Logarithmic Corrections to Extremal Black Hole Entropy from Quantum Entropy Function

TL;DR

This paper calculates quantum corrections to extremal black hole entropy in N=4 supergravity, showing that matter multiplet contributions cancel out, aligning with microscopic predictions.

Contribution

It provides the first detailed computation of matter multiplet contributions to logarithmic black hole entropy corrections using the quantum entropy function formalism.

Findings

Net logarithmic contribution from matter multiplets vanishes.

Logarithmic corrections are independent of matter multiplet count.

Spectrum of matter multiplet fluctuations determined.

Abstract

We evaluate the one loop determinant of matter multiplet fields of N=4 supergravity in the near horizon geometry of quarter BPS black holes, and use it to calculate logarithmic corrections to the entropy of these black holes using the quantum entropy function formalism. We show that even though individual fields give non-vanishing logarithmic contribution to the entropy, the net contribution from all the fields in the matter multiplet vanishes. Thus logarithmic corrections to the entropy of quarter BPS black holes, if present, must be independent of the number of matter multiplet fields in the theory. This is consistent with the microscopic results. During our analysis we also determine the complete spectrum of small fluctuations of matter multiplet fields in the near horizon geometry.