Localization vs holography in $4d$ $\mathcal{N}=2$ quiver theories

TL;DR

This paper compares localization and holography methods in 4d $ abla=2$ superconformal quiver theories, providing exact correlator computations at any coupling and confirming results via supergravity at strong coupling.

Contribution

It introduces a unified approach to compute correlators in $ abla=2$ quiver theories using localization and holography, revealing their agreement at strong coupling.

Findings

Exact correlators valid for any 't Hooft coupling in planar limit

Simplified strong-coupling expressions for correlators

Perfect match between localization and supergravity results at strong coupling

Abstract

We study 4-dimensional $\mathcal{N}=2$ superconformal quiver gauge theories obtained with an orbifold projection from $\mathcal{N}=4$ SYM, and compute the 2- and 3-point correlation functions among chiral/anti-chiral single-trace scalar operators and the corresponding structure constants. Exploiting localization, we map the computation to an interacting matrix model and obtain expressions for the correlators and the structure constants that are valid for any value of the 't Hooft coupling in the planar limit of the theory. At strong coupling, these expressions simplify and allow us to extract the leading behavior in an analytic way. Finally, using the AdS/CFT correspondence, we compute the structure constants from the dual supergravity theory and obtain results that perfectly match the strong-coupling predictions from localization.