Strong-coupling results for $\mathcal{N}=2$ superconformal quivers and holography

TL;DR

This paper computes exact strong-coupling correlators in four-dimensional $ =2$ superconformal quiver gauge theories using localization and matrix models, revealing a $1/\lambda$ behavior that aligns with holographic predictions.

Contribution

It introduces a method to evaluate twisted sector correlators at all couplings in $ =2$ superconformal quivers, connecting localization results with holography.

Findings

Correlators are proportional to 1/λ at strong coupling.

Localization maps the problem to a matrix model valid for all λ.

Numerical checks confirm the extrapolated strong-coupling behavior.

Abstract

We consider $\mathcal{N}=2$ superconformal quiver gauge theories in four dimensions and evaluate the chiral/anti-chiral correlators of single-trace operators. We show that it is convenient to form particular twisted and untwisted combinations of these operators suggested by the dual holographic description of the theory. The various twisted sectors are orthogonal and the correlators in each sector have always the same structure, as we show at the lowest orders in perturbation theory with Feynman diagrams. Using localization we then map the computation to a matrix model. In this way we are able to obtain formal expressions for the twisted correlators in the planar limit that are valid for all values of the 't Hooft coupling $\lambda$, and find that they are proportional to $1/\lambda$ at strong coupling. We successfully test the correctness of our extrapolation against a direct numerical evaluation of the matrix model and argue that the $1/\lambda$ behavior qualitatively agrees with the holographic description.