Witten index and wall crossing

Kentaro Hori, Heeyeon Kim, Piljin Yi

Research output: Contribution to journalArticlepeer-review

87 Scopus citations


Abstract: We compute the Witten index of one-dimensional gauged linear sigma models with at least = 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. The result is applied to many examples, including quiver quantum mechanics that is relevant for BPS states in d = 4 =2 theories.

Original languageEnglish (US)
JournalJournal of High Energy Physics
Issue number1
StatePublished - 2015
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Nuclear and High Energy Physics


  • D-branes
  • Field Theories in Lower Dimensions
  • Supersymmetric gauge theory


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