Correlation functions in four-dimensional superconformal long circular quivers

TL;DR

This paper analyzes two- and three-point correlation functions of chiral primary operators in four-dimensional superconformal quiver theories, revealing their structure across coupling regimes and uncovering an emergent fifth dimension with a specific mass spectrum.

Contribution

It introduces a matrix integral and Fredholm determinant approach to study correlation functions in superconformal quiver theories, including strong coupling behavior and an emergent fifth dimension.

Findings

Correlation functions expressed as Fredholm determinants.

Exponential decay of correlators with node separation.

Mass spectrum given by zeros of Bessel functions.

Abstract

We study two- and three-point correlation functions of chiral primary half-BPS operators in four-dimensional $\mathcal{N}=2$ superconformal circular, cyclic symmetric quiver theories. Using supersymmetric localization, these functions can be expressed as matrix integrals which, in the planar limit, reduce to Fredholm determinants of certain semi-infinite matrices. This powerful representation allows us to investigate the correlation functions across the parameter space of the quiver theory, including both weak and strong coupling regimes and various limits of the number of nodes and the operator scaling dimensions. At strong coupling, the standard semiclassical AdS/CFT expansion diverges in the long quiver limit. However, by incorporating both perturbative corrections (in negative powers of the 't Hooft coupling) and an infinite tower of nonperturbative, exponentially suppressed contributions, we derive a remarkably simple expression for the correlation functions in this limit. These functions exhibit exponential decay with increasing node separation and admit an interpretation within a five-dimensional effective theory. We determine the mass spectrum of excitations propagating along the emergent fifth dimension within this theory, finding it to be given by the zeros of Bessel functions.