Quantum ’t Hooft Loops of SYM $${{\mathcal N}=4}$$ as Instantons of YM2 in Dual Groups SU(N) and SU(N)/ZN

Bassetto, A.; Thambyahpillai, Shiyamala

doi:10.1007/s11005-011-0480-2

Cited by 4 publications

(3 citation statements)

References 34 publications

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“…Normalization by the expectation value of the Wilson (3.20) brings this result into the full agreement with the string-theory calculation. Localization allows one to study much wider class of correlation functions involving Wilson loops of different shape [82,92], in higher representations of the gauge group [78], 't Hooft loops [78,93,94], correlators of two Wilson loops [83,84,95,85] as well as multi-point correlation functions [85].…”

Section: Operator Product Expansionmentioning

confidence: 99%

Localization and AdS/CFT correspondence

Zarembo¹

2017

J. Phys. A: Math. Theor.

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An interplay between localization and holography is reviewed with the emphasis on the AdS 5 /CF T 4 correspondence. This is a contribution to the review volume "Localization techniques in quantum field theories" (eds. V. Pestun and M. Zabzine) which contains 17 Chapters available at [1] Integrating out Z we get back to the matrix model (3.8) for the circular Wilson loop as expected.The OPE coefficients map to the following correlation function in the two-matrix matrix model (6.7):tr Z J tr e 2πΦ . (6.8)

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Section: Operator Product Expansionmentioning

confidence: 99%

Localization and AdS/CFT correspondence

Zarembo¹

2017

J. Phys. A: Math. Theor.

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“…Under this map, on the 2d YM side we should extract only the perturbative, or zero-instanton, contribution. In fact, non-trivial instantons on the 2d side also have an interpretation in 4d: they correspond to turning on 1/2-BPS 't Hooft loop operators along a S 1 linked with the S 2 [24] (see also [27]). In this paper we will not consider 't Hooft loops and focus on Wilson loops and local operators.…”

Section: Review Of Supersymmetric Subsector and Relation To 2dmentioning

confidence: 99%

“…The correlation function of a Wilson loop and a local operator in this sector was computed in [23], giving support and generalizing the original conjecture of [25] for the correlator of a 1/2-BPS Wilson loop and a chiral primary (see also [26] for the study of the large R-charge limit of this correlator). In [24] [27], the exact results implied by the relation to 2d were also used to obtain some explicit tests of the S-duality symmetry of the N = 4 SYM theory.…”

Section: Introductionmentioning

confidence: 99%

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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Pucci

2012

J. High Energ. Phys.

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We study supersymmetric 't Hooft loop operators in N = 4 super Yang-Mills, generalizing the well-known circular 1/2 BPS case and investigating their S-duality properties. We derive the BPS condition for a generic line operator describing pointlike monopoles and discuss its solutions in some particular case. In particular, we present the explicit construction of the magnetic counterpart of Zarembo and DGRT Wilson loops and provide the general dyonic configurations for an abelian gauge group. The quantum definition of these supersymmetric 't Hooft loop operators is carefully discussed and we attempt some computations to next-to-leading order in perturbation theory.

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Quantum ’t Hooft Loops of SYM $${{\mathcal N}=4}$$ as Instantons of YM2 in Dual Groups SU(N) and SU(N)/ZN

Cited by 4 publications

References 34 publications

Localization and AdS/CFT correspondence

Localization and AdS/CFT correspondence

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

More on ’t Hooft loops in $ \mathcal{N}=4 $ SYM

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