Abstract
We consider the expectation value leftlangle mathcal{W}rightrangle of the circular BPS Wilson loop in mathcal{N} = 2 superconformal SU(N) gauge theory containing a vector multiplet coupled to two hypermultiplets in rank-2 symmetric and antisymmetric representations. This theory admits a regular large N expansion, is planar-equivalent to mathcal{N} = 4 SYM theory and is expected to be dual to a certain orbifold/orientifold projection of AdS5× S5 superstring theory. On the string theory side leftlangle mathcal{W}rightrangle is represented by the path integral expanded near the same AdS2 minimal surface as in the maximally supersymmetric case. Following the string theory argument in [5], we suggest that as in the mathcal{N} = 4 SYM case and in the mathcal{N} = 2 SU(N) × SU(N) superconformal quiver theory discussed in [19], the coefficient of the leading non-planar 1/N2 correction in leftlangle mathcal{W}rightrangle should have the universal λ3/2 scaling at large ’t Hooft coupling. We confirm this prediction by starting with the localization matrix model representation for leftlangle mathcal{W}rightrangle . We complement the analytic derivation of the λ3/2 scaling by a numerical high-precision resummation and extrapolation of the weak-coupling expansion using conformal mapping improved Padé analysis.
Highlights
We consider the expectation value W of the circular BPS Wilson loop in N = 2 superconformal SU(N ) gauge theory containing a vector multiplet coupled to two hypermultiplets in rank-2 symmetric and antisymmetric representations
On the string theory side W is represented by the path integral expanded near the same AdS2 minimal surface as in the maximally supersymmetric case
Following the string theory argument in [5], we suggest that as in the N = 4 SYM case and in the N = 2 SU(N ) × SU(N ) superconformal quiver theory discussed in [19], the coefficient of the leading non-planar 1/N 2 correction in W should have the universal λ3/2 scaling at large ’t Hooft coupling
Summary
Taking the large N limit we find that ∆q in (2.9) can be represented as in (1.11), i.e. The insertion of a factor of tr m2 is the same as the insertion of the free action in (2.3) and it can be obtained by differentiating the partition function (2.2) over λ. Taking the large N limit we find that ∆q in (2.9) can be represented as in (1.11), i.e This is essentially the same relation as was observed to hold in the N = 2 orbifold model in [19] (up to factor of 2 due to the SU(N ) × SU(N ) instead of SU(N ) gauge group). Since the leading non-planar correction to the Wilson loop can be expressed (2.13) in terms of ∆F (λ), in what follows we shall concentrate on the study of its structure both at weak and strong coupling. This measure is same as in (2.4) when written in terms of the eigenvalues and dropping the “angular” part that cancels in expectation values of relevant correlators (functions of traces of matrix a)
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