Correlators in superconformal quivers made QUICK

TL;DR

This paper completes the perturbative analysis of $ ext{N}=2$ superconformal quiver theories in 4D, introducing a Mathematica package to automate the computation of correlators involving multitrace operators and Wilson loops.

Contribution

It provides a comprehensive solution for computing correlators in superconformal quiver theories using a multi-matrix model and introduces QUICK, a Mathematica package for automation.

Findings

Automated computation of correlators in superconformal quiver theories.

Extension of solutions to both $SU(N)$ and $U(N)$ gauge groups.

Applicability of the package to SCQCD, $ ext{N}=4$ SYM, and orbifold theories.

Abstract

In this paper we conclude the program of 2012.15792 and 2105.00257 about perturbative approaches for $\mathcal{N}=2$ superconformal quiver theories in 4D. We consider several classes of observables that involve multitrace local operators and Wilson loops scattered in all the possible ways among the quiver. We evaluate them exploiting the multi-matrix model arising from supersymmetric localisation and we generalise the solution to both $SU(N)$ and $U(N)$ cases. Moreover, we provide QUICK (QUIver Correlator Kit) a Wolfram Mathematica package designed to automatise the perturbative solution of the $A_{q-1}$ multi-matrix model for all the observables mentioned above. Given the interpolating nature of the superconformal quiver theories $A_{q-1}$, the package is an efficient tool to compute correlators also in SCQCD, $\mathcal{N}=4$ SYM and its $\mathbb{Z}_q$ orbifolds. This manuscript includes a user guide and some pedagogical examples.