The planar limit of the $\mathcal{N} = 2$ $\mathbf{E}$-theory: numerical calculations and the large $\lambda$ expansion

TL;DR

This paper develops numerical methods to compute correlation functions and Wilson loops in a 4d $ abla$=2 superconformal gauge theory, providing analytic strong coupling expansions and predictions for string theory corrections.

Contribution

It introduces efficient numerical techniques for calculating correlators in the $ extbf{E}$-theory and derives analytic expressions up to sixth order in the strong coupling expansion.

Findings

Explicit strong coupling expansions for correlators and Wilson loops.

Analytic expressions valid up to sixth order in $ ext{lambda}^{-1/2}$.

Predictions for $ ext{alpha}'$ corrections in string theory.

Abstract

We study correlation functions of local operators and Wilson loop expectation values in the planar limit of a 4d $\mathcal{N}=2$ superconformal ${\rm SU}(N)$ YM theory with hypermultiplets in the symmetric and antisymmetric representations of the gauge group. This so-called $\mathbf{E}$ theory is closely related to $\mathcal{N}=4$ SYM and has a holographic description in terms of a $\mathbb{Z}_2$ orientifold of AdS$_5\times S^5$. Using recent matrix model results based on supersymmetric localization we develop efficient numerical methods to calculate two- and three-point functions of certain single trace operators as well as 1/2-BPS Wilson loop expectation values as a function of the 't Hooft coupling $\lambda$. We use our numerical results to arrive at simple analytic expressions for these correlators valid up to the sixth order in the $\lambda^{-1/2}$ strong coupling expansion. These results provide explicit field theory predictions for the $\alpha'$ corrections to the supergravity approximation of type IIB string theory on the AdS$_5\times S^5/\mathbb{Z}_2$ orientifold.