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

Abstract

We analyze the vacuum structure of N = 3, D = 4 supergravity coupled to 9 vector multiplets with gauge group SO(3) × SU(3). Aside from the central N = 3 AdS 4 vacuum at the origin, on which the supermultiplet structure reproduces the massless sector of M-theory compactified on N 0,1,0 , we find a rich structure of AdS 4 vacua preserving 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: 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 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, N = 3 gauged supergravities. In particular we provide formulas involving the fermion shift tensors and mass matrices in N = 3 theories, which can be applied to a generic gauging.

Higher derivative invariants in four dimensional 𝒩 = 3 Poincaré supergravity

“…Constructing these supergravity theories is important in the context of classifying supergravity theories in four dimensions. Further, in the light of JHEP02(2023)145 gauge/gravity duality, N = 3 AdS 4 solutions and the associated field representations were studied in [11][12][13] and have seen renewed interest [14][15][16][17][18][19]. This provides the motivation to construct higher derivative invariants in N = 3 supergravity as they are known to provide important insights for holography [20][21][22].…”