Moduli space of ${\cal N}=4$ Super Yang-Mills from AdS/CFT

TL;DR

This paper explores the moduli space of ${\cal N}=4$ Super Yang-Mills theory on a circle using holography, revealing how supergravity solutions encode the vacuum structure and scalar configurations of the dual field theory.

Contribution

It provides a complete holographic description of the vacuum structure of ${\cal N}=4$ SYM with scalar VEVs and current sources, including both supersymmetric and non-supersymmetric solutions.

Findings

Supergravity solutions encode the full vacuum structure.

Explicit reconstruction of the supersymmetric moduli space.

Identification of current sources as geometric twists on $S^5$.

Abstract

We study ${\cal N}=4$ super Yang-Mills theory compactified on a circle at zero temperature, with VEVs for two scalar bilinears and three independent current sources. We show that type IIB supergravity provides a complete holographic description of this setup, admitting both supersymmetric and non-supersymmetric AdS soliton solutions, which are asymptotically AdS$_5$ and smooth in the IR. The current sources correspond in (2+1) dimensions to Q-ball charge densities for $U(1)^3\subset SO(6)_R$, and are geometrically realized as twists along three angular directions of the $S^5$. We demonstrate that the bulk dynamics encodes the full vacuum structure of the dual field theory and explicitly reconstruct the supersymmetric moduli space.