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

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.

Figures (1)

• Figure 1: Moduli Space. Supersymmetric solutions exist below the orange line. Above the green line $\langle \mathcal{O}_1 \rangle<0$ and below the green line $\langle \mathcal{O}_1 \rangle>0$, $\langle \mathcal{O}_1 \rangle=0$ on the green line. The solutions that lie on the blue line have $\langle \mathcal{O}_2\rangle=0$ and are the supersymmetric solitons of Anabalon:2024che. Above the blue line $\langle \mathcal{O}_2 \rangle>0$ and below the blue line $\langle \mathcal{O}_2\rangle<0$. The point of intersection between the green and blue lines happens at $\lvert \psi_1 \rvert=\lvert \psi_2\rvert=\lvert \psi_3\rvert=\frac{1}{3}$, which is the supersymmetric soliton of Anabalon:2021tua.