Non-Holomorphic Cycles and Non-BPS Black Branes

TL;DR

This paper investigates extremal non-BPS black holes and strings in M-theory on Calabi-Yau threefolds, proposing a conjectural formula for non-holomorphic cycle volumes and analyzing their stability and entropy implications.

Contribution

It introduces a conjectural formula for volumes of non-holomorphic cycles and explores the stability and entropy of non-BPS black objects in M-theory compactifications.

Findings

Conjectural formula for asymptotic volumes of non-holomorphic cycles

Examples of stable non-BPS strings with recombined cycles

Connection between non-BPS string central charges and black hole entropy

Abstract

We study extremal non-BPS black holes and strings arising in M-theory compactifications on Calabi-Yau threefolds, obtained by wrapping M2 branes on non-holomorphic 2-cycles and M5 branes on non-holomorphic 4-cycles. Using the attractor mechanism we compute the black hole mass and black string tension, leading to a conjectural formula for the asymptotic volumes of connected, locally volume-minimizing representatives of non-holomorphic, even-dimensional homology classes in the threefold, without knowledge of an explicit metric. In the case of divisors we find examples where the volume of the representative corresponding to the black string is less than the volume of the minimal piecewise-holomorphic representative, predicting recombination for those homology classes and leading to stable, non-BPS strings. We also compute the central charges of non-BPS strings in F-theory via a near-horizon $AdS_3$ limit in 6d which, upon compactification on a circle, account for the asymptotic entropy of extremal non-supersymmetric 5d black holes (i.e., the asymptotic count of non-holomorphic minimal 2-cycles).