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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| Дата: | 2008 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
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Інститут математики НАН України
2008
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/149017 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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| id |
irk-123456789-149017 |
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dspace |
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irk-123456789-1490172019-02-20T01:26:41Z Wall Crossing, Discrete Attractor Flow and Borcherds Algebra Cheng, Miranda C.N. Verlinde, E.P. 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. 2008 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/149017 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Cheng, Miranda C.N. Verlinde, E.P. |
| spellingShingle |
Cheng, Miranda C.N. Verlinde, E.P. Wall Crossing, Discrete Attractor Flow and Borcherds Algebra Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Cheng, Miranda C.N. Verlinde, E.P. |
| author_sort |
Cheng, Miranda C.N. |
| title |
Wall Crossing, Discrete Attractor Flow and Borcherds Algebra |
| title_short |
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_sort |
wall crossing, discrete attractor flow and borcherds algebra |
| publisher |
Інститут математики НАН України |
| publishDate |
2008 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/149017 |
| 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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
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2023-05-20T17:31:37Z |
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1796153499970437120 |