Moduli space of N = 4 super Yang-Mills from AdS/CFT

We study N = 4 super Yang-Mills theory compactified on an S¹ 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 that are asymptotically AdS₅ and smooth in the IR. The current sources correspond in 2+1 dimensions to Q-ball charge densities for U(1)³ ⊂ SO(6)_R, and are geometrically realized as twists along three angular directions of the S⁵. We demonstrate that the bulk dynamics encodes the full vacuum structure of the dual field theory and explicitly reconstruct the supersymmetric moduli space.