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

Abstract

We apply the localization technique to compute the free energy on four-sphere and the circular BPS Wilson loop in the four-dimensional $\mathcal{N}$=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 $\mathcal{N}$=2 superconformal models that are planar-equivalent to $\mathcal{N}$=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 $\mathcal{O}(e^{-\sqrt{\lambda }})$ corrections and consider a generalization to the case when the fundamental hypermultiplets have a non-zero mass. The string theory dual of this $\mathcal{N}$=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.

arXiv comment41 pages. v2: minor correction; v3: eqs.(2.41) and (2.43) corrected

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• Wilson loop correlators at strong coupling in $\mathcal{N}=2$ quiver gauge theories
• Conformal Four-Point Integrals: Recursive Structure, Toda Equations and Double Copy
• Integrated correlators with a Wilson line in a $\mathcal{N}=2$ quiver gauge theory at strong coupling
• Integrability treatment of AdS/CFT orbifolds