Noncompact gauging of N=2 7D supergravity and AdS/CFT holography

Half-maximal gauged supergravity in seven dimensions coupled to n vector multiplets contains n + 3 vectors and 3n + 1 scalars parametrized by R+ x SO(3, n)/SO(3) x SO(3) coset manifold. The two-form field in the gravity multiplet can be dualized to a three-form field which admits a topological mass term. Possible non-compact gauge groups take the form of G(0) x H subset of SO(3, n) with a compact group H. G(0) is one of the five possibilities; SO(3, 1), SL(3, R), SO(2, 2), SO(2, 1) and SO(2, 2) x SO(2, 1). We investigate all of these possible non-compact gauge groups and classify their vacua. Unlike the gauged supergravity without a topological mass term, there are new supersymmetric AdS(7) vacua in the SO(3, 1) and gaugings. These correspond to new N = (1, 0) superconformal field theories (SCFT) in six dimensions. Additionally, we find a class of AdS(5) x S-2 and AdS(5) x H-2 backgrounds with SO(2) and SO(2)xSO(2) symmetries. These should correspond to N = 1 SCFTs in four dimensions obtained from twisted compactifications of six-dimensional field theories on S-2 or H-2. We also study RG flows from six-dimensional N = (1, 0) SCFT to N =1 SCFT in four dimensions and RG flows from a four-dimensional N =1 SCFT to a six-dimensional SYM in the IR. The former are driven by a vacuum expectation value of a dimension-four operator dual to the supergravity dilaton while the latter are driven by vacuum expectation values of marginal operators.