Abstract
We calculate the first three Seeley-DeWitt coefficients for fluctuation of the massless fields of a mathcal{N} = 2 Einstein-Maxwell supergravity theory (EMSGT) distributed into different multiplets in d = 4 space-time dimensions. By utilizing the Seeley-DeWitt data in the quantum entropy function formalism, we then obtain the logarithmic correction contribution of individual multiplets to the entropy of extremal Kerr-Newman family of black holes. Our results allow us to find the logarithmic entropy corrections for the extremal black holes in a fully matter coupled mathcal{N} = 2, d = 4 EMSGT, in a particular class of mathcal{N} = 1, d = 4 EMSGT as consistent decomposition of mathcal{N} = 2 multiplets ( mathcal{N} = 2 → mathcal{N} = 1) and in mathcal{N} ≥ 3, d = 4 EMSGTs by decomposing them into mathcal{N} = 2 multiplets ( mathcal{N} ≥ 3 → mathcal{N} = 2). For completeness, we also obtain logarithmic entropy correction results for the non-extremal Kerr-Newman black holes in the matter coupled mathcal{N} ≥ 1, d = 4 EMSGTs by employing the same Seeley-DeWitt data into a different Euclidean gravity approach developed in [17].
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