Recently a general principle, called c-extremization, which determines the exact R-symmetry of two-dimensional CFTs with N = (0, 2) supersymmetry was identified. In this note we show that the supergravity dual corresponds to the extremization of the T -tensor of N = 2 gauged supergravity in three-dimensions. To support this claim, we demonstrate that the expected central charge of CFTs arising from twisted compactifications of four-dimensional N = 4 SYM on Riemann surfaces, whose gravity dual is a reduction of five-dimensional U (1) 3 gauged supergravity, is recovered in the three-dimensional framework.

We study N = 2 seven-dimensional gauged supergravity coupled to three vector multiplets with SO(4) gauge group. The resulting gauged supergravity contains 10 scalars consisting of the dilaton and 9 vector multiplet scalars parametrized by SO(3, 3)/SO(3)×SO(3) coset manifold. The maximally supersymmetric AdS 7 vacuum with unbroken SO(4) symmetry is identified with a (1, 0) SCFT in six dimensions. We find one new supersymmetric AdS 7 critical point preserving SO(3) diag ⊂ SO(3) × SO(3) ∼ SO(4) and study a holographic RG flow interpolating between the SO(4) and the new SO(3) supersymmetric critical points. The RG flow is driven by a vacuum expectation value of a dimension-four operator and describes a deformation of the UV (1, 0) SCFT to another supersymmetric fixed point in the IR. In addition, a number of non-supersymmetric critical points are identified, and some of them are stable with all scalar masses above the BF bound. RG flows to non-conformal N = (1, 0) Super Yang-Mills with SO(2) × SO(2) and SO(2) symmetries are also investigated. Some of these flows have physically acceptable IR singularities since the scalar potential is bounded above. These provide physical RG flows from (1, 0) SCFT to non-conformal field theories in six dimensions.

Abstract:We study critical points of F (4) gauged supergravity in six dimensions coupled to three vector multiplets. Scalar fields are described by R + × SO(4,3) SO(4)×SO (3) coset space, and the gauge group is given by SO(3) R × SO(3) with SO(3) R being the R-symmetry. The maximally supersymmetric critical point with all scalars vanishing preserves the full SO(3) R × SO(3) symmetry. This is dual to a superconformal field theories (SCFT 5 ) arising from a near horizon geometry of the D4-D8 brane system in type I ′ theory with an enhanced global symmetry E 1 ∼ SU(2). Apart from this trivial critical point, we identify a new supersymmetric critical point preserving the full supersymmetry with the SO(3) R × SO(3) symmetry broken to its diagonal subgroup. This critical point should correspond to a new SCFT in five dimensions. We study an RG flow solution interpolating between the SCFT with E 1 symmetry and the new supersymmetric critical point. The flow describes a supersymmetric deformation driven by a vacuum expectation value of relevant operators of dimension 3. We identify the dual operators with the mass terms for hypermultiplet scalars in the dual field theory. The solution provides an example of analytic supersymmetric RG flows in AdS 6 /CFT 5 correspondence.