The twisted index and topological saddles

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

doi:10.1007/jhep05(2022)116

The twisted index and topological saddles

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

Authors

Professor Mathew Bullimore mathew.r.bullimore@durham.ac.uk
Early Career Fellowship

Andrea Ferrari andrea.ferrari@durham.ac.uk
Academic Visitor

Heeyeon Kim

Guangyu Xu

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

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Open Access . This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.