The 3d twisted index and wall-crossing

Bullimore, Mathew; Ferrari, Andrea; Kim, Heeyeon

Abstract

We study the twisted index of 3d N = 2 supersymmetric gauge theories on S 1 ×Σ in the presence of a real FI parameter deformation. This parameter induces a 1d FI parameter for the effective supersymmetric quantum mechanics on S 1 . Using supersymmetric localisation, the twisted index can be expressed as a contour integral. We show that the contour prescription is modified in the presence of the 1d FI parameter, leading to wall-crossing phenomena for the twisted index. In particular, we derive a general wallcrossing formula for abelian gauge theories. We also examine the origin of wall-crossing as change of stability condition in the algebro-geometric interpretation of the twisted index. These ideas are illustrated for abelian theories with N = 4 supersymmetry and in a non-abelian example that reproduces wall-crossing phenomena associated to moduli spaces of stable pairs.

Citation

Bullimore, M., Ferrari, A., & Kim, H. (2022). The 3d twisted index and wall-crossing. SciPost Physics, 12(6), Article 186. https://doi.org/10.21468/scipostphys.12.6.186

• Journal Article Type: Article
• Acceptance Date: May 10, 2022
• Online Publication Date: Jun 8, 2022
• Publication Date: 2022-06
• Deposit Date: Jun 8, 2022
• Publicly Available Date: Jun 8, 2022
• Journal: SciPost Physics.
• Print ISSN: 2542-4653
• Electronic ISSN: 2542-4653
• Publisher: SciPost
• Peer Reviewed: Peer Reviewed
• Volume: 12
• Issue: 6
• Article Number: 186
• DOI: https://doi.org/10.21468/scipostphys.12.6.186
• Public URL: https://durham-repository.worktribe.com/output/1201763