Abstract
We construct a new representation for two- and three-point correlators of operators from sl(2) sector of planar N = 4 SYM. The spin and twist of operators are arbitrary. We start with the correlation function of light-ray operators and carry out a projection to particular local operators using Sklyanin’s method of Separation of Variables. With the same procedure we obtain polynomials which are dual to wave functions of sl(2, R) spin-chain.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
N. Gromov, V. Kazakov and P. Vieira, Exact Spectrum of Anomalous Dimensions of Planar N = 4 Supersymmetric Yang-Mills Theory, Phys. Rev. Lett. 103 (2009) 131601 [arXiv:0901.3753] [INSPIRE].
G. Arutyunov and S. Frolov, Thermodynamic Bethe Ansatz for the AdS 5 × S 5 Mirror Model, JHEP 05 (2009) 068 [arXiv:0903.0141] [INSPIRE].
D. Bombardelli, D. Fioravanti and R. Tateo, Thermodynamic Bethe Ansatz for planar AdS/CFT: A Proposal, J. Phys. A 42 (2009) 375401 [arXiv:0902.3930] [INSPIRE].
N. Gromov, V. Kazakov, A. Kozak and P. Vieira, Exact Spectrum of Anomalous Dimensions of Planar N = 4 Supersymmetric Yang-Mills Theory: TBA and excited states, Lett. Math. Phys. 91 (2010) 265 [arXiv:0902.4458] [INSPIRE].
A. Cavaglia, D. Fioravanti and R. Tateo, Extended Y-system for the AdS 5 /CFT 4 correspondence, Nucl. Phys. B 843 (2011) 302 [arXiv:1005.3016] [INSPIRE].
N. Gromov, V. Kazakov, S. Leurent and D. Volin, Quantum Spectral Curve for Planar \( \mathcal{N}= \) super-Yang-Mills Theory, Phys. Rev. Lett. 112 (2014) 011602 [arXiv:1305.1939] [INSPIRE].
J. Escobedo, N. Gromov, A. Sever and P. Vieira, Tailoring Three-Point Functions and Integrability, JHEP 09 (2011) 028 [arXiv:1012.2475] [INSPIRE].
J. Escobedo, N. Gromov, A. Sever and P. Vieira, Tailoring Three-Point Functions and Integrability II. Weak/strong coupling match, JHEP 09 (2011) 029 [arXiv:1104.5501] [INSPIRE].
N. Gromov, A. Sever and P. Vieira, Tailoring Three-Point Functions and Integrability III. Classical Tunneling, JHEP 07 (2012) 044 [arXiv:1111.2349] [INSPIRE].
O. Foda, N=4 SYM structure constants as determinants, JHEP 03 (2012) 096 [arXiv:1111.4663] [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].
D. Serban, A note on the eigenvectors of long-range spin chains and their scalar products, JHEP 01 (2013) 012 [arXiv:1203.5842] [INSPIRE].
I. Kostov, Classical Limit of the Three-Point Function of N = 4 Supersymmetric Yang-Mills Theory from Integrability, Phys. Rev. Lett. 108 (2012) 261604 [arXiv:1203.6180] [INSPIRE].
I. Kostov, Three-point function of semiclassical states at weak coupling, J. Phys. A 45 (2012) 494018 [arXiv:1205.4412] [INSPIRE].
N. Gromov and P. Vieira, Tailoring Three-Point Functions and Integrability IV. Theta-morphism, JHEP 04 (2014) 068 [arXiv:1205.5288] [INSPIRE].
P. Vieira and T. Wang, Tailoring Non-Compact Spin Chains, JHEP 1410 (2014) 35 [arXiv:1311.6404] [INSPIRE].
O. Foda, Y. Jiang, I. Kostov and D. Serban, A tree-level 3-point function in the SU(3)-sector of planar N = 4 SYM, JHEP 10 (2013) 138 [arXiv:1302.3539] [INSPIRE].
L.F. Alday and A. Bissi, Higher-spin correlators, JHEP 10 (2013) 202 [arXiv:1305.4604] [INSPIRE].
V. Kazakov and E. Sobko, Three-point correlators of twist-2 operators in N = 4 SYM at Born approximation, JHEP 06 (2013) 061 [arXiv:1212.6563] [INSPIRE].
G. Georgiou, SL(2) sector: weak/strong coupling agreement of three-point correlators, JHEP 09 (2011) 132 [arXiv:1107.1850] [INSPIRE].
B. Eden, P. Heslop, G.P. Korchemsky and E. Sokatchev, Hidden symmetry of four-point correlation functions and amplitudes in N = 4 SYM, Nucl. Phys. B 862 (2012) 193 [arXiv:1108.3557] [INSPIRE].
B. Eden, P. Heslop, G.P. Korchemsky and E. Sokatchev, Constructing the correlation function of four stress-tensor multiplets and the four-particle amplitude in N = 4 SYM, Nucl. Phys. B 862 (2012) 450 [arXiv:1201.5329] [INSPIRE].
B. Eden, Three-loop universal structure constants in N = 4 SUSY Yang-Mills theory, arXiv:1207.3112 [INSPIRE].
E.K. Sklyanin, Quantum inverse scattering method. Selected topics, hep-th/9211111 [INSPIRE].
E.K. Sklyanin, Separation of variables - new trends, Prog. Theor. Phys. Suppl. 118 (1995) 35 [solv-int/9504001] [INSPIRE].
S.E. Derkachov, G.P. Korchemsky and A.N. Manashov, Noncompact Heisenberg spin magnets from high-energy QCD: 1. Baxter Q operator and separation of variables, Nucl. Phys. B 617 (2001) 375 [hep-th/0107193] [INSPIRE].
S.E. Derkachov, G.P. Korchemsky and A.N. Manashov, Separation of variables for the quantum SL(2, \( \mathrm{\mathbb{R}} \)) spin chain, JHEP 07 (2003) 047 [hep-th/0210216] [INSPIRE].
F.A Smirnov, Structure of Matrix Elements in Quantum Toda Chain, J. Phys. A 31 (1998) 8953 [math-ph/9805011].
Y. Kazama, S. Komatsu and T. Nishimura, A new integral representation for the scalar products of Bethe states for the XXX spin chain, JHEP 09 (2013) 013 [arXiv:1304.5011] [INSPIRE].
S.E. Derkachov, Baxter’s Q-operator for the homogeneous XXX spin chain, J. Phys. A 32 (1999) 5299 [solv-int/9902015] [INSPIRE].
A.V. Belitsky, V.M. Braun, A.S. Gorsky and G.P. Korchemsky, Integrability in QCD and beyond, Int. J. Mod. Phys. A 19 (2004) 4715 [hep-th/0407232] [INSPIRE].
S. Derkachov, G.P. Korchemsky and A.N. Manashov, Dual conformal symmetry on the light-cone, Nucl. Phys. B 886 (2014) 1102 [arXiv:1306.5951] [INSPIRE].
I.I. Balitsky and V.M. Braun, Evolution Equations for QCD String Operators, Nucl. Phys. B 311 (1989) 541 [INSPIRE].
M.S. Costa, J. Penedones, D. Poland and S. Rychkov, Spinning Conformal Correlators, JHEP 11 (2011) 071 [arXiv:1107.3554] [INSPIRE].
M.S. Costa, J. Penedones, D. Poland and S. Rychkov, Spinning Conformal Blocks, JHEP 11 (2011) 154 [arXiv:1109.6321] [INSPIRE].
E. Sobko, to appear.
N. Gromov, Quantum spectral curve at work, Talk at IGST 2013.
I. Balitsky, V. Kazakov and E. Sobko, Two-point correlator of twist-2 light-ray operators in N =4 SYM in BFKL approximation, arXiv:1310.3752 [INSPIRE].
M. Kirch and A.N. Manashov, Noncompact SL(2, \( \mathrm{\mathbb{R}} \)) spin chain, JHEP 06 (2004) 035 [hep-th/0405030] [INSPIRE].
Open Access
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1311.6957v2
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Sobko, E. A new representation for two- and three-point correlators of operators from sl(2) sector. J. High Energ. Phys. 2014, 101 (2014). https://doi.org/10.1007/JHEP12(2014)101
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP12(2014)101