Holographic RG flows and $$AdS_5$$ AdS5 black strings from 5D half-maximal gauged supergravity

Abstract

Abstract We study five-dimensional $$N=4$$ N=4 gauged supergravity coupled to five vector multiplets with compact and non-compact gauge groups $$U(1)\times SU(2)\times SU(2)$$ U(1)×SU(2)×SU(2) and $$U(1)\times SO(3,1)$$ U(1)×SO(3,1) . For $$U(1)\times SU(2)\times SU(2)$$ U(1)×SU(2)×SU(2) gauge group, we identify $$N=4$$ N=4 $$AdS_5$$ AdS5 vacua with $$U(1)\times SU(2)\times SU(2)$$ U(1)×SU(2)×SU(2) and $$U(1)\times SU(2)_{\text {diag}}$$ U(1)×SU(2)diag symmetries and analytically construct the corresponding holographic RG flow interpolating between these critical points. The flow describes a deformation of the dual $$N=2$$ N=2 SCFT driven by vacuum expectation values of dimension-two operators. In addition, we study $$AdS_3\times \Sigma _2$$ AdS3×Σ2 geometries, for $$\Sigma _2$$ Σ2 being a two-sphere $$S^2$$ S2 or a two-dimensional hyperbolic space $$H^2$$ H2 , dual to twisted compactifications of $$N=2$$ N=2 SCFTs with flavor symmetry SU(2). We find a number of $$AdS_3\times H^2$$ AdS3×H2 solutions preserving eight supercharges for different twists from $$U(1)\times U(1)\times U(1)$$ U(1)×U(1)×U(1) and $$U(1)\times U(1)_{\text {diag}}$$ U(1)×U(1)diag gauge fields. We numerically construct various RG flow solutions interpolating between $$N=4$$ N=4 $$AdS_5$$ AdS5 critical points and these $$AdS_3\times H^2$$ AdS3×H2 geometries in the IR. The solutions can also be interpreted as supersymmetric black strings in asymptotically $$AdS_5$$ AdS5 space. These types of holographic solutions are also studied in non-compact $$U(1)\times SO(3,1)$$ U(1)×SO(3,1) gauge group. In this case, only one $$N=4$$ N=4 $$AdS_5$$ AdS5 vacuum exists, and we give an RG flow solution from this $$AdS_5$$ AdS5 to a singular geometry in the IR corresponding to an $$N=2$$ N=2 non-conformal field theory. An $$AdS_3\times H^2$$ AdS3×H2 solution together with an RG flow between this vacuum and the $$N=4$$ N=4 $$AdS_5$$ AdS5 are also given.