Seeley-DeWitt coefficients in mathcal{N} = 2 Einstein-Maxwell supergravity theory and logarithmic corrections to mathcal{N} = 2 extremal black hole entropy

Abstract

We investigate the heat kernel method for one-loop effective action following the Seeley-DeWitt expansion technique of heat kernel with Seeley-DeWitt coefficients. We also review a general approach of computing the Seeley-DeWitt coefficients in terms of background or geometric invariants. We, then consider the Einstein-Maxwell theory em-bedded in minimal mathcal{N} = 2 supergravity in four dimensions and compute the first three Seeley-DeWitt coefficients of the kinetic operator of the bosonic and the fermionic fields in an arbitrary background field configuration. We find the applications of these results in the computation of logarithmic corrections to Bekenstein-Hawking entropy of the extremal Kerr-Newman, Kerr and Reissner-Nordström black holes in minimal mathcal{N} = 2 Einstein-Maxwell supergravity theory following the quantum entropy function formalism.