The Holographic Ward identity: Examples from 2+1 gravity
Abstract
In the AdS/CFT correspondence the boundary Ward identities are encoded in the bulk constraints. We study the three-dimensional version of this result using the Chern-Simons formulation of gravity. Due the metric boundary conditions the conformal identities cannot be derived in a straightforward way from the chiral ones. We pay special attention to this case and find the necessary modifications to the chiral currents in order to find the two Virasoro operators. The supersymmetric Ward identities are studied as well.
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.