Gaugings of four-dimensional N=3 supergravity and AdS4/CFT3 holography

Abstract

We study matter-coupled $N=3$ gauged supergravity in four dimensions with various semisimple gauge groups. When coupled to $n$ vector multiplets, the gauged supergravity contains $3+n$ vector fields and $3n$ complex scalars parametrized by $SU(3,n)/SU(3)\times SU(n)\times U(1)$ coset manifold. Semisimple gauge groups take the form of $G_0\times H\subset SO(3,n)\subset SU(3,n)$ with $H$ being a compact subgroup of $SO(n+3-\text{dim}(G_0))$. The $G_0$ groups considered in this paper are of the form $SO(3)$, $SO(3,1)$, $SO(2,2)$, $SL(3,\mathbb{R})$ and $SO(2,1)\times SO(2,2)$. We find that $SO(3)\times SO(3)$, $SO(3,1)$ and $SL(3,\mathbb{R})$ gauge groups admit a maximally supersymmetric $Ad{S}_4$ critical point. The $SO(2,1)\times SO(2,2)$ gauge group admits a supersymmetric Minkowski vacuum while the remaining gauge groups admit both half-supersymmetric domain wall vacua and $Ad{S}_4$ vacua with completely broken supersymmetry. For the $SO(3)\times SO(3)$ gauge group, there exists another supersymmetric $N=3$ $Ad{S}_4$ critical point with $SO(3{)}_{\text{diag}}$ symmetry. We explicitly give a detailed study of various holographic RG flows between $Ad{S}_4$ critical points, flows to non-conformal theories and supersymmetric domain walls in each gauge group. The results provide gravity duals of $N=3$ Chern-Simons-Matter theories in three dimensions.

29 pages, no figures, typos corrected and a few references added

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• Maximally Supersymmetric AdS Solutions and their Moduli Spaces
• N = 3 Conformal Supergravity in Four Dimensions
• Supersymmetric solutions from N=5 gauged supergravity
• Supersymmetric solutions from N=6 gauged supergravity
• Holographic RG flows and Janus solutions from matter-coupled N=4 gauged supergravity
• Higher derivative invariants in four dimensional N=3 Poincare supergravity
• Holographic RG flows and symplectic deformations of N=4 gauged supergravity
• Supersymmetric AdS4 black holes from matter-coupled N=3,4 gauged supergravities
• Gauged $\mathcal{N}=3,D=4$ Supergravity: a new web of marginally connected vacua