Path integral derivation of the Brown-Henneaux central charge

Details Path integral derivation of the Brown-Henneaux central charge Path integral derivation of the Brown-Henneaux central charge

2001-02-16

arxiv.org/abs/hep-th/0102097v2

Phys.Rev. D64 (2001) 064016

Physics

High Energy Physics

High Energy Physics - Theory

18 pages, some clarifying comments are added

Scientific paper

10.1103/PhysRevD.64.064016

We rederive the Brown-Henneaux commutation relation and central charge in the framework of the path integral. To obtain the Ward-Takahashi identity, we can use either the asymptotic symmetry or its leading part. If we use the asymptotic symmetry, the central charge arises from the transformation law of the charge itself. Thus, this central charge is clearly different from the quantum anomaly which can be understood as the Jacobian factor of the path integral measure. Alternatively, if we use the leading transformation, the central charge arises from the fact that the boundary condition of the path integral is not invariant under the transformation. This is in contrast to the usual quantum central charge which arises from the fact that the measure of the path integral is not invariant under the relevant transformation. Moreover, we discuss the implications of our analysis in relation to the black hole entropy.

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