Mock Modularity at Work, or Black Holes in a Forest
Mock modular forms, first invented by Ramanujan, provide a beautiful generalization of the usual modular forms. In recent years, it was found that they capture the generating functions of the number of microstates of BPS black holes appearing in compactifications of string theory with 8 and 16 super...
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2025-07-01
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| author | Sergei Alexandrov |
| author_facet | Sergei Alexandrov |
| author_sort | Sergei Alexandrov |
| collection | DOAJ |
| description | Mock modular forms, first invented by Ramanujan, provide a beautiful generalization of the usual modular forms. In recent years, it was found that they capture the generating functions of the number of microstates of BPS black holes appearing in compactifications of string theory with 8 and 16 supercharges. This review describes these results and their applications, which range from the actual computation of these generating functions for both compact and non-compact compactification manifolds (encoding, respectively, Donaldson–Thomas and Vafa–Witten topological invariants) to the construction of new non-commutative structures on moduli spaces of Calabi–Yau threefolds. |
| format | Article |
| id | doaj-art-db86768147f043f5821061a9ea4cb7cd |
| institution | Matheson Library |
| issn | 1099-4300 |
| language | English |
| publishDate | 2025-07-01 |
| publisher | MDPI AG |
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| series | Entropy |
| spelling | doaj-art-db86768147f043f5821061a9ea4cb7cd2025-07-25T13:22:19ZengMDPI AGEntropy1099-43002025-07-0127771910.3390/e27070719Mock Modularity at Work, or Black Holes in a ForestSergei Alexandrov0Laboratoire Charles Coulomb (L2C), Université de Montpellier, CNRS, F-34095 Montpellier, FranceMock modular forms, first invented by Ramanujan, provide a beautiful generalization of the usual modular forms. In recent years, it was found that they capture the generating functions of the number of microstates of BPS black holes appearing in compactifications of string theory with 8 and 16 supercharges. This review describes these results and their applications, which range from the actual computation of these generating functions for both compact and non-compact compactification manifolds (encoding, respectively, Donaldson–Thomas and Vafa–Witten topological invariants) to the construction of new non-commutative structures on moduli spaces of Calabi–Yau threefolds.https://www.mdpi.com/1099-4300/27/7/719mock modular formblack holeCalabi–YauBPS indexDonaldson–Thomas invariantcompactification |
| spellingShingle | Sergei Alexandrov Mock Modularity at Work, or Black Holes in a Forest Entropy mock modular form black hole Calabi–Yau BPS index Donaldson–Thomas invariant compactification |
| title | Mock Modularity at Work, or Black Holes in a Forest |
| title_full | Mock Modularity at Work, or Black Holes in a Forest |
| title_fullStr | Mock Modularity at Work, or Black Holes in a Forest |
| title_full_unstemmed | Mock Modularity at Work, or Black Holes in a Forest |
| title_short | Mock Modularity at Work, or Black Holes in a Forest |
| title_sort | mock modularity at work or black holes in a forest |
| topic | mock modular form black hole Calabi–Yau BPS index Donaldson–Thomas invariant compactification |
| url | https://www.mdpi.com/1099-4300/27/7/719 |
| work_keys_str_mv | AT sergeialexandrov mockmodularityatworkorblackholesinaforest |