Logarithmic correction to the entropy of extremal black holes in N=1 Einstein-Maxwell supergravity.

We study one-loop covariant effective action of "non-minimally coupled" N=1, d=4 Einstein-Maxwell supergravity theory by heat kernel tool. By fluctuating the fields around the classical background, we study the functional determinant of Laplacian differential operator following Seeley-DeWitt technique of heat kernel expansion in proper time. We then compute the Seeley-DeWitt coefficients obtained through the expansion. A particular Seeley-DeWitt coefficient is used for determining the logarithmic correction to Bekenstein-Hawking entropy of extremal black holes using quantum entropy function formalism. We thus determine the logarithmic correction to the entropy of Kerr-Newman, Kerr and Reissner-Nordstrom black holes in "non-minimally coupled" N=1, d=4 Einstein-Maxwell supergravity theory.