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arXiv · 0806.2337

Wall Crossing, Discrete Attractor Flow and Borcherds Algebra

Miranda C. N. Cheng·Erik P. Verlinde
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Abstract

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.

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Miranda C. N. Cheng, Erik P. Verlinde. 2008-10-07. Wall Crossing, Discrete Attractor Flow and Borcherds Algebra. https://doi.org/10.3842/sigma.2008.068

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