Abstract
We calculate the four-point correlation function of half-BPS operators with weights 2, 3, 3, 4 in \( \mathcal{N}=4 \) SYM to two-loop order. The OPE of this correlation function provides a nontrivial check of the integrability conjecture for a class of three-point functions formulated in arXiv:1311.6404. Our perturbative calculation exploits the supergraph formalism in \( \mathcal{N}=4 \) harmonic superspace.
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References
P. Vieira and T. Wang, Tailoring non-compact spin chains, JHEP 10 (2014) 035 [arXiv:1311.6404] [INSPIRE].
J. Escobedo, N. Gromov, A. Sever and P. Vieira, Tailoring three-point functions and integrability, JHEP 09 (2011) 028 [arXiv:1012.2475] [INSPIRE].
N. Gromov and P. Vieira, Quantum integrability for three-point functions of maximally supersymmetric Yang-Mills theory, Phys. Rev. Lett. 111 (2013) 211601 [arXiv:1202.4103] [INSPIRE].
G. Arutyunov, S. Penati, A. Santambrogio and E. Sokatchev, Four point correlators of BPS operators in N = 4 SYM at order g**4, Nucl. Phys. B 670 (2003) 103 [hep-th/0305060] [INSPIRE].
B. Eden, A.C. Petkou, C. Schubert and E. Sokatchev, Partial nonrenormalization of the stress tensor four point function in N = 4 SYM and AdS/CFT, Nucl. Phys. B 607 (2001) 191 [hep-th/0009106] [INSPIRE].
G. Arutyunov and E. Sokatchev, On a large-N degeneracy in N = 4 SYM and the AdS/CFT correspondence, Nucl. Phys. B 663 (2003) 163 [hep-th/0301058] [INSPIRE].
N.I. Usyukina and A.I. Davydychev, An approach to the evaluation of three and four point ladder diagrams, Phys. Lett. B 298 (1993) 363 [INSPIRE].
N.I. Usyukina and A.I. Davydychev, Exact results for three and four point ladder diagrams with an arbitrary number of rungs, Phys. Lett. B 305 (1993) 136 [INSPIRE].
M. Bianchi, B. Eden, G. Rossi and Y.S. Stanev, On operator mixing in N = 4 SYM, Nucl. Phys. B 646 (2002) 69 [hep-th/0205321] [INSPIRE].
L.I. Uruchurtu, Next-next-to-extremal four point functions of N = 4 1/2 BPS operators in the AdS/CFT correspondence, JHEP 08 (2011) 133 [arXiv:1106.0630] [INSPIRE].
L. Berdichevsky and P. Naaijkens, Four-point functions of different-weight operators in the AdS/CFT correspondence, JHEP 01 (2008) 071 [arXiv:0709.1365] [INSPIRE].
M. D’Alessandro and L. Genovese, A wide class of four point functions of BPS operators in N = 4 SYM at order g 4, Nucl. Phys. B 732 (2006) 64 [hep-th/0504061] [INSPIRE].
A. Galperin, E. Ivanov, S. Kalitsyn, V. Ogievetsky and E. Sokatchev, Unconstrained N = 2 matter, Yang-Mills and supergravity theories in harmonic superspace, Class. Quant. Grav. 1 (1984) 469 [Erratum ibid. 2 (1985) 127] [INSPIRE].
A.S. Galperin, E.A. Ivanov, V.I. Ogievetsky and E.S. Sokatchev, Harmonic superspace, Cambridge University Press, Cambridge U.K. (2001).
P.S. Howe, C. Schubert, E. Sokatchev and P.C. West, Explicit construction of nilpotent covariants in N = 4 SYM, Nucl. Phys. B 571 (2000) 71 [hep-th/9910011] [INSPIRE].
B. Eden, C. Schubert and E. Sokatchev, Three loop four point correlator in N = 4 SYM, Phys. Lett. B 482 (2000) 309 [hep-th/0003096] [INSPIRE].
B. Eden, G.P. Korchemsky and E. Sokatchev, From correlation functions to scattering amplitudes, JHEP 12 (2011) 002 [arXiv:1007.3246] [INSPIRE].
G. Arutyunov, F.A. Dolan, H. Osborn and E. Sokatchev, Correlation functions and massive Kaluza-Klein modes in the AdS/CFT correspondence, Nucl. Phys. B 665 (2003) 273 [hep-th/0212116] [INSPIRE].
B. Eden, P. Heslop, G.P. Korchemsky and E. Sokatchev, The super-correlator/super-amplitude duality: Part II, Nucl. Phys. B 869 (2013) 378 [arXiv:1103.4353] [INSPIRE].
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ArXiv ePrint: 1408.3527
UMR 5108 du CNRS, associée à l’Université de Savoie.
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Chicherin, D., Sokatchev, E. A note on four-point correlators of half-BPS operators in \( \mathcal{N}=4 \) SYM. J. High Energ. Phys. 2014, 139 (2014). https://doi.org/10.1007/JHEP11(2014)139
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DOI: https://doi.org/10.1007/JHEP11(2014)139