The Resolution of an Entropy Puzzle for 4D non-BPS Black Holes

TL;DR

This paper demonstrates the equivalence of macroscopic and microscopic entropy calculations for a specific class of four-dimensional non-supersymmetric black holes, resolving a longstanding entropy puzzle.

Contribution

It provides the first verification of entropy matching for non-BPS black holes in four-dimensional supergravity, incorporating higher-derivative corrections and anomaly effects.

Findings

Macroscopic entropy matches microscopic calculations up to first subleading order.

Higher-derivative supersymmetric invariants are crucial for the entropy computation.

Anomalous gauge gravitational Chern-Simons terms play a key role in the microscopic analysis.

Abstract

We show the equality between macroscopic and microscopic black hole entropy for a class of four dimensional non-supersymmetric black holes in ${\cal N}=2$ supergravity theory, up to the first subleading order in their charges. This solves a long standing entropy puzzle for this class of black holes. The macroscopic entropy has been computed in the presence of a newly derived higher-derivative supersymmetric invariant of \cite{{Butter:2013lta}}, connected to the five dimensional supersymmetric Weyl squared Lagrangian. Microscopically, the crucial role in obtaining the equivalence is played by the anomalous gauge gravitational Chern-Simons term.