Vacua of Maximal Gauged D=3 Supergravities

Abstract

We analyze the scalar potentials of maximal gauged three-dimensional supergravities which reveal a surprisingly rich structure. In contrast to maximal supergravities in dimensions D>3, all these theories admit a maximally supersymmetric (N=16) ground state with negative cosmological constant Lambda<0, except for the gauge group SO(4,4)^2, for which Lambda=0. We compute the mass spectra of bosonic and fermionic fluctuations around these vacua and identify the unitary irreducible representations of the relevant background (super)isometry groups to which they belong. In addition, we find several stationary points which are not maximally supersymmetric, and determine their complete mass spectra as well. In particular, we show that there are analogs of all stationary points found in higher dimensions, among them de Sitter vacua in the theories with noncompact gauge groups SO(5,3)^2 and SO(4,4)^2, as well as anti-de Sitter vacua in the compact gauged theory preserving 1/4 and 1/8 of the supersymmetries. All the dS vacua have tachyonic instabilities, whereas there do exist non-supersymmetric AdS vacua which are stable, again in contrast to the D>3 theories.

arXiv commentLaTeX2e, 46 pages

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• Maximally Supersymmetric AdS Solutions and their Moduli Spaces
• Hidden symmetries in minimal five-dimensional supergravity
• Introducing LambdaTensor1.0 - A package for explicit symbolic and numeric Lie algebra and Lie group calculations
• Old and new vacua of 5D maximal supergravity
• Gaugings of N=4 three dimensional gauged supergravity with exceptional coset manifolds