Anomalous effective action, Noether current, Virasoro algebra and Horizon entropy

Several investigations show that in a very small length scale there exists corrections to the entropy of black hole horizon. Due to fluctuations of the background metric and the external fields the action incorporates corrections. In the low energy regime, the one loop effective action in four dimensions leads to trace anomaly. We start from the Noether current corresponding to the Einstein-Hilbert plus the one loop effective action to calculate the charge for the diffeomorphisms which preserve the Killing horizon structure. Then a bracket among the charges is calculated. We show that the Fourier modes of the bracket is exactly similar to Virasoro algebra. Then using Cardy formula the entropy is evaluated. Finally, the explicit terms of the entropy expression is calculated for a classical background. It turns out that the usual expression for entropy; i.e. the Bekenstein-Hawking form, is not modified.

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