BPS Spectra, Barcodes and Walls
BPS spectra give important insights into the non-perturbative regimes of supersymmetric theories. Often, from the study of BPS states, one can infer properties of the geometrical or algebraic structures underlying such theories. In this paper, we approach this problem from the perspective of persist...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2019 |
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| Format: | Artikel |
| Sprache: | English |
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Інститут математики НАН України
2019
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/210243 |
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| Zitieren: | BPS Spectra, Barcodes and Walls / M. Cirafici // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 66 назв. — англ. |
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Cirafici, M. 2025-12-04T13:10:08Z 2019 BPS Spectra, Barcodes and Walls / M. Cirafici // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 66 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 83E30; 81Q60; 55N99 arXiv: 1511.01421 https://nasplib.isofts.kiev.ua/handle/123456789/210243 https://doi.org/10.3842/SIGMA.2019.052 BPS spectra give important insights into the non-perturbative regimes of supersymmetric theories. Often, from the study of BPS states, one can infer properties of the geometrical or algebraic structures underlying such theories. In this paper, we approach this problem from the perspective of persistent homology. Persistent homology is at the base of topological data analysis, which aims at extracting topological features from a set of points. We use these techniques to investigate the topological properties that characterize the spectra of several supersymmetric models in field and string theory. We discuss how such features change upon crossing walls of marginal stability in a few examples. Then we look at the topological properties of the distributions of BPS invariants in string compactifications on compact threefolds, used to engineer black hole microstates. Finally, we discuss the interplay between persistent homology and modularity by considering certain number theoretical functions used to count dyons in string compactifications and by studying equivariant elliptic genera in the context of the Mathieu moonshine. I wish to thank the Applied Topology group at Stanford University for making javaplex available in [64]. I also thank the theory division at CERN and IHES for hospitality and support during the reparation of this note. This work was partially supported by FCT/Portugal and IST-ID through UID/MAT/04459/2013, EXCL/MAT-GEO/0222/2012, and the program Investigador FCT IF2014, under contract IF/01426/2014/CP1214/CT0001. I am a member of INDAM-GNFM, I am supported by INFN via the Iniziativa Specifica GAST and by the FRA2018 project "K-theoretic Enumerative Geometry in Mathematical Physics". en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications BPS Spectra, Barcodes and Walls Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
BPS Spectra, Barcodes and Walls |
| spellingShingle |
BPS Spectra, Barcodes and Walls Cirafici, M. |
| title_short |
BPS Spectra, Barcodes and Walls |
| title_full |
BPS Spectra, Barcodes and Walls |
| title_fullStr |
BPS Spectra, Barcodes and Walls |
| title_full_unstemmed |
BPS Spectra, Barcodes and Walls |
| title_sort |
bps spectra, barcodes and walls |
| author |
Cirafici, M. |
| author_facet |
Cirafici, M. |
| publishDate |
2019 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
BPS spectra give important insights into the non-perturbative regimes of supersymmetric theories. Often, from the study of BPS states, one can infer properties of the geometrical or algebraic structures underlying such theories. In this paper, we approach this problem from the perspective of persistent homology. Persistent homology is at the base of topological data analysis, which aims at extracting topological features from a set of points. We use these techniques to investigate the topological properties that characterize the spectra of several supersymmetric models in field and string theory. We discuss how such features change upon crossing walls of marginal stability in a few examples. Then we look at the topological properties of the distributions of BPS invariants in string compactifications on compact threefolds, used to engineer black hole microstates. Finally, we discuss the interplay between persistent homology and modularity by considering certain number theoretical functions used to count dyons in string compactifications and by studying equivariant elliptic genera in the context of the Mathieu moonshine.
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| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/210243 |
| citation_txt |
BPS Spectra, Barcodes and Walls / M. Cirafici // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 66 назв. — англ. |
| work_keys_str_mv |
AT ciraficim bpsspectrabarcodesandwalls |
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2025-12-07T21:24:53Z |
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2025-12-07T21:24:53Z |
| _version_ |
1850886264577851392 |