Wall-crossing made smooth

Open Access
Regular Article - Theoretical Physics

Abstract

In D = 4, \( \mathcal{N}=2 \) theories on \( {\mathbb{R}}^{3,1} \), the index receives contributions not only from single-particle BPS states, counted by the BPS indices, but also from multi-particle states made of BPS constituents. In a recent work [1], a general formula expressing the index in terms of the BPS indices was proposed, which is smooth across walls of marginal stability and reproduces the expected single-particle contributions. In this note, I analyze the two-particle contributions predicted by this formula, and show agreement with the spectral asymmetry of the continuum of scattering states in the supersymmetric quantum mechanics of two non-relativistic, mutually non-local dyons. This may provide a physical justification for the error function profile used in the mathematics literature on indefinite theta series, and in the physics literature on black hole partition functions.

Keywords

Extended Supersymmetry Supersymmetric Effective Theories Brane Dynamics in Gauge Theories Black Holes in String Theory 

Notes

Open Access

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Copyright information

© The Author(s) 2015

Authors and Affiliations

  1. 1.CERN PH-THCase C01600, CERNGeneva 23Switzerland
  2. 2.Sorbonne Universités, UPMC Université Paris 6, UMR 7589ParisFrance
  3. 3.Laboratoire de Physique Théorique et Hautes Energies, CNRS UMR 7589Université Pierre et Marie CurieParis cedex 05France

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