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.

arXiv commentV4: the Kerr-Newman results in eqs. (6.14) and (6.15) are simplified into a topological form

References in corpus (24)

• Heat kernel expansion: user's manual
• Quantum Entropy Function from AdS(2)/CFT(1) Correspondence
• Logarithmic Corrections to N=2 Black Hole Entropy: An Infrared Window into the Microstates
• Logarithmic Corrections to N=4 and N=8 Black Hole Entropy: A One Loop Test of Quantum Gravity
• Logarithmic Corrections to Extremal Black Hole Entropy from Quantum Entropy Function
• Kretschmann Scalar for a Kerr-Newman Black Hole
• Logarithmic Corrections to Rotating Extremal Black Hole Entropy in Four and Five Dimensions
• Black hole determinants and quasinormal modes
• Entropy Function and AdS(2)/CFT(1) Correspondence
• Second Order Scalar Invariants of the Riemann Tensor: Applications to Black Hole Spacetimes
• Arithmetic of Quantum Entropy Function
• The Heat Kernel on AdS_3 and its Applications
• The Heat Kernel on $AdS$
• A note on the heat kernel method applied to fermions
• Heat Kernel Expansion and Extremal Kerr-Newmann Black Hole Entropy in Einstein-Maxwell Theory
• Logarithmic correction to the Cardy-Verlinde formula in Topological Reissner-Nordström de Sitter Space
• Logarithmic Corrections to Extremal Black Hole Entropy in N = 2, 4 and 8 Supergravity
• Logarithmic Corrections to Black Hole Entropy: the Non-BPS Branch
• Generalized mirror symmetry and trace anomalies
• Non-Renormalization For Non-Supersymmetric Black Holes
• Logarithmic Corrections to Twisted Indices from the Quantum Entropy Function
• U(N) Gauged N=2 Supergravity and Partial Breaking of Local N=2 Supersymmetry
• General heat kernel coefficients for massless free spin-3/2 Rarita-Schwinger field
• One loop partition function of six dimensional conformal gravity using heat kernel on AdS

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• Quantum Thermodynamics of an M2-M5 Brane System
• Logarithmic correction to black hole entropy in universal low-energy string theory models
• Non-topological logarithmic corrections in minimal gauged supergravity
• Generalized Einstein-Maxwell theory: Seeley-DeWitt coefficients and logarithmic corrections to the entropy of extremal and non-extremal black holes
• Logarithmic corrections to black hole entropy in matter coupled $\mathcal{N}\ge 1$ Einstein-Maxwell supergravity
• Logarithmic correction to the entropy of extremal black holes in $\mathcal{N}=1$ Einstein-Maxwell supergravity
• 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