Holographic RG Flows and Universal Structures on the Coulomb Branch of N=2 Supersymmetric Large n Gauge Theory

TL;DR

This paper explores holographic renormalization group flows in N=2 supersymmetric gauge theories, revealing universal structures and a simple underlying model related to integrable systems, through analysis of supergravity solutions and moduli space metrics.

Contribution

It introduces a class of supergravity solutions governed by a single differential equation, linking gauge theory RG flows to integrable models like Calogero-Moser.

Findings

Universal square root branch cut structure on the complex plane.

Explicit metric on the Coulomb branch moduli space.

Evidence for a simple underlying matrix model.

Abstract

We report on our results of D3-brane probing a large class of generalised type IIB supergravity solutions presented very recently in the literature. The structure of the solutions is controlled by a single non-linear differential equation. These solutions correspond to renormalisation group flows from pure N=4 supersymmetric gauge theory to an N=2 gauge theory with a massive adjoint scalar. The gauge group is SU(n) with n large. After presenting the general result, we focus on one of the new solutions, solving for the specific coordinates needed to display the explicit metric on the moduli space. We obtain an appropriately holomorphic result for the coupling. We look for the singular locus, and interestingly, the final result again manifests itself in terms of a square root branch cut on the complex plane, as previously found for a set of solutions for which the details are very different. This, together with the existence of the single simple non-linear differential equation, is further evidence in support of an earlier suggestion that there is a very simple model --perhaps a matrix model with relation to the Calogero-Moser integrable system-- underlying this gauge theory physics.