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

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.

10 pages, sign errors in Eq.(18) are corrected, accepted for publication in Phys. Lett. B

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