Asymptotic Symmetries In Einstein-Scalar Theory in three dimensions.

Abstract

The identification of infinite-dimensional symmetries at the boundary of spacetime have served as an important tool to unfold the holographic properties of gravity at a quantum level, through the asymptotic symmetry groups that happens to be the global symmetries groups of a lower dimensional, dual field theory. For example, one can determine that the isometry group of Schwarzschild in AdS4 is R×SO(3) [1], however, in the asymptotic region, the asymptotic symmetry group is identified as SO(3, 2) corresponding to the algebra of global symmetries found in a conformal field theory in 3 dimensions. In this scenario, one can assert that the conformal field theory (CFT) serves as the dual theory to the gravitational theory in an Anti-de Sitter (AdS) configuration. Considering all the information above, we encounter a fundamental concept known as the holographic principle [2, 3]. This principle essentially establishes a connection between a gravitational theory in D + 1 dimensions with a quantum theory living in D dimensions.