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Ladder limit for correlators of Wilson loops. (English) Zbl 1391.81156
Summary: We study the correlator of concentric circular Wilson loops for arbitrary radii, spatial and internal space separations. For real values of the parameters specifying the dual string configuration, a typical Gross-Ooguri phase transition is observed. In addition, we explore some analytic continuation of a parameter $$\gamma$$ that characterizes the internal space separation. This enables a ladder limit in which ladder resummation and string theory computations precisely agree in the strong coupling limit. Finally, we find a critical value of $$\gamma$$ for which the correlator is supersymmetric and ladder diagrams can be exactly resummed for any value of the coupling constant.

##### MSC:
 81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics 81T60 Supersymmetric field theories in quantum mechanics
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##### References:
 [1] Maldacena, J., Wilson loops in large N field theories, Phys. Rev. Lett., 80, 4859, (1998) · Zbl 0947.81128 [2] Rey, S-J; Yee, J-T, Macroscopic strings as heavy quarks in large N gauge theory and anti-de Sitter supergravity, Eur. Phys. J., C 22, 379, (2001) · Zbl 1072.81555 [3] D. J. Gross and H. Ooguri, Aspects of large N gauge theory dynamics as seen by string theory, hep-th/9805129. [4] Berenstein, DE; Corrado, R.; Fischler, W.; Maldacena, JM, The operator product expansion for Wilson loops and surfaces in the large N limit, Phys. Rev., D 59, 105023, (1999) [5] K. Zarembo, Wilson loop correlator in the AdS/CFT correspondence, hep-th/9904149. · Zbl 0987.81540 [6] Zarembo, K., String breaking from ladder diagrams in SYM theory, JHEP, 03, 042, (2001) [7] P. Olesen and K. Zarembo, Phase transition in Wilson loop correlator from AdS/CFT correspondence, hep-th/0009210 [INSPIRE]. [8] Kim, H.; Park, DK; Tamarian, S.; Muller-Kirsten, HJW, Gross-ooguri phase transition at zero and finite temperature: two circular Wilson loop case, JHEP, 03, 003, (2001) [9] Plefka, J.; Staudacher, M., Two loops to two loops in N = 4 supersymmetric Yang-Mills theory, JHEP, 09, 031, (2001) [10] Drukker, N.; Fiol, B., On the integrability of Wilson loops in ads_{5} × S\^{5}: some periodic ansatze, JHEP, 01, 056, (2006) [11] Burrington, BA; Pando Zayas, LA, Phase transitions in Wilson loop correlator from integrability in global AdS, Int. J. Mod. Phys., A 27, 1250001, (2012) · Zbl 1247.81352 [12] Dekel, A.; Klose, T., Correlation function of circular Wilson loops at strong coupling, JHEP, 11, 117, (2013) [13] C. Ahn, Two circular Wilson loops and marginal deformations, hep-th/0606073 [INSPIRE]. [14] Armoni, A.; Piai, M.; Teimouri, A., Correlators of circular Wilson loops from holography, Phys. Rev., D 88, (2013) [15] L. Griguolo, S. Mori, F. Nieri and D. Seminara, Correlators of Hopf Wilson loops in the AdS/CFT correspondence, Phys. Rev.D 86 (2012) 046006 [arXiv:1203.3413] [INSPIRE]. [16] Liu, C-Y, Wilson surface correlator in the ads_{7}/CF T_{6} correspondence, JHEP, 07, 009, (2013) · Zbl 1342.83397 [17] Ziama, S., Holographic calculations of euclidean Wilson loop correlator in Euclidean anti-de Sitter space, JHEP, 04, 020, (2015) · Zbl 1388.81612 [18] Giataganas, D.; Irges, N., On the holographic width of flux tubes, JHEP, 05, 105, (2015) · Zbl 1388.83249 [19] M. Preti, D. Trancanelli, and E. Vescovi, Quark-antiquark potential in defect conformal field theory, [arXiv:1708.04884]. · Zbl 1383.81252 [20] Aguilera-Damia, J.; etal., Strings in bubbling geometries and dual Wilson loop correlators, JHEP, 12, 109, (2017) · Zbl 1383.83144 [21] S. Giombi and S. Komatsu, Exact correlators on the Wilson loop in$$\mathcal{N}=4$$SYM: localization, defect CFT and integrability, JHEP05 (2018) 109 [arXiv:1802.05201] [INSPIRE]. · Zbl 1391.81162 [22] E. Sysoeva, Wilson loop and its correlators in the limit of large coupling constant, arXiv:1803.00649 [INSPIRE]. · Zbl 1388.81890 [23] Correa, D.; Henn, J.; Maldacena, J.; Sever, A., The cusp anomalous dimension at three loops and beyond, JHEP, 05, 098, (2012) · Zbl 1348.81442 [24] Bykov, D.; Zarembo, K., Ladders for Wilson loops beyond leading order, JHEP, 09, 057, (2012) · Zbl 1397.81076 [25] Henn, JM; Huber, T., Systematics of the cusp anomalous dimension, JHEP, 11, 058, (2012) · Zbl 1397.81077 [26] D. Marmiroli, Resumming planar diagrams for the N = 6 ABJM cusped Wilson loop in light-cone gauge, arXiv:1211.4859 [INSPIRE]. [27] 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, JHEP09 (2013) 147 [arXiv:1304.6418] [INSPIRE]. · Zbl 1388.83249 [28] Bonini, M.; Griguolo, L.; Preti, M.; Seminara, D., Surprises from the resummation of ladders in the ABJ(M) cusp anomalous dimension, JHEP, 05, 180, (2016) · Zbl 1388.81250 [29] Kim, M.; Kiryu, N.; Komatsu, S.; Nishimura, T., Structure constants of defect changing operators on the 1/2 BPS Wilson loop, JHEP, 12, 055, (2017) · Zbl 1383.81238 [30] A. Cavaglià, N. Gromov and F. Levkovich-Maslyuk, Quantum spectral curve and structure constants in N = 4 SYM: cusps in the ladder limit, arXiv:1802.04237 [INSPIRE]. [31] Drukker, N.; Gross, DJ; Ooguri, H., Wilson loops and minimal surfaces, Phys. Rev., D 60, 125006, (1999) [32] J. Erickson, G. Semenoff and K. Zarembo, Wilson loops in supersymmetric Yang-Mills theory, Nucl. Phys. B582 (2000) 155 [hep-th/0003055]. · Zbl 0984.81154 [33] N. Drukker and D.J. Gross, An exact prediction of N = 4 supersymmetric Yang-Mills theory for string theory, J, Math. Phys.42 (2001) 2896 [hep-th/0010274]. · Zbl 1036.81041 [34] Pestun, V., Localization of gauge theory on a four-sphere and supersymmetric Wilson loops, Commun. Math. Phys., 313, 71, (2012) · Zbl 1257.81056 [35] M. Preti, Studies on Wilson loops, correlators and localization in supersymmetric quantum field theories, Ph.D. thesis, Parma University, Parma, Italy (2016). [36] Giombi, S.; Pestun, V., Correlators of local operators and 1/8 BPS Wilson loops on S\^{2} from 2d YM and matrix models, JHEP, 10, 033, (2010) · Zbl 1291.81249 [37] A. Bassetto et al., Correlators of supersymmetric Wilson-loops, protected operators and matrix models in N = 4 SYM, JHEP08 (2009) 061 [arXiv:0905.1943] [INSPIRE]. [38] Giombi, S.; Pestun, V.; Ricci, R., Notes on supersymmetric Wilson loops on a two-sphere, JHEP, 07, 088, (2010) · Zbl 1290.81066
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