Statistical Entropy of the Kaluza-Klein Black Hole from the Horizon Conformal Field Theory

The statistical entropy of the Kaluza-Klein black hole is studied by counting the black hole states which form an algebra of diffeomorphism at Killing horizon with a central charge. It is shown that the entropy yielded by the standard Cardy formula agrees with the Bekenstein-Hawking entropy only if we take period T of function u as the periodicity of the Euclidean black hole. On the other hand, the first-order quantum correction to the entropy is proportional to logarithm of the Bekenstein-Hawking entropy with a factor -1/2.