New supersymmetric AdS${}_5$ black strings from 5D N = 4 gauged supergravity

We find a large class of new supersymmetric AdS${}_5$ black strings from five-dimensional N = 4 gauged supergravity coupled to five vector multiplets with SO(2)${}_D$ × SO(3) × SO(3) gauge group. These solutions have near horizon geometries of the form AdS${}_3$ × Σ${}^2$ for Σ${}^2$ being a two-sphere (S${}^2)$ or a hyperbolic space (H${}^2$). There are four supersymmetric AdS${}_5$ vacua with N = 4 and N = 2 supersymmetries. By performing topological twists along Σ${}^2$ with SO(2) × SO(2)${}_{diag}$ and SO(2)${}_{diag}$ gauge fields, we find a number of AdS${}_3$ × Σ${}^2$ fixed points describing near horizon geometries of black strings in asymptotically AdS${}_5$ spaces. Most of the solutions take the form of AdS${}_3$ × H${}^2$ with only one being AdS${}_3$ × S${}^2$ preserving SO(2)${}_{diag}$ symmetry. We also give the corresponding black string solutions interpolating between asymptotically locally AdS${}_5$ vacua and the near horizon AdS${}_3$ × Σ${}^2$ geometries. There are a number of solutions flowing from one, two or three AdS${}_5$ vacua to an AdS${}_3$ × Σ${}^2$ fixed point. These solutions can also be considered as holographic RG flows across dimensions from N = 2 and N = 1 SCFTs in four dimensions to two-dimensional SCFTs with N=(2,0) or N=(0,2) supersymmetry.