Abstract
We calculate the first three Seeley-DeWitt coefficients for fluctuation of the massless fields of a $$ \mathcal{N} $$
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 $$ \mathcal{N} $$
N
= 2, d = 4 EMSGT, in a particular class of $$ \mathcal{N} $$
N
= 1, d = 4 EMSGT as consistent decomposition of $$ \mathcal{N} $$
N
= 2 multiplets ($$ \mathcal{N} $$
N
= 2 → $$ \mathcal{N} $$
N
= 1) and in $$ \mathcal{N} $$
N
≥ 3, d = 4 EMSGTs by decomposing them into $$ \mathcal{N} $$
N
= 2 multiplets ($$ \mathcal{N} $$
N
≥ 3 → $$ \mathcal{N} $$
N
= 2). For completeness, we also obtain logarithmic entropy correction results for the non-extremal Kerr-Newman black holes in the matter coupled $$ \mathcal{N} $$
N
≥ 1, d = 4 EMSGTs by employing the same Seeley-DeWitt data into a different Euclidean gravity approach developed in [17].
Seeley-DeWitt coefficients in $$ \mathcal{N} $$ = 2 Einstein-Maxwell supergravity theory and logarithmic corrections to $$ \mathcal{N} $$ = 2 extremal black hole entropy
