The Brown-Henneaux's central charge from the path-integral boundary condition

TL;DR

This paper derives the Brown-Henneaux central charge using a path integral approach, showing it emerges from boundary condition invariance issues under asymptotic symmetries.

Contribution

It provides a novel derivation of the Brown-Henneaux central charge within the path integral framework, emphasizing boundary condition effects.

Findings

Central charge arises from boundary condition non-invariance.

Path integral boundary conditions influence asymptotic symmetry algebra.

Derivation of commutation relations consistent with Brown-Henneaux results.

Abstract

We derive Brown-Henneaux's commutation relation and central charge in the framework of the path integral. If we use the leading part of the asymptotic symmetry to derive the Ward-Takahashi identity, we can see the central charge arises from the fact that the boundary condition of the path integral is not invariant under the transformation.