Non-Holomorphic Cycles and Non-BPS Black Branes Arxiv
Non-Holomorphic Cycles and Non-BPS Black Branes Cody Long,1;2 Artan Sheshmani,2;3;4 Cumrun Vafa,1 and Shing-Tung Yau2;5 1Jefferson Physical Laboratory, Harvard University Cambridge, MA 02138, USA 2Center for Mathematical Sciences and Applications, Harvard University Cambridge, MA 02139, USA 3Institut for Matematik, Aarhus Universitet 8000 Aarhus C, Denmark 4 National Research University Higher School of Economics, Russian Federation, Laboratory of Mirror Symmetry, Moscow, Russia, 119048 5Department of Mathematics, Harvard University Cambridge, MA 02138, USA We study extremal non-BPS black holes and strings arising in M-theory compactifica- tions 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 for- mula for the asymptotic volumes of connected, locally volume-minimizing representa- tives of non-holomorphic, even-dimensional homology classes in the threefold, without arXiv:2104.06420v1 [hep-th] 13 Apr 2021 knowledge of an explicit metric. In the case of divisors we find examples where the vol- ume 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 AdS3 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).
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