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 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.

V4: the Kerr-Newman results in eqs. (6.14) and (6.15) are simplified into a topological form

References in corpus (7)

• Quantum Entropy Function from AdS(2)/CFT(1) Correspondence
• Logarithmic Corrections to Extremal Black Hole Entropy from Quantum Entropy Function
• Entropy Function and AdS(2)/CFT(1) Correspondence
• Arithmetic of Quantum Entropy Function
• Generalized mirror symmetry and trace anomalies
• Logarithmic Corrections to Twisted Indices from the Quantum Entropy Function
• U(N) Gauged N=2 Supergravity and Partial Breaking of Local N=2 Supersymmetry

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• Logarithmic corrections to black hole entropy in matter coupled $\mathcal{N}\ge 1$ Einstein-Maxwell supergravity
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• Logarithmic corrections to the entropy of non-extremal black holes in $\mathcal{N}=1$ Einstein-Maxwell supergravity
• Logarithmic correction to the entropy of a Kerr-Newman family of black holes in $U(1{)}^2$-charged STU supergravity models
• Scattering approach for calculating one-loop effective action and vacuum energy