New supersymmetric AdS_5 black strings from 5D N=4 gauged supergravity

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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)_Dtimes SO(3)times SO(3) gauge group. These solutions have near horizon geometries of the form AdS_3times Sigma ^2 for Sigma ^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 Sigma ^2 with SO(2)times SO(2)_{text {diag}} and SO(2)_{text {diag}} gauge fields, we find a number of AdS_3times Sigma ^2 fixed points describing near horizon geometries of black strings in asymptotically AdS_5 spaces. Most of the solutions take the form of AdS_3times H^2 with only one being AdS_3times S^2 preserving SO(2)_{text {diag}} symmetry. We also give the corresponding black string solutions interpolating between asymptotically locally AdS_5 vacua and the near horizon AdS_3times Sigma ^2 geometries. There are a number of solutions flowing from one, two or three AdS_5 vacua to an AdS_3times Sigma ^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.