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

Abstract

We study $\mathcal{N}=4$ 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.

17 pages, one figure