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

A bstract We study $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 4 super Yang-Mills theory compactified on an S 1 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 AdS 5 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 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.