Geodesic
An Index Formula for Supersymmetric Quantum Mechanics
Journal of Singularities, Tome 15 (2016), pp. 14-35

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We derive a localization formula for the refined index of gauged quantum mechanics with four supercharges. Our answer takes the form of a residue integral on the complexified Cartan subalgebra of the gauge group. The formula captures the dependence of the index on Fayet-Iliopoulos parameters and the presence of a generic superpotential. The residue formula provides an efficient method for computing cohomology of quiver moduli spaces. Our result has broad applications to the counting of BPS states in four-dimensional N=2 systems. In that context, the wall-crossing phenomenon appears as discontinuities in the value of the residue integral as the integration contour is varied. We present several examples illustrating the various aspects of the index formula. 
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     author = {Clay C\'ordova and Shu-Heng Shao},
     title = {An {Index} {Formula} for {Supersymmetric} {Quantum} {Mechanics}},
     journal = {Journal of Singularities},
     pages = {14--35},
     publisher = {mathdoc},
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     year = {2016},
     doi = {10.5427/jsing.2016.15b},
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Clay Córdova; Shu-Heng Shao. An Index Formula for Supersymmetric Quantum Mechanics. Journal of Singularities, Tome 15 (2016), pp. 14-35. doi: 10.5427/jsing.2016.15b

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