RG flows from (1,0) 6D SCFTs to N = 1 SCFTs in four and three dimensions

Abstract

Abstract: We study AdS 5 × Σ 2 and AdS 4 × Σ 3 solutions of N = 2, SO(4) gauged supergravity in seven dimensions with Σ 2,3 being S 2,3 or H 2,3. The SO(4) gauged supergravity is obtained from coupling three vector multiplets to the pure N = 2, SU(2) gauged supergravity. With a topological mass term for the 3-form field, the SO(4) ∼ SU(2) × SU(2) gauged supergravity admits two supersymmetric AdS 7 critical points, with SO(4) and SO(3) symmetries, provided that the two SU(2) gauge couplings are different. These vacua correspond to N = (1, 0) superconformal field theories (SCFTs) in six dimensions. In the case of Σ 2, we find a class of AdS 5 × S 2 and AdS 5 × H 2 solutions preserving eight supercharges and SO(2) × SO(2) symmetry, but only AdS 5 × H 2 solutions exist for SO(2) symmetry. These should correspond to some N = 1 four-dimensional SCFTs. We also give RG flow solutions from the N = (1, 0) SCFTs in six dimensions to these four-dimensional fixed points including a two-step flow from the SO(4) N = (1, 0) SCFT to the SO(3) N = (1, 0) SCFT that eventually flows to the N = 1 SCFT in four dimensions. For AdS 4 × Σ 3, we find a class of AdS 4 × S 3 and AdS 4 × H 3 solutions with four supercharges, corresponding to N =1 SCFTs in three dimensions. When the two SU(2) gauge couplings are equal, only AdS 4 × H 3 are possible. The uplifted solutions for equal SU(2) gauge couplings to eleven dimensions are also given.