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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Опубліковано в: :Symmetry, Integrability and Geometry: Methods and Applications
Дата:2008
Автори: Cheng, Miranda C.N., Verlinde, E.P.
Формат: Стаття
Мова:English
Опубліковано: Інститут математики НАН України 2008
Онлайн доступ: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
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 nasplib_isofts_kiev_ua-123456789-149017
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
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
title Wall Crossing, Discrete Attractor Flow and Borcherds Algebra
spellingShingle Wall Crossing, Discrete Attractor Flow and Borcherds Algebra
Cheng, Miranda C.N.
Verlinde, E.P.
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
author Cheng, Miranda C.N.
Verlinde, E.P.
author_facet Cheng, Miranda C.N.
Verlinde, E.P.
publishDate 2008
language English
container_title Symmetry, Integrability and Geometry: Methods and Applications
publisher Інститут математики НАН України
format Article
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.
issn 1815-0659
url https://nasplib.isofts.kiev.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.
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first_indexed 2025-12-07T20:34:17Z
last_indexed 2025-12-07T20:34:17Z
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