Cheng, Miranda C. N.; Verlinde, Erik P. Wall crossing, discrete attractor flow and Borcherds algebra. (English) Zbl 1164.81009 SIGMA, Symmetry Integrability Geom. Methods Appl. 4, Paper 068, 33 p. (2008). Summary: 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 \(PGL(2,\mathbb{Z})\) 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. Cited in 32 Documents MSC: 81R10 Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, \(W\)-algebras and other current algebras and their representations 17B67 Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras Keywords:generalized Kac-Moody algebra; black hole; dyons PDFBibTeX XMLCite \textit{M. C. N. Cheng} and \textit{E. P. Verlinde}, SIGMA, Symmetry Integrability Geom. Methods Appl. 4, Paper 068, 33 p. (2008; Zbl 1164.81009) Full Text: DOI arXiv EuDML