Abstract
By considering a Gaussian truncation of \( \mathcal{N} \) = 4 super Yang-Mills, we derive a set of Dyson equations that account for the ladder diagram contribution to connected correlators of circular Wilson loops. We consider different numbers of loops, with different relative orientations. We show that the Dyson equations admit a spectral representation in terms of eigenfunctions of a Schrödinger problem, whose classical limit describes the strong coupling limit of the ladder resummation. We also verify that in supersymmetric cases the exact solution to the Dyson equations reproduces known matrix model results.
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J.K. Erickson, G.W. Semenoff and K. Zarembo, Wilson loops in N = 4 supersymmetric Yang-Mills theory, Nucl. Phys. B 582 (2000) 155 [hep-th/0003055] [INSPIRE].
N. Drukker and D.J. Gross, An Exact prediction of N = 4 SUSYM theory for string theory, J. Math. Phys. 42 (2001) 2896 [hep-th/0010274] [INSPIRE].
V. Pestun, Localization of gauge theory on a four-sphere and supersymmetric Wilson loops, Commun. Math. Phys. 313 (2012) 71 [arXiv:0712.2824] [INSPIRE].
K. Zarembo, Localization and AdS/CFT Correspondence, J. Phys. A 50 (2017) 443011 [arXiv:1608.02963] [INSPIRE].
D. Correa, J. Henn, J. Maldacena and A. Sever, The cusp anomalous dimension at three loops and beyond, JHEP 05 (2012) 098 [arXiv:1203.1019] [INSPIRE].
N. Gromov and F. Levkovich-Maslyuk, Quark-anti-quark potential in \( \mathcal{N} \) = 4 SYM, JHEP 12 (2016) 122 [arXiv:1601.05679] [INSPIRE].
M. Kim, N. Kiryu, S. Komatsu and T. Nishimura, Structure Constants of Defect Changing Operators on the 1/2 BPS Wilson Loop, JHEP 12 (2017) 055 [arXiv:1710.07325] [INSPIRE].
A. Cavaglià, N. Gromov and F. Levkovich-Maslyuk, Quantum spectral curve and structure constants in \( \mathcal{N} \) = 4 SYM: cusps in the ladder limit, JHEP 10 (2018) 060 [arXiv:1802.04237] [INSPIRE].
K. Zarembo, String breaking from ladder diagrams in SYM theory, JHEP 03 (2001) 042 [hep-th/0103058] [INSPIRE].
D.H. Correa, P. Pisani and A. Rios Fukelman, Ladder Limit for Correlators of Wilson Loops, JHEP 05 (2018) 168 [arXiv:1803.02153] [INSPIRE].
D.J. Gross and H. Ooguri, Aspects of large N gauge theory dynamics as seen by string theory, Phys. Rev. D 58 (1998) 106002 [hep-th/9805129] [INSPIRE].
J.K. Erickson, G.W. Semenoff, R.J. Szabo and K. Zarembo, Static potential in N = 4 supersymmetric Yang-Mills theory, Phys. Rev. D 61 (2000) 105006 [hep-th/9911088] [INSPIRE].
I.R. Klebanov, J.M. Maldacena and C.B. Thorn, III, Dynamics of flux tubes in large N gauge theories, JHEP 04 (2006) 024 [hep-th/0602255] [INSPIRE].
D. Bykov and K. Zarembo, Ladders for Wilson Loops Beyond Leading Order, JHEP 09 (2012) 057 [arXiv:1206.7117] [INSPIRE].
J.M. Henn and T. Huber, The four-loop cusp anomalous dimension in \( \mathcal{N} \) = 4 super Yang-Mills and analytic integration techniques for Wilson line integrals, JHEP 09 (2013) 147 [arXiv:1304.6418] [INSPIRE].
D. Marmiroli, Resumming planar diagrams for the N = 6 ABJM cusped Wilson loop in light-cone gauge, arXiv:1211.4859 [INSPIRE].
M. Bonini, L. Griguolo, M. Preti and D. Seminara, Surprises from the resummation of ladders in the ABJ(M) cusp anomalous dimension, JHEP 05 (2016) 180 [arXiv:1603.00541] [INSPIRE].
K. Zarembo, Wilson loop correlator in the AdS/CFT correspondence, Phys. Lett. B 459 (1999) 527 [hep-th/9904149] [INSPIRE].
P. Olesen and K. Zarembo, Phase transition in Wilson loop correlator from AdS/CFT correspondence, hep-th/0009210 [INSPIRE].
H. Kim, D.K. Park, S. Tamarian and H.J.W. Muller-Kirsten, Gross-Ooguri phase transition at zero and finite temperature: Two circular Wilson loop case, JHEP 03 (2001) 003 [hep-th/0101235] [INSPIRE].
J.M. Maldacena, Wilson loops in large N field theories, Phys. Rev. Lett. 80 (1998) 4859 [hep-th/9803002] [INSPIRE].
J. Plefka and M. Staudacher, Two loops to two loops in N = 4 supersymmetric Yang-Mills theory, JHEP 09 (2001) 031 [hep-th/0108182] [INSPIRE].
G. Arutyunov, J. Plefka and M. Staudacher, Limiting geometries of two circular Maldacena-Wilson loop operators, JHEP 12 (2001) 014 [hep-th/0111290] [INSPIRE].
N. Drukker and B. Fiol, On the integrability of Wilson loops in AdS 5 × S 5 : Some periodic ansatze, JHEP 01 (2006) 056 [hep-th/0506058] [INSPIRE].
H. Dorn, On Wilson loops for two touching circles with opposite orientation, arXiv:1811.00799 [INSPIRE].
G. Akemann and P.H. Damgaard, Wilson loops in N = 4 supersymmetric Yang-Mills theory from random matrix theory, Phys. Lett. B 513 (2001) 179 [Erratum ibid. B 524 (2002) 400] [hep-th/0101225] [INSPIRE].
S. Giombi, V. Pestun and R. Ricci, Notes on supersymmetric Wilson loops on a two-sphere, JHEP 07 (2010) 088 [arXiv:0905.0665] [INSPIRE].
S. Giombi and V. Pestun, Correlators of Wilson Loops and Local Operators from Multi-Matrix Models and Strings in AdS, JHEP 01 (2013) 101 [arXiv:1207.7083] [INSPIRE].
N. Drukker, S. Giombi, R. Ricci and D. Trancanelli, More supersymmetric Wilson loops, Phys. Rev. D 76 (2007) 107703 [arXiv:0704.2237] [INSPIRE].
N. Drukker, S. Giombi, R. Ricci and D. Trancanelli, Wilson loops: From four-dimensional SYM to two-dimensional YM, Phys. Rev. D 77 (2008) 047901 [arXiv:0707.2699] [INSPIRE].
N. Drukker, S. Giombi, R. Ricci and D. Trancanelli, Supersymmetric Wilson loops on S 3, JHEP 05 (2008) 017 [arXiv:0711.3226] [INSPIRE].
S. Giombi and S. Komatsu, Exact Correlators on the Wilson Loop in \( \mathcal{N} \) = 4 SYM: Localization, Defect CFT and Integrability, JHEP 05 (2018) 109 [Erratum ibid. 11 (2018) 123] [arXiv:1802.05201] [INSPIRE].
A.A. Migdal, Loop Equations and 1/N Expansion, Phys. Rept. 102 (1983) 199 [INSPIRE].
Yu. Makeenko, Loop equations in matrix models and in 2-D quantum gravity, Mod. Phys. Lett. A 6 (1991) 1901 [INSPIRE].
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Correa, D., Pisani, P., Fukelman, A.R. et al. Dyson equations for correlators of Wilson loops. J. High Energ. Phys. 2018, 100 (2018). https://doi.org/10.1007/JHEP12(2018)100
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DOI: https://doi.org/10.1007/JHEP12(2018)100