Abstract: In D = 4,N=2 theories on (Formula presented.), 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.
CITATION STYLE
Pioline, B. (2015). Wall-crossing made smooth. Journal of High Energy Physics, 2015(4). https://doi.org/10.1007/JHEP04(2015)092
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