# Seeley-DeWitt Coefficients in $\mathcal{N}=2$ Einstein-Maxwell Supergravity Theory and Logarithmic Corrections to $\mathcal{N}=2$ Extremal Black Hole Entropy

## TL;DR

This paper computes Seeley-DeWitt coefficients in $ ext{N}=2$ supergravity to analyze quantum corrections to black hole entropy, providing explicit results for various black hole backgrounds using heat kernel techniques.

## Contribution

It presents the first detailed calculation of Seeley-DeWitt coefficients in $ ext{N}=2$ Einstein-Maxwell supergravity and applies these to evaluate logarithmic entropy corrections for extremal black holes.

## Key findings

- Explicit Seeley-DeWitt coefficients for bosonic and fermionic fields in $ ext{N}=2$ supergravity.
- Derivation of logarithmic entropy corrections for extremal Kerr-Newman, Kerr, and Reissner-Nordstrom black holes.
- Demonstration of the heat kernel method's effectiveness in supergravity black hole entropy calculations.

## 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 embedded 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-Nordstrom black holes in minimal $\mathcal{N}=2$ Einstein-Maxwell supergravity theory following the quantum entropy function formalism.