Semiclassical correlation functions of Wilson loops and local vertex operators

Hernández, Rafael

doi:10.1016/j.nuclphysb.2012.05.013

Cited by 9 publications

(2 citation statements)

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“…We then use this solution to obtain the string prediction for W O J 1 O J 2 at J 1 ∼ √ λ ≫ J 2 , again observing perfect agreeement with the exact solution of the three-matrix model in the appropriate limit. In this paper we do not find the string solution which should describe W O J 1 O J 2 in the 4 Some examples of (non-supersymmetric) correlation functions of Wilson loop and local operators in the limit of large charges were recently studied also in [39] [40]. 5 There is a vast literature on multi-matrix models, see e.g.…”

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confidence: 90%

Correlators of Wilson loops and local operators from multi-matrix models and strings in AdS

Giombi

Pestun

2013

J. High Energ. Phys.

126

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We study correlation functions of Wilson loops and local operators in a subsector of N = 4 SYM which preserves two supercharges. Localization arguments allow to map the problem to a calculation in bosonic two-dimensional Yang-Mills theory. In turn, this can be reduced to computing correlators in certain Gaussian multi-matrix models. We focus on the correlation function of a Wilson loop and two local operators, and solve the corresponding three-matrix model exactly in the planar limit. We compare the strong coupling behavior to string theory in AdS 5 × S 5 , finding precise agreement. We pay particular attention to the case in which the local operators have large R-charge J ∼ √ λ at strong coupling. * On leave of absence from ITEP, 117218, Moscow, Russia IntroductionExact results in non-abelian gauge theories are rare and clearly of great importance. In supersymmetric gauge theories, the powerful technique of localization allows sometimes for such exact results for certain observables preserving some fermionic symmetries of the theory. For example the exact expressions conjectured in [1, 2] for the circular 1/2-BPS Wilson loop in N = 4 SYM were proved using localization in [3], as well as extendend to a large class of N = 2 theories.In N = 4 SYM, a wide generalization of the 1/2-BPS circle to lower supersymmetric Wilson loops of arbitrary shapes was introduced in [4-6] and then classified in [7]. An interesting subfamily of that construction consists of operators supported on any loop on a two-sphere S 2 embedded into the R 4 spacetime. Generically, these Wilson loops are 1/8-BPS, and it was conjectured in [4][5][6] that their quantum correlators are exactly captured by a purely perturbative calculation in bosonic 2d Yang-Mills. The conjecture was later strongly supported by the localization calculation in [8], where it was shown that the path-integral with insertions of those loop operators localizes on a 2d gauge theory closely related to the Hitchin/Higgs-Yang Mills system [9][10][11], which can be seen to be perturbatively equivalent to ordinary bosonic 2d Yang-Mills. 2 The calculation in the 2d theory can be then mapped to certain Gaussian multi-matrix models, which allow for an exact evaluation of the correlators. Several checks of the relation to 2d YM have appeared [12][13][14][15][16][17]. 3 In particular, recently the localization result for the expectation value of a Wilson loop in this family was used in [18] (see also [19]) to derive an exact expression for the low-angle limit of the cusp anomalous dimension. This has been checked using integrability up to three loops in [20] (see also [21]) and analytically to all loops in [22], providing a first link between localization and integrability results.The calculation in [8] also suggested that localization applies in fact not only to the Wilson loops, but to a larger sector of operators that are annihilated by the same supercharge. This include certain chiral primary operators inserted on the S 2 [23] as well as 't Hooft loops linked with the S 2 [24]. T...

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confidence: 90%

Correlators of Wilson loops and local operators from multi-matrix models and strings in AdS

Giombi

Pestun

2013

J. High Energ. Phys.

126

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“…7 The study of such more general correlators may be of interest in trying to understand better the relation [15] between the correlator of null-separated local operators and the square of corresponding cusped Wilson loop. Finally, let us mention some recent related work that appeared in [36,37,38].…”

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confidence: 99%

Correlation function of null polygonal Wilson loop with local operator

Tseytlin¹

2012

Proceedings of Proceedings of the Corfu Summer Institute 2011 — PoS(CORFU2011)

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We consider the correlator of a light-like polygonal Wilson loop with n cusps with a local (dilaton or chiral primary) operator in planar N = 4 super Yang-Mills theory. Following arXiv:1107.5702 we review the structure of such correlator implied by conformal symmetry. The first non-trivial case is n = 4 when the correlator depends on just one conformal ratio. We compute it at leading order in both the strong coupling regime (using semiclassical string theory) and the weak coupling regime (using perturbative gauge theory).

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