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We construct a 2-dimensional CFT, in the form of a Liouville theory, in thenear horizon limit of 4- and 3-dimensional black holes. The near horizon CFTassumes 2-dimensional black hole solutions first introduced by Christensen andFulling and expanded to a greater class of black holes via Robinson andWilczek. The 2-dimensional black holes admit a Diff($S^1$) subalgebra, whichupon quantization in the horizon limit becomes Virasoro with calculable centralcharge. This charge and lowest Virasoro eigen-mode reproduce the correctBekenstein-Hawking entropy of the 4- and 3-dimensional black holes via theknown Cardy formula. Furthermore, the 2-dimensional CFT's energy momentumtensor is anomalous. However, In the horizon limit the energy momentum tensorbecomes holomorphic equaling the Hawking flux of the 4- and 3-dimensional blackholes. This encoding of both entropy and temperature provides a uniformity inthe calculation of black hole thermodynamic and statistical quantities for thenon local effective action approach.

Entropy and Temperature From Black-Hole/Near-Horizon-CFT Duality