Abstract
In this paper we compute the vacuum expectation value of the Wilson loop and its correlators with chiral primary operators in mathcal{N} = 2, 4 superconformal U(N ) gauge theories at large N . After localization these quantities can be computed in terms of a deformed U(N ) matrix model. The Wilson loops we deal with are in the fundamental and symmetric representations.
Highlights
A solid link between the computations performed in N = 4 SYM and the matrix model
In this paper we compute the vacuum expectation value of the Wilson loop and its correlators with chiral primary operators in N = 2, 4 superconformal U(N ) gauge theories at large N. After localization these quantities can be computed in terms of a deformed U(N ) matrix model
The same type of interacting matrix model arises in the studies of N = 2 theories [5, 10], where the interactions account for higher loop corrections and mass deformations
Summary
We generally follow the notation of [9] and consider deformed N = 4 SYM theory on S4 in terms of N = 2 SYM theory with one vector multiplet and one adjoint hypermultiplet of matter. We choose the contour such that |x | = 1 As it was shown in [9], the vev of a WL in the fundamental representation in this case can be written as a U(N ) matrix model average. The averages in the matrix model are defined as 1 f (a) def = Z d[a]f (a) e−NV (a) = 1 Z da ∆(a) f (a) e−NV (a) , where. With d[a] being the Lebesgue measure in the space of Hermitian N × N matrices, da =. In the following subsections we consider different types of the potential V (a)
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