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Wall-crossing made smooth
In $D=4,N=2$ theories on $R^{3,1}$, 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 [arXiv:1406.2360], a general formula expressing the index in terms of the BPS indi...
Autor principal: | |
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Lenguaje: | eng |
Publicado: |
2015
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Materias: | |
Acceso en línea: | https://dx.doi.org/10.1007/JHEP04(2015)092 http://cds.cern.ch/record/1980359 |
Sumario: | In $D=4,N=2$ theories on $R^{3,1}$, 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 [arXiv:1406.2360], 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 provides 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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