Some Aspects of Gauged Supergravity

Abstract

We study N = 5 and N = 6 Chern-Simons gauged supergravity in three dimensions and applications thereof. The classification is determined by their gauged groups which are as follows: compact, non-compact and non-semisimple gauge groups. The gaugings are realized by the notion of embedding tensors. The manifolds of N = 5 and N = 6 theories are in the form of G/H = USp(4; k)/USp(4) USp(k) and G/H = SU(4; k)/S(U(4) U(k)), respectively. The number of independent supermultiplets is specified by k which is an even integer in N = 5 theories and an integer in N = 6. For N = 5, we restrict ourselves to k = 2; 4 cases whereas for N = 6, we confine to k = 1; 2; 3; 4 cases. For non-compact and non-semisimple cases, the consistent condition is checked unlike the compact cases which are already classified. The scalar potentials which play an important role for the further analysis of grou nd states of theories and holographic RG flows are calculated. The potentials can be achieved by parametrization of scalar manifolds. We paramatrize full manifold for some cases and for the rest we simply parametrize submanifold thereof. The parametrizations are either unitary gauge or Euler angle parametrization. Many supersymmetric AdS3 critical points are found and they are required for solving RG flows solutions interpolating between those critical points. The ratios of central charges cUV /cIR are calculated and they are in perfect agreement with the Zamolodchikov c-theorem. For non-semisimple gaugings, the gauge groups are in the form of SO(N)nTdimSO(N). We pay a special attention to the non-semisimple gaugings since they both are linked to four dimensional gauged supergravity via dimensional reduction on the orbifold S1/Z2. We found maximally supersymmetric AdS3 critical points with superconformal group Osp(5j2;R) Sp(2;R) in N = 5 non-semisimple gauging theory while a halfsupersymmetric domain wall solution is found in N = 6 non-semisimple gauging theory.