Derives a distributional real-line integral formula for abelian observables in A-twisted N=(2,2) theories on S², verifies it on the CP^{N-1} GLSM correlator, and uses hyperfunctions to equate it with contour integrals matching the Jeffrey-Kirwan prescription.
An Index Formula for Supersymmetric Quantum Mechanics
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abstract
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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Hyperfunctions in $A$-model Localization
Derives a distributional real-line integral formula for abelian observables in A-twisted N=(2,2) theories on S², verifies it on the CP^{N-1} GLSM correlator, and uses hyperfunctions to equate it with contour integrals matching the Jeffrey-Kirwan prescription.
- Localisation of $\mathcal{N} = (2,2)$ theories on spindles of both twists