New Black Hole Solutions in N = 2 and N = 8 Gauged Supergravity

We review a special class of N=2 supergravity model that interpolates all the single-dilaton truncations of the maximal SO(8) gauged supergravity. We also provide explicit non-extremal, charged black hole solutions and their supersymmetric limits, asymptotic charges, thermodynamics and boundary conditions. We also discuss a suitable Hamilton–Jacobi formulation and related BPS flow equations for the supersymmetric configurations, with an explicit form for the superpotential function. Finally, we briefly analyze certain models within the class under consideration as consistent truncations of the maximal, N=8 gauged supergravity in four dimensions.

Hamilton-Jacobi formulation of holographic entanglement entropy

We review classical results on holographic entanglement entropy utilizing the Hamilton-Jacobi approach. Possibility of using the entanglement entropy as a probe of confinement is shortly discussed in the context of lattice data.

The Hamilton-Jacobi equation and holographic renormalization group flows on sphere

We study the Hamilton-Jacobi formulation of effective mechanical actions associated with holographic renormalization group flows when the field theory is put on the sphere and mass terms are turned on. Although the system is supersymmetric and it is described by a superpotential, Hamilton’s characteristic function is not readily given by the superpotential when the boundary of AdS is curved. We propose a method to construct the solution as a series expansion in scalar field degrees of freedom. The coefficients are functions of the warp factor to be determined by a differential equation one obtains when the ansatz is substituted into the Hamilton-Jacobi equation. We also show how the solution can be derived from the BPS equations without having to solve differential equations. The characteristic function readily provides information on holographic counterterms which cancel divergences of the on-shell action near the boundary of AdS.