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ITFA-2008-20 Wall Crossing, Discrete Attractor Flow, and Borcherds Algebra

By A C. N. Cheng and Erik P. Verlinde


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 P GL(2, Z) of the theory, and the walls of Weyl chambers as the walls of marginal stability for the relevant twocentered 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 chargeand moduli-dependent highest weight vector and the dyon degeneracy, and show that the wall-crossing formula following from our proposal agrees with the wallcrossing formula obtained from the supergravity analysis. This can be thought o

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