Non-Holomorphic Cycles and Non-BPS Black Branes

Communications in Mathematical Physics. 2023. Vol. 399. No. 3. P. 1991–2043.

Sheshmani A., Long C., Vafa C., Yau S.

We study extremal non-BPS black holes and strings arising in M-theory
compactifications on Calabi–Yau threefolds, obtained by wrapping M2 branes on nonholomorphic
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 theminimal 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 AdS3 limit in 6d which,
upon compactification on a circle, account for the asymptotic entropy of extremal nonsupersymmetric
5d black holes (i.e., the asymptotic count of non-holomorphic minimal
2-cycles).

Keywords: attractors, SELF-INTERACTION

Publication based on the results of: Spectral networks, spectra and F-bundles (2023)