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.
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Pioline, B. Wall-crossing made smooth. J. High Energ. Phys. 2015, 92 (2015). https://doi.org/10.1007/JHEP04(2015)092
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DOI: https://doi.org/10.1007/JHEP04(2015)092