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.

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

References in corpus (17)

• Higher spins in AdS_5 at one loop: vacuum energy, boundary conformal anomalies and AdS/CFT
• Exact properties of an integrated correlator in $\mathcal{N}=4$ $SU(N)$ SYM
• New Modular Invariants in $\mathcal{N}=4$ Super-Yang-Mills Theory
• Octagon at finite coupling
• N=2 Conformal SYM theories at large N
• F-theoretic vs microscopic description of a conformal N=2 SYM theory
• $1/N$ expansion of circular Wilson loop in $\mathcal{N}=2$ superconformal $SU(N)\times SU(N)$ quiver
• Strong coupling expansion of circular Wilson loops and string theories in AdS${}_5\times {\mathrm{S}}^5$ and AdS${}_4\times {\mathrm{CP}}^3$
• Crossing bridges with strong Szego limit theorem
• Modular invariant holographic correlators for $\mathcal{N}=4$ SYM with general gauge group
• Localization vs holography in $4d$ $\mathcal{N}=2$ quiver theories
• Exact probes of orientifolds
• The planar limit of $\mathcal{N}=2$ superconformal field theories
• Three-point functions in a $\mathcal{N}=2$ superconformal gauge theory and their strong-coupling limit
• Large $N$ expansion of an integrated correlator in $\mathcal{N}=4$ SYM
• On type IIB supergravity action on $M^5\times X^5$ solutions
• On ${\alpha }^{\prime }$-effects from $D$-branes in $4d\mathcal{N}=1$

Cited by in corpus (6)

• The AdS Veneziano amplitude at small curvature
• Non-planar corrections in orbifold/orientifold $\mathcal{N}=2$ superconformal theories from localization
• 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