Dying Dyons Don't Count

Details Dying Dyons Don't Count Dying Dyons Don't Count

2007-06-17

arxiv.org/abs/0706.2363v2

JHEP 0709:070,2007

Physics

High Energy Physics

High Energy Physics - Theory

27 pages, 2 figures; one minus sign corrected

Scientific paper

10.1088/1126-6708/2007/09/070

The dyonic 1/4-BPS states in 4D string theory with N=4 spacetime supersymmetry are counted by a Siegel modular form. The pole structure of the modular form leads to a contour dependence in the counting formula obscuring its duality invariance. We exhibit the relation between this ambiguity and the (dis-)appearance of bound states of 1/2-BPS configurations. Using this insight we propose a precise moduli-dependent contour prescription for the counting formula. We then show that the degeneracies are duality-invariant and are correctly adjusted at the walls of marginal stability to account for the (dis-)appearance of the two-centered bound states. Especially, for large black holes none of these bound states exists at the attractor point and none of these ambiguous poles contributes to the counting formula. Using this fact we also propose a second, moduli-independent contour which counts the "immortal dyons" that are stable everywhere.

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