Beijing Institute of Mathematical Sciences and Applications

AdS/CFT duality, also known as holographic duality, has been the cornerstone of developments in HEP-TH area in the last quarter century. A limit of the duality, the gauge/gravity correspondence, where the AdS side reduces to classical gravity on AdS space and the CFT side to the planar limit, is the most commonly used and studied limit of the duality. To state the duality or the correspondence, one needs to specify boundary conditions of the fields on a time-like codimension one boundary in AdS. The canonical formulation and the mostly studied cases adopts Dirichlet boundary conditions on the AdS causal/conformal asymptotic boundary. In these lecture series we develop Freelance Holography Program, a formal framework to extend the correspondence to cases with arbitrary boundary conditions on arbitrary codimension one time-like boundary in the AdS. Our formulation is based on Covariant Phase Space Formalism (CPSF) and encomapsses and extends recently very much discussed TT-bar deformations. We discuss motivations and physical significance of the freelance holography program and some of its physical implications.