AdS${}_3$ vacua and RG flows in three dimensional gauged supergravities

Abstract

We study $Ad{S}_3$ supersymmetric vacua in N=4 and N=8, three dimensional gauged supergravities, with scalar manifolds $(\frac{SO(4,4)}{SO(4)\times SO(4)}{)}^2$ and $\frac{SO(8,8)}{SO(8)\times SO(8)}$, non-semisimple Chern-Simons gaugings $SO(4)⋉{\mathbf{R}}^6$ and $(SO(4)⋉{\mathbf{R}}^6{)}^2$, respectively. These are in turn equivalent to SO(4) and $SO(4)\times SO(4)$ Yang-Mills theories coupled to supergravity. For the N=4 case, we study renormalization group flows between UV and IR $Ad{S}_3$ vacua with the same amount of supersymmetry: in one case, with (3,1) supersymmetry, we can find an analytic solution whereas in another, with (2,0) supersymmetry, we give a numerical solution. In both cases, the flows turn out to be v.e.v. flows, i.e. they are driven by the expectation value of a relevant operator in the dual $SCF{T}_2$. These provide examples of v.e.v. flows between two $Ad{S}_3$ vacua within a gauged supergravity framework.

35 pages in JHEP form, 3 figures, typos corrected, references added

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