The twisted index and topological saddles

Bullimore, Mathew; Ferrari, Andrea E.V.; Kim, Heeyeon; Xu, Guangyu

Abstract

The twisted index of 3d N = 2 gauge theories on S 1 × Σ has an algebrogeometric interpretation as the Witten index of an effective supersymmetric quantum mechanics. In this paper, we consider the contributions to the supersymmetric quantum mechanics from topological saddle points in supersymmetric localisation of abelian gauge theories. Topological saddles are configurations where the matter fields vanish and the gauge symmetry is unbroken, which exist for non-vanishing effective Chern-Simons levels. We compute the contributions to the twisted index from both topological and vortex-like saddles points and show that their combination recovers the Jeffrey-Kirwan residue prescription for the twisted index and its wall-crossing.

Citation

Bullimore, M., Ferrari, A. E., Kim, H., & Xu, G. (2022). The twisted index and topological saddles. Journal of High Energy Physics, 2022(5), Article 116. https://doi.org/10.1007/jhep05%282022%29116

• Journal Article Type: Article
• Acceptance Date: Apr 25, 2022
• Online Publication Date: May 18, 2022
• Publication Date: 2022-05
• Deposit Date: May 19, 2022
• Publicly Available Date: May 19, 2022
• Journal: Journal of High Energy Physics
• Print ISSN: 1126-6708
• Electronic ISSN: 1029-8479
• Publisher: Scuola Internazionale Superiore di Studi Avanzati (SISSA)
• Peer Reviewed: Peer Reviewed
• Volume: 2022
• Issue: 5
• Article Number: 116
• DOI: https://doi.org/10.1007/jhep05%282022%29116
• Public URL: https://durham-repository.worktribe.com/output/1207989