Two-dimensional SCFTs from matter-coupled $$7D~N=2$$ 7DN=2 gauged supergravity

Abstract

Abstract We study supersymmetric $$AdS_3\times M^4$$ AdS3×M4 solutions of $$N=2$$ N=2 gauged supergravity in seven dimensions coupled to three vector multiplets with $$SO(4)\sim SO(3)\times SO(3)$$ SO(4)∼SO(3)×SO(3) gauge group and $$M^4$$ M4 being a four-manifold with constant curvature. The gauged supergravity admits two supersymmetric $$AdS_7$$ AdS7 critical points with SO(4) and SO(3) symmetries corresponding to $$N=(1,0)$$ N=(1,0) superconformal field theories (SCFTs) in six dimensions. For $$M^4=\Sigma ^2\times \Sigma ^2$$ M4=Σ2×Σ2 with $$\Sigma ^2$$ Σ2 being a Riemann surface, we obtain a large class of supersymmetric $$AdS_3\times \Sigma ^2\times \Sigma ^2$$ AdS3×Σ2×Σ2 solutions preserving four supercharges and $$SO(2)\times SO(2)$$ SO(2)×SO(2) symmetry for one of the $$\Sigma ^2$$ Σ2 being a hyperbolic space $$H^2$$ H2 , and the solutions are dual to $$N=(2,0)$$ N=(2,0) SCFTs in two dimensions. For a smaller symmetry SO(2), only $$AdS_3\times H^2\times H^2$$ AdS3×H2×H2 solutions exist. Some of these are also solutions of pure $$N=2$$ N=2 gauged supergravity with $$SU(2)\sim SO(3)$$ SU(2)∼SO(3) gauge group. We numerically study domain walls interpolating between the two supersymmetric $$AdS_7$$ AdS7 vacua and these geometries. The solutions describe holographic RG flows across dimensions from $$N=(1,0)$$ N=(1,0) SCFTs in six dimensions to $$N=(2,0)$$ N=(2,0) two-dimensional SCFTs in the IR. Similar solutions for $$M^4$$ M4 being a Kahler four-cycle with negative curvature are also given. In addition, unlike $$M^4=\Sigma ^2\times \Sigma ^2$$ M4=Σ2×Σ2 case, it is possible to twist by $$SO(3)_{\text {diag}}$$ SO(3)diag gauge fields resulting in two-dimensional $$N=(1,0)$$ N=(1,0) SCFTs. Some of the solutions can be uplifted to eleven dimensions and provide a new class of $$AdS_3\times M^4\times S^4$$ AdS3×M4×S4 solutions in M-theory.