The chiral ring of gauge theories in eight dimensions

TL;DR

This paper investigates non-perturbative effects in eight-dimensional U(N) gauge theories, revealing how chiral correlators depend on the full gauge group and providing compact formulas for their generating functions.

Contribution

It demonstrates the non-trivial gauge group dependence of chiral correlators and derives compact expressions for the resolvent in eight and four dimensions.

Findings

Chiral correlators depend on the full gauge group in 8D and 4D.

A plethystic formula captures the 8D prepotential dependence.

Compact forms for the resolvent are obtained in both dimensions.

Abstract

We study the non-perturbative corrections generated by exotic instantons in U(N) gauge theories in eight and four dimensions. As it was shown previously, the eight-dimensional prepotential can be resummed using a plethystic formula showing only a dependence from the center of mass and from a U(1) gauge factor. On the contrary, chiral correlators in eight and four dimensions display a non-trivial dependence from the full gauge group. Furthermore the resolvent, the generating function for the eight and four dimensional correlators, can be written in a compact form both in the eight and four dimensional cases.