Holographic Solutions from N = 5 Gauged Supergravity

Abstract

In this senior project, we find holographic solutions in the forms of supersymmetric domain walls, supersymmetric Janus solutions, and supersymmetric AdS4 black holes from N = 5 gauged supergravity with local SO(5) symmetry. There is only one N = 5 supersymmetric AdS4 vacuum preserving the full SO(5) symmetry dual to an N = 5 SCFT in three dimensions in the language of holographic duality. A number of supersymmetric domain wall solutions interpolating between this AdS₄ fixed point and singular geometries in the IR with SO(4) and SO(3) symmetries are presented. Holographically, these solutions describe RG flows from the N = 5 SCFT in the presence of mass deformations. Some of these solutions are precisely in agreement with the previously known mass deformations within the dual N = 5 SCFT. In addition, universal domain wall solutions subjected to specific unbroken supersymmetry are analyzed. Then, we provide a number of projectors and BPS equations required for the existence of Janus solutions in parallel to the case of domain wall solutions. As a result, we find supersymmetric Janus solutions describing two-dimensional conformal defects in the N = 5 SCFT with N = (4, 1) and N = (1, 1) supersymmetries on the defects in the form of AdS₃−sliced domain wall solutions. Finally, we perform an analysis as similar to the two previous cases for solutions of the form AdS₂ ⇥ E2, with E2 = S²,H² being a Riemann surface, corresponding to near horizon geometries of AdS4 black holes. We study both magnetic and dyonic solutions and show that there exists a class of AdS₂ ⇥ H² solutions with SO(2) symmetry. In the language of holography, these solutions correspond to twisted compactification of N = 5 SCFT to superconformal quantum mechanics.