Witten Index and Wall Crossing
High Energy Physics - Theory
2015-06-22 v3
Abstract
We compute the Witten index of one-dimensional gauged linear sigma models with at least 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. The result is applied to many examples, including quiver quantum mechanics that is relevant for BPS states in theories.
Cite
@article{arxiv.1407.2567,
title = {Witten Index and Wall Crossing},
author = {Kentaro Hori and Heeyeon Kim and Piljin Yi},
journal= {arXiv preprint arXiv:1407.2567},
year = {2015}
}
Comments
123 pages, v3: the discussion on the smooth transition (Section 4.4) is improved, more minor corrections made; v2: references added, minor corrections made