Holographic RG Flow in a New $SO(3)\times SO(3)$ Sector of $\omega$-Deformed $SO(8)$ Gauged ${\cal N}=8$ Supergravity

TL;DR

This paper explores a new stable, non-supersymmetric AdS vacuum in a specific sector of $ ext{SO}(8)$ supergravity with $ ext{SO}(3) imes ext{SO}(3)$ symmetry, constructs domain walls with non-zero pseudoscalars, and analyzes their holographic duals.

Contribution

It identifies a new stable, non-supersymmetric AdS vacuum in the $ ext{SO}(3) imes ext{SO}(3)$ sector of $ ext{SO}(8)$ supergravity for $ ext{omega} eq 0$, and constructs novel domain wall solutions with non-vanishing pseudoscalars.

Findings

Discovery of a new stable, non-supersymmetric AdS vacuum for $ ext{omega} eq 0$.

Construction of domain wall solutions with non-zero pseudoscalars.

Analysis of holographic duals involving mass deformations and Coulomb-branch flows.

Abstract

We consider a certain ${\cal N}=1$ supersymmetric, $SO(3)\times SO(3)$ invariant, subsector of the $\omega$-deformed family of $SO(8)$-gauged ${\cal N}=8$ four-dimensional supergravities. The theory contains two scalar fields and two pseudoscalar fields. We look for stationary points of the scalar potential, corresponding to AdS vacua in the theory. One of these, which breaks all supersymmetries but is nonetheless stable, is new. It exists only when $\omega\ne 0$. We construct supersymmetric domain wall solutions in the truncated theory, and we give a detailed analysis of their holographic dual interpretations using the AdS/CFT correspondence. Domain walls where the pseudoscalars vanish were studied previously, but those with non-vanishing pseudoscalars, which we analyse numerically, are new. The pseudoscalars are associated with supersymmetric mass deformations in the CFT duals. When $\omega$ is zero, the solutions can be lifted to M-theory, where they approach the Coulomb-branch flows of dielectric M5-branes wrapped on $S^3$ in the deep IR.