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Wall Crossing, Discrete Attractor Flow and Borcherds Algebra
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2008, том 4
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Wall Crossing, Discrete Attractor Flow and Borcherds Algebra
Інший ID:
2000 Mathematics Subject Classification: 81R10; 17B67
Посилання:
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.
Підтримка:
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).
Дата:
2008
Переглядів:
711
Завантажень:
238
Анотація:
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.
