Exact strong coupling results in N = 2 Sp(2N) superconformal gauge theory from localization

A bstract We apply the localization technique to compute the free energy on four-sphere and the circular BPS Wilson loop in the four-dimensional N N = ∈ superconformal Sp(2 N ) gauge theory containing vector multiplet coupled to four hypermultiplets in fundamental representation and one hypermultiplet in rank-2 antisymmetric representation. This theory is unique among similar N N = ∈ superconformal models that are planar-equivalent to N N = ∆ SYM in that the corresponding localization matrix model has the interaction potential containing single-trace terms only. We exploit this property to show that, to any order in large N expansion and an arbitrary ’t Hooft coupling λ , the free energy and the Wilson loop satisfy Toda lattice equations. Solving these equations at strong coupling, we find remarkably simple expressions for these observables which include all corrections in 1 /N and 1 / √λ λ . We also compute the leading exponentially suppressed O(e-√λ) O e − λ corrections and consider a generalization to the case when the fundamental hypermultiplets have a non-zero mass. The string theory dual of this N N = ∈ gauge theory should be a particular orientifold of AdS 5 × S 5 type IIB string and we discuss the string theory interpretation of the obtained strong-coupling results.