Wall Crossing, Discrete Attractor Flow and Borcherds Algebra

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2008
• Main Authors: Cheng, Miranda C.N., Verlinde, E.P.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2008
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/149017
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: 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.

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.