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

TL;DR

This paper uses localization to derive exact strong-coupling results for free energy and Wilson loops in a specific $ cal=2$ superconformal $Sp(2N)$ gauge theory, revealing simple formulas valid at all orders in large $N$ and coupling.

Contribution

It derives exact strong-coupling expressions for key observables in an $ cal=2$ superconformal $Sp(2N)$ gauge theory using Toda lattice equations, including all $1/N$ and $1/ ootontig ext{ m extstyle extstyle}\lambda$ corrections.

Findings

Exact formulas for free energy and Wilson loop at strong coupling.

Inclusion of all $1/N$ and $1/ ootontig ext{ m extstyle extstyle}\lambda$ corrections.

Leading exponential corrections and mass deformations analyzed.

Abstract

We apply the localization technique to compute the free energy on four-sphere and the circular BPS Wilson loop in the four-dimensional $\cal N$=2 superconformal $Sp(2N)$ 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 $\cal N$=2 superconformal models that are planar-equivalent to $\cal N$=4 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 $\lambda$, 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 $1/\sqrt{\lambda}$. We also compute the leading exponentially suppressed ${\cal O}(e^{-\sqrt{\lambda}})$ corrections and consider a generalization to the case when the fundamental hypermultiplets have a non-zero mass. The string theory dual of this $\cal N$=2 gauge theory should be a particular orientifold of AdS$_5 \times S^5$ type IIB string and we discuss the string theory interpretation of the obtained strong-coupling results.