Global Charges in Chern-Simons theory and the 2+1 black hole

TL;DR

This paper employs the Regge-Teitelboim approach to identify global charges in Chern-Simons theory, revealing boundary symmetry generators and their algebra, with implications for 2+1 gravity and boundary conditions.

Contribution

It derives boundary symmetry generators as global charges in Chern-Simons theory and clarifies the impact of boundary conditions on the algebra, including classical contributions to the central charge.

Findings

Affine and Virasoro generators are identified as boundary charges.

Boundary conditions influence the structure of the symmetry algebra.

Classical contributions to the Virasoro central charge are established.

Abstract

We use the Regge-Teitelboim method to treat surface integrals in gauge theories to find global charges in Chern-Simons theory. We derive the affine and Virasoro generators as global charges associated with symmetries of the boundary. The role of boundary conditions is clarified. We prove that for diffeomorphisms that do not preserve the boundary there is a classical contribution to the central charge in the Virasoro algebra. The example of anti-de Sitter 2+1 gravity is considered in detail.