Abstract
We study the asymptotic volume dependence of the heavy-heavy-light three-point functions in the \( \mathcal{N}=4 \) Super-Yang-Mills theory using the hexagon bootstrap approach, where the volume is the length of the heavy operator. We extend the analysis of our previous short letter [1] to the general case where the heavy operators can be in any rank one sector and the light operator being a generic non-BPS operator. We prove the conjecture of Bajnok, Janik and Wereszczynski [2] up to leading finite size corrections.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Y. Jiang and A. Petrovskii, Diagonal form factors and hexagon form factors, JHEP 07 (2016) 120 [arXiv:1511.06199] [INSPIRE].
Z. Bajnok, R.A. Janik and A. Wereszczyński, HHL correlators, orbit averaging and form factors, JHEP 09 (2014) 050 [arXiv:1404.4556] [INSPIRE].
F. Smirnov, Form-factors in completely integrable models of quantum field theory, Adv. Ser. Math. Phys. 14 (1992) 1 [INSPIRE].
K. Okuyama and L.-S. Tseng, Three-point functions in N = 4 SYM theory at one-loop, JHEP 08 (2004) 055 [hep-th/0404190] [INSPIRE].
L.F. Alday, J.R. David, E. Gava and K.S. Narain, Structure constants of planar N = 4 Yang-Mills at one loop, JHEP 09 (2005) 070 [hep-th/0502186] [INSPIRE].
R. Roiban and A. Volovich, Yang-Mills correlation functions from integrable spin chains, JHEP 09 (2004) 032 [hep-th/0407140] [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, 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].
O. Foda and M. Wheeler, Partial domain wall partition functions, JHEP 07 (2012) 186 [arXiv:1205.4400] [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].
E. Bettelheim and I. Kostov, Semi-classical analysis of the inner product of Bethe states, J. Phys. A 47 (2014) 245401 [arXiv:1403.0358] [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].
N. Gromov and P. Vieira, Tailoring three-point functions and integrability IV. Theta-morphism, JHEP 04 (2014) 068 [arXiv:1205.5288] [INSPIRE].
Y. Jiang, I. Kostov, F. Loebbert and D. Serban, Fixing the quantum three-point function, JHEP 04 (2014) 019 [arXiv:1401.0384] [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].
P. Vieira and T. Wang, Tailoring non-compact spin chains, JHEP 10 (2014) 35 [arXiv:1311.6404] [INSPIRE].
J. Caetano and T. Fleury, Three-point functions and su(1|1) spin chains, JHEP 09 (2014) 173 [arXiv:1404.4128] [INSPIRE].
Y. Jiang, S. Komatsu, I. Kostov and D. Serban, The hexagon in the mirror: the three-point function in the SoV representation, J. Phys. A 49 (2016) 174007 [arXiv:1506.09088] [INSPIRE].
E. Sobko, A new representation for two- and three-point correlators of operators from sl(2) sector, JHEP 12 (2014) 101 [arXiv:1311.6957] [INSPIRE].
R.A. Janik and A. Wereszczynski, Correlation functions of three heavy operators: the AdS contribution, JHEP 12 (2011) 095 [arXiv:1109.6262] [INSPIRE].
Y. Kazama and S. Komatsu, On holographic three point functions for GKP strings from integrability, JHEP 01 (2012) 110 [Erratum ibid. 06 (2012) 150] [arXiv:1110.3949] [INSPIRE].
Y. Kazama and S. Komatsu, Wave functions and correlation functions for GKP strings from integrability, JHEP 09 (2012) 022 [arXiv:1205.6060] [INSPIRE].
Y. Kazama and S. Komatsu, Three-point functions in the SU(2) sector at strong coupling, JHEP 03 (2014) 052 [arXiv:1312.3727] [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].
I. Balitsky, V. Kazakov and E. Sobko, Structure constant of twist-2 light-ray operators in the Regge limit, Phys. Rev. D 93 (2016) 061701 [arXiv:1506.02038] [INSPIRE].
I. Balitsky, V. Kazakov and E. Sobko, Three-point correlator of twist-2 light-ray operators in N = 4 SYM in BFKL approximation, arXiv:1511.03625 [INSPIRE].
T. Bargheer, J.A. Minahan and R. Pereira, Computing three-point functions for short operators, JHEP 03 (2014) 096 [arXiv:1311.7461] [INSPIRE].
J.A. Minahan and R. Pereira, Three-point correlators from string amplitudes: mixing and Regge spins, JHEP 04 (2015) 134 [arXiv:1410.4746] [INSPIRE].
M.S. Costa, V. Goncalves and J. Penedones, Conformal Regge theory, JHEP 12 (2012) 091 [arXiv:1209.4355] [INSPIRE].
M.S. Costa, J. Drummond, V. Goncalves and J. Penedones, The role of leading twist operators in the Regge and Lorentzian OPE limits, JHEP 04 (2014) 094 [arXiv:1311.4886] [INSPIRE].
T. Klose and T. McLoughlin, Worldsheet form factors in AdS/CFT, Phys. Rev. D 87 (2013) 026004 [arXiv:1208.2020] [INSPIRE].
Z. Bajnok and R.A. Janik, String field theory vertex from integrability, JHEP 04 (2015) 042 [arXiv:1501.04533] [INSPIRE].
Z. Bajnok and R.A. Janik, The kinematical AdS 5 × S 5 Neumann coefficient, JHEP 02 (2016) 138 [arXiv:1512.01471] [INSPIRE].
Y. Jiang, I. Kostov, A. Petrovskii and D. Serban, String bits and the spin vertex, Nucl. Phys. B 897 (2015) 374 [arXiv:1410.8860] [INSPIRE].
Y. Jiang and A. Petrovskii, From spin vertex to string vertex, JHEP 06 (2015) 172 [arXiv:1412.2256] [INSPIRE].
Y. Kazama, S. Komatsu and T. Nishimura, Novel construction and the monodromy relation for three-point functions at weak coupling, JHEP 01 (2015) 095 [Erratum ibid. 08 (2015) 145] [arXiv:1410.8533] [INSPIRE].
B. Basso, S. Komatsu and P. Vieira, Structure constants and integrable bootstrap in planar N = 4 SYM theory, arXiv:1505.06745 [INSPIRE].
B. Eden and A. Sfondrini, Three-point functions in \( \mathcal{N}=4 \) SYM: the hexagon proposal at three loops, JHEP 02 (2016) 165 [arXiv:1510.01242] [INSPIRE].
B. Basso, V. Goncalves, S. Komatsu and P. Vieira, Gluing hexagons at three loops, Nucl. Phys. B 907 (2016) 695 [arXiv:1510.01683] [INSPIRE].
K. Zarembo, Holographic three-point functions of semiclassical states, JHEP 09 (2010) 030 [arXiv:1008.1059] [INSPIRE].
M.S. Costa, R. Monteiro, J.E. Santos and D. Zoakos, On three-point correlation functions in the gauge/gravity duality, JHEP 11 (2010) 141 [arXiv:1008.1070] [INSPIRE].
L. Hollo, Y. Jiang and A. Petrovskii, Diagonal form factors and heavy-heavy-light three-point functions at weak coupling, JHEP 09 (2015) 125 [arXiv:1504.07133] [INSPIRE].
B. Pozsgay and G. Takács, Form factors in finite volume. II. Disconnected terms and finite temperature correlators, Nucl. Phys. B 788 (2008) 209 [arXiv:0706.3605] [INSPIRE].
A. Leclair and G. Mussardo, Finite temperature correlation functions in integrable QFT, Nucl. Phys. B 552 (1999) 624 [hep-th/9902075] [INSPIRE].
B. Pozsgay, Form factor approach to diagonal finite volume matrix elements in integrable QFT, JHEP 07 (2013) 157 [arXiv:1305.3373] [INSPIRE].
B. Pozsgay, I.M. Szecsenyi and G. Takács, Exact finite volume expectation values of local operators in excited states, JHEP 04 (2015) 023 [arXiv:1412.8436] [INSPIRE].
. Beisert, The analytic Bethe ansatz for a chain with centrally extended su(2|2) symmetry, J. Stat. Mech. 01 (2007) P01017 [nlin/0610017].
N. Beisert, B. Eden and M. Staudacher, Transcendentality and crossing, J. Stat. Mech. 0701 (2007) P01021 [hep-th/0610251] [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: 1601.06926
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
Jiang, Y. Diagonal form factors and hexagon form factors II. Non-BPS light operator. J. High Energ. Phys. 2017, 21 (2017). https://doi.org/10.1007/JHEP01(2017)021
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP01(2017)021