Thomas Fischbacher

Non-Semisimple and Complex Gaugings of N=16 Supergravity

Maximal and non-maximal supergravities in three dimensions allow for a large variety of semisimple (Chern-Simons) gauge groups. In this paper, we analyze non-semisimple and complex gauge groups that satisfy the pertinent consistency relations for a maximal (N=16) gauged supergravity to exist. We give a general procedure how to generate non-semisimple gauge groups from known admissible semisimple gauge groups by a singular boost within E8(8). Examples include the theories with gauge group SO(8)×T28 that describe the reduction of IIA/IIB supergravity on the seven-sphere. In addition, we exhibit two ‘strange embeddings’ of the complex gauge group into (real) E8(8) and prove that both can be consistently gauged. We discuss the structure of the associated scalar potentials as well as their relation to those of D≥4 gauged supergravities.

Vacua of maximal gauged D = 3 supergravities

We analyse the scalar potentials of maximal gauged three-dimensional supergravities which reveal a surprisingly rich structure. In contrast to maxima ls upergravities in dimensions D 4, all these theories possess a maximally supersymmetric (N = 16) ground state with negative cosmological constant �< 0, except for the SO(4, 4) 2 gauged theory, whose maximally supersymmetric groundstate has � = 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 whic ht hey 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 analogues of all stationary points found in higher dimensions, among them are de Sitter (dS) vacua in the theories with noncompact gauge groups SO(5, 3) 2 and SO(4, 4) 2 ,a s well a sa nti-de Sitter (AdS) vacua in the compact gauged theory preserving 1 and 1 of the supersymmetries. All the dS vacua hav et achyonic instabilities, whereas there do exist nonsupersymmetric AdS vacua which are stable, again in contrast to the D 4t heories. PACS number: 0465

Some stationary points of gauged N=16 D=3 supergravity

Five nontrivial stationary points are found for maximal gauged N=16 supergravity in three dimensions with gauge group SO(8) × SO(8) by restricting the potential to a submanifold of the space of SU(3) ⊂ (SO(8) × SO(8)) diag singlets. The construction presented here uses the embedding of E7(+7) ⊂ E8(+8) to lift the analysis of N = 8, D = 4 supergravity performed by N. Warner to N = 16, D = 3, and hence, these stationary points correspond to some of the known extrema of gauged N = 8, D = 4 supergravity.

Bulk Witten Indices from D = 10 Yang Mills Integrals

Values for the bulk Witten indices for D = 10 Yang-Mills integrals for regular simple groups of rank 4 and 5 are calculated by employing the BRST deformation technique by Moore, Nekrasov and Shatashvili. The results cannot be reconciled with the double assumption that the number of normalizable ground states is given by certain simple partition functions given by Kac and Smilga as well as that the corresponding boundary term is always negative.