Strong coupling expansions in $\mathcal{N}=2$ quiver gauge theories

TL;DR

This paper derives exact relations for 3-point functions in four-dimensional $ =2$ superconformal quiver theories, enabling the calculation of strong-coupling expansions and predictions for string corrections in holography.

Contribution

It introduces Ward-like identities linking 3-point and 2-point functions, allowing for strong-coupling expansions and sub-leading order predictions in $ =2$ quiver gauge theories.

Findings

Exact Ward-like identities relate 3-point and 2-point functions.

Asymptotic strong-coupling expansion of 3-point functions obtained.

Predictions for sub-leading string corrections in holographic duals.

Abstract

We study the 3-point functions of gauge-invariant scalar operators in four dimensional $\mathcal{N}=2$ superconformal quiver theories using supersymmetric localization in the planar limit of a large number of colors. By exploiting a web of nontrivial relations, we show that the 3-point functions can be expressed in terms of the 2-point functions through exact Ward-like identities that are valid for all values of the coupling constant. In this way, using recent results about the 2-point functions, we are able to obtain the asymptotic strong-coupling expansion of the 3-point functions and of the corresponding structure constants in the planar limit. Our results extend to sub-leading orders what has been recently found at leading order, where a precise match with calculations within the AdS/CFT correspondence at the supergravity level is possible. Therefore, our findings can be interpreted also as a prediction for the sub-leading string corrections to these holographic calculations.