplet shortening and the \(AdS_5/SCFT_4\) correspondence · Zbl 1071.81576
[32] Gonzalez-Rey, F.; Park, I.; Schalm, K., A note on four-point functions of conformal operators in \(N=4\) super-Yang-Mills, Phys. Lett. B, 448, 37 (1999) · Zbl 1058.81708
[33] Eden, B.; Howe, P. S.; Schubert, C.; Sokatchev, E.; West, P. C., Four-point functions in \(N=4\) supersymmetric Yang-Mills theory at two loops, Nucl. Phys. B, 557, 355 (1999) · Zbl 1068.81602
[34] Eden, B.; Howe, P. S.; Schubert, C.; Sokatchev, E.; West, P. C., Simplifications of four-point functions in \(N=4\) supersymmetric Yang-Mills theory at two loops, Phys. Lett. B, 466, 20 (1999) · Zbl 0971.81156
[35] Bianchi, M.; Kovacs, S.; Rossi, G.; Stanev, Y. S., On logarithmic behaviour in \(N=4\) SYM theory, JHEP, 9908, 020 (1999)
[36] Eden, B.; Schubert, C.; Sokatchev, E., Three-loop four-point correlator in \(N=4\) SYM, Phys. Lett. B, 482, 309 (2000) · Zbl 0990.81121
[37] Bianchi, M.; Kovacs, S.; Rossi, G.; Stanev, Y. S., Anomalous dimensions in \(N=4\) SYM at order \(g^4\), Nucl. Phys. B, 584, 216 (2000) · Zbl 0984.81155
[38] Bianchi, M.; Green, M.; Kovacs, S.; Rossi, G., Instantons in supersymmetric Yang-Mills and \(D\)-instantons in IIB superstrings theory, JHEP, 9808, 013 (1998)
[39] Dorey, N.; Khoze, V.; Mattis, M.; Vandoren, S., Yang-Mills instantons in the large \(N\) limit and the AdS/CFT correspondence, Phys. Lett. B, 442, 145 (1998) · Zbl 1002.81560
[40] Dorey, N.; Hollowood, T.; Khoze, V.; Mattis, M.; Vandoren, S., Multi-instantons and Maldacena’s conjecture, JHEP, 9906, 023 (1999) · Zbl 0961.81110
[41] Dorey, N.; Hollowood, T.; Khoze, V.; Mattis, M.; Vandoren, S., Multi-instanton calculus and the AdS/CFT correspondence in \(N=4\) superconformal field theory, Nucl. Phys. B, 552, 88 (1999) · Zbl 0958.81185
[42] Eden, B.; Petkou, A.; Schubert, C.; Sokatchev, E., Partial non-renormalization of the stress-tensor four-point function in \(N=4\) SYM and AdS/CFT · Zbl 0969.81576
[43] Intriligator, K.; Skiba, W., Bonus symmetry and the operator product expansion of \(N=4\) super-Yang-Mills · Zbl 0957.81078
[44] Anselmi, D., The \(N=4\) quantum conformal algebra, Nucl. Phys. B, 541, 369 (1999) · Zbl 0947.81118
[45] Osborn, H.; Petkou, A. C., Implications of conformal invariance in field theories for general dimensions, Ann. Phys., 231, 311 (1994) · Zbl 0795.53073
[46] Anselmi, D., Quantum conformal algebras and closed conformal field theory, Nucl. Phys. B, 554, 415 (1999) · Zbl 0958.81019
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