Witten Index and Wall Crossing

Understand

We compute the Witten index of one-dimensional gauged linear sigma models with at least ${\mathcal N}=2$ supersymmetry.

• In the phase where the gauge group is broken to a finite group, the index is expressed as a certain residue integral.
• It is subject to a change as the Fayet-Iliopoulos parameter is varied through the phase boundaries.
• The wall crossing formula is expressed as an integral at infinity of the Coulomb branch.