AdS$_3$ Freelance Holography, A Detailed Analysis

Abstract: Freelance holography program is an extension of the gauge/gravity correspondence in which the boundary theory can reside on any timelike codimension-one surface in AdS space, and the boundary conditions on the bulk fields can be chosen arbitrarily. Freelance holography provides the framework for a systematic study of various boundary conditions and associated bulk geometries. In this work, we analyze in detail the AdS$_3$ freelance holography. One can explicitly solve for the bulk AdS$_3$ Einstein gravity equations of motion. For generic boundary conditions, the solutions are described by two arbitrary functions of one variable. We study holographic renormalization group (RG) flows, the interpolation between different boundary conditions at different boundaries and associated surface charges and their algebras.