Wall Crossing, Discrete Attractor Flow and Borcherds Algebra
The appearance of a generalized (or Borcherds-) Kac-Moody algebra in the spectrum of BPS dyons in N=4, d=4 string theory is elucidated. From the low-energy supergravity analysis, we identify its root lattice as the lattice of the T-duality invariants of the dyonic charges, the symmetry group of the...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2008 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2008
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/149017 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Wall Crossing, Discrete Attractor Flow and Borcherds Algebra / Miranda C.N. Cheng, E.P. Verlinde // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 44 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862744169126035456 |
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| author | Cheng, Miranda C.N. Verlinde, E.P. |
| author_facet | Cheng, Miranda C.N. Verlinde, E.P. |
| citation_txt | Wall Crossing, Discrete Attractor Flow and Borcherds Algebra / Miranda C.N. Cheng, E.P. Verlinde // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 44 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | The appearance of a generalized (or Borcherds-) Kac-Moody algebra in the spectrum of BPS dyons in N=4, d=4 string theory is elucidated. From the low-energy supergravity analysis, we identify its root lattice as the lattice of the T-duality invariants of the dyonic charges, the symmetry group of the root system as the extended S-duality group PGL(2,Z) of the theory, and the walls of Weyl chambers as the walls of marginal stability for the relevant two-centered solutions. This leads to an interpretation for the Weyl group as the group of wall-crossing, or the group of discrete attractor flows. Furthermore we propose an equivalence between a ''second-quantized multiplicity'' of a charge- and moduli-dependent highest weight vector and the dyon degeneracy, and show that the wall-crossing formula following from our proposal agrees with the wall-crossing formula obtained from the supergravity analysis. This can be thought of as providing a microscopic derivation of the wall-crossing formula of this theory.
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| first_indexed | 2025-12-07T20:34:17Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-149017 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T20:34:17Z |
| publishDate | 2008 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Cheng, Miranda C.N. Verlinde, E.P. 2019-02-19T13:05:11Z 2019-02-19T13:05:11Z 2008 Wall Crossing, Discrete Attractor Flow and Borcherds Algebra / Miranda C.N. Cheng, E.P. Verlinde // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 44 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 81R10; 17B67 https://nasplib.isofts.kiev.ua/handle/123456789/149017 The appearance of a generalized (or Borcherds-) Kac-Moody algebra in the spectrum of BPS dyons in N=4, d=4 string theory is elucidated. From the low-energy supergravity analysis, we identify its root lattice as the lattice of the T-duality invariants of the dyonic charges, the symmetry group of the root system as the extended S-duality group PGL(2,Z) of the theory, and the walls of Weyl chambers as the walls of marginal stability for the relevant two-centered solutions. This leads to an interpretation for the Weyl group as the group of wall-crossing, or the group of discrete attractor flows. Furthermore we propose an equivalence between a ''second-quantized multiplicity'' of a charge- and moduli-dependent highest weight vector and the dyon degeneracy, and show that the wall-crossing formula following from our proposal agrees with the wall-crossing formula obtained from the supergravity analysis. This can be thought of as providing a microscopic derivation of the wall-crossing formula of this theory. This paper is a contribution to the Special Issue on Kac–Moody Algebras and Applications. We would like to thank Atish Dabholkar, Frederik Denef, Axel Kleinschmidt, Greg Moore, Daniel Persson, Boris Pioline and Curum Vafa for useful discussions. E.V. would like to thank Harvard University for hospitality during the completion of this work. M.C. is supported by the Netherlands Organisation for Scientific Research (NWO). The research of E.V. is partly supported by the Foundation of Fundamental Research on Matter (FOM). en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Wall Crossing, Discrete Attractor Flow and Borcherds Algebra Article published earlier |
| spellingShingle | Wall Crossing, Discrete Attractor Flow and Borcherds Algebra Cheng, Miranda C.N. Verlinde, E.P. |
| title | Wall Crossing, Discrete Attractor Flow and Borcherds Algebra |
| title_full | Wall Crossing, Discrete Attractor Flow and Borcherds Algebra |
| title_fullStr | Wall Crossing, Discrete Attractor Flow and Borcherds Algebra |
| title_full_unstemmed | Wall Crossing, Discrete Attractor Flow and Borcherds Algebra |
| title_short | Wall Crossing, Discrete Attractor Flow and Borcherds Algebra |
| title_sort | wall crossing, discrete attractor flow and borcherds algebra |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/149017 |
| work_keys_str_mv | AT chengmirandacn wallcrossingdiscreteattractorflowandborcherdsalgebra AT verlindeep wallcrossingdiscreteattractorflowandborcherdsalgebra |