Generalized Mirror Symmetry and Quantum Black Hole Entropy

TL;DR

This paper explores the relationship between gravitational trace anomalies and logarithmic entropy corrections in supersymmetric black holes, revealing universal relations and extending understanding to various supergravity theories.

Contribution

It establishes general relations between trace anomalies and entropy corrections in N>1 supergravity black holes, including new results for self-mirror theories and conjectures for N=1 cases.

Findings

For self-mirror theories, Delta S_N = 2 - N/2.

In generic theories, trace anomaly relates to entropy correction as tildeA_N = 2Delta S_N - 1.

Universal relations between anomalies and entropy corrections are identified.

Abstract

We find general relations between the on-shell gravitational trace anomaly A_N, and the logarithmic correction Delta S_N to the entropy of "large" BPS extremal black holes in N>1 supergravity theories in D=4 space-time dimensions (recently computed by Sen [arXiv:1108.3842]). For (generalized) self-mirror theories (all having A_N = 0), we obtain the result DeltaS_N = - Delta S_(8-N) = 2 - N/2, whereas for generic theories the trace anomaly tildeA_N of the fully dualized theory turns out to coincide with 2Delta S_N, up to a model-independent shift: tildeA_N = 2Delta S_N - 1. We also speculate on N=1 theories displaying "large" extremal black hole solutions.