Supersymmetric Wilson loops on S 3

Self Cite

153

221

We construct the Wilson loop operator of N = 6 super Chern-Simons-matter which is invariant under half of the supercharges of the theory and is dual to the simplest macroscopic open string in AdS 4 × CP 3 . The Wilson loop couples, in addition to the gauge and scalar fields of the theory, also to the fermions in the bi-fundamental representation of the U(N ) × U(M ) gauge group. These ingredients are naturally combined into a superconnection whose holonomy gives the Wilson loop, which can be defined for any representation of the supergroup U(N |M ). Explicit expressions for loops supported along an infinite straight line and along a circle are presented. Using the localization calculation of Kapustin et al. we show that the circular loop is computed by a supermatrix model and discuss the connection to pure Chern-Simons theory with supergroup U(N |M ).

Section: Jhep02(2010)058mentioning

confidence: 99%

A supermatrix model for $$ \mathcal{N} $$ = 6 super Chern-Simons-matter theory

Drukker

Trancanelli

2010

Self Cite

153

221

“…In [7,8] Wilson loops have been defined on a three sphere in space-time, which couple to scalars through the invariant one-forms of S 3 and preserve 1/16 of the supersymmetry. When the Wilson loop contour is restricted to a maximal two sphere, supersymmetry gets enhanced and gives rise to 1/8 BPS configurations.…”

Section: Introductionmentioning

confidence: 99%

The 1/2 BPS Wilson loop in ABJ(M) at two loops: the details

Bianchi

Giribet

Leoni

et al. 2013

Abstract:We compute the expectation value of the 1/2 BPS circular Wilson loop operator in ABJ(M) theory at two loops in perturbation theory. Our result turns out to be in exact agreement with the weak coupling limit of the prediction coming from localization, including finite N contributions associated to non-planar diagrams. It also confirms the identification of the correct framing factor that connects framingzero and framing-one expressions, previously proposed. The evaluation of the 1/2 BPS operator is made technically difficult in comparison with other observables of ABJ(M) theory by the appearance of integrals involving the coupling between fermions and gauge fields, which are absent for instance in the 1/6 BPS case. We describe in detail how to analytically solve these integrals in dimensional regularization with dimensional reduction (DRED). By suitably performing the physical limit to three dimensions we clarify the role played by short distance divergences on the final result and the mechanism of their cancellation.

“…On the other hand, localization reduces the calculation of the Wilson loops to the solution of a Gaussian matrix model [30][31][32][33][34], which, in principle, is exact in both, λ and N and provides an easier path to an asymptotic 1/N -expansion [35][36][37][38][39][40][41]. Wilson loops in N = 4 Super-Yang-Mills theory with fewer symmetries have been studied, e.g., in [42][43][44][45][46].Localization can be applied more generally in N = 2 Super-Yang-Mills theories. Interested readers are referred to the recent paper [47] and references therein.The purpose of this paper is to further develop a recent result [48], which relates the connected correlators of multiply-wound Wilson loops in N = 4 Super-Yang-Mills theory [40] to the exact solution of the corresponding Hermitian matrix model.…”

mentioning

confidence: 99%

Combinatorics of Wilson loops in $$ \mathcal{N} $$ = 4 SYM theory

Mück

2019

The theory of Wilson loops for gauge theories with unitary gauge groups is formulated in the language of symmetric functions. The main objects in this theory are two generating functions, which are related to each other by the involution that exchanges an irreducible representation with its conjugate. Both of them contain all information about the Wilson loops in arbitrary representations as well as the correlators of multiply-wound Wilson loops. This general framework is combined with the results of the Gaussian matrix model, which calculates the expectation values of 1/2-BPS circular Wilson loops in N = 4 Super-Yang-Mills theory. General, explicit, formulas for the connected correlators of multiply-wound Wilson loops in terms of the traces of symmetrized matrix products are obtained, as well as their inverses. It is shown that the generating functions for Wilson loops in mutually conjugate representations are related by a duality relation whenever they can be calculated by a Hermitian matrix model. * localization techniques [8,9] have provided a wealth of new solutions, in particular for highly symmetric loop configurations in supersymmetric gauge theories. A paradigmatic case is the case of 1 2 -BPS circular Wilson loops in N = 4 Super-Yang-Mills theory with gauge group U(N ) or SU(N ). On the one hand, the holographic dual fully captures the planar approximation in the limit of large 't Hooft coupling λ [10-15], and a lot of effort has been dedicated to obtain corrections in 1/λ [16][17][18][19][20][21][22][23][24][25][26][27][28][29]. On the other hand, localization reduces the calculation of the Wilson loops to the solution of a Gaussian matrix model [30][31][32][33][34], which, in principle, is exact in both, λ and N and provides an easier path to an asymptotic 1/N -expansion [35][36][37][38][39][40][41]. Wilson loops in N = 4 Super-Yang-Mills theory with fewer symmetries have been studied, e.g., in [42][43][44][45][46].Localization can be applied more generally in N = 2 Super-Yang-Mills theories. Interested readers are referred to the recent paper [47] and references therein.The purpose of this paper is to further develop a recent result [48], which relates the connected correlators of multiply-wound Wilson loops in N = 4 Super-Yang-Mills theory [40] to the exact solution of the corresponding Hermitian matrix model. This relation was worked out explicitly in [40] for the connected n-loop correlators with n ≤ 4 and was generalized in [48] to any n by recognizing the combinatorical pattern. In [48], it was conjectured that the relation has a deeper, group-theoretical, origin. It will be shown here that this is indeed true. To achieve this goal, it turns out to be most natural and effective to employ the framework of symmetric functions. Symmetric functions have already been used in the matrix model solution of the 1/2-BPS Wilson loops in general representations [34]. However, the generality of this framework does not seem to be widely appreciated. In fact, it allows to define the generating function(s) for ...