Gauged $\mathcal{N}=3,D=4$ Supergravity: a new web of marginally connected vacua

TL;DR

This paper explores the complex vacuum landscape of $ =3$, $D=4$ supergravity with gauge group ${ m SO}(3) imes { m SU}(3)$, revealing new vacua with varying supersymmetry and their relation to dual CFT deformations.

Contribution

It identifies a rich set of AdS$_4$ vacua with different supersymmetries and describes their organization in a scalar manifold, also providing a comprehensive review of the embedding tensor formalism.

Findings

Discovery of multiple AdS$_4$ vacua with $ =0,1,2,3$ supersymmetry.

Vacua arranged in a $T^3/K$ manifold representing marginal deformations.

Analysis of RG flows and higher-dimensional origins of vacua.

Abstract

We analyze the vacuum structure of $\mathcal{N}=3,D=4$ supergravity coupled to 9 vector multiplets with gauge group ${\rm SO}(3)\times {\rm SU}(3)$. Aside from the central $\mathcal{N}=3$ AdS$_4$ vacuum at the origin, on which the supermultiplet structure reproduces the massless sector of M-theory compactified on $\mathrm{N^{0,1,0}}$, we find a rich structure of AdS$_4$ vacua preserving $\mathcal{N}=0,1,2,3$ supersymmetry. These new vacua are arranged in a manifold spanned by scalar fields corresponding to exactly marginal deformations of the dual CFT. This manifold has the form $T^3/K$, where $K$ is a discrete subgroup of the gauge group: $\mathcal{N}=3,2$ and $1$ vacua correspond, respectively, to a point, a line and a surface in the three-dimensional vacuum manifold. We study RG flows from the central $\mathcal{N}=3$ vacuum and elaborate on the possible higher dimensional origin of the new vacua. For the reader's convenience we also provide a review of the embedding tensor formulation of $D=4$, $\mathcal{N}=3$ gauged supergravities. In particular we provide formulas involving the fermion shift tensors and mass matrices in $\mathcal{N}=3$ theories, which can be applied to a generic gauging.