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

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