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The 3d twisted index and wall-crossing

Bullimore, Mathew; Ferrari, Andrea; Kim, Heeyeon

The 3d twisted index and wall-crossing Thumbnail


Andrea Ferrari

Heeyeon Kim


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.


Bullimore, M., Ferrari, A., & Kim, H. (2022). The 3d twisted index and wall-crossing. SciPost Physics, 12(6), Article 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
Publisher SciPost
Peer Reviewed Peer Reviewed
Volume 12
Issue 6
Article Number 186


Published Journal Article (500 Kb)

Publisher Licence URL

Copyright Statement
Copyright M. Bullimore et al.<br /> This work is licensed under the Creative Commons<br /> Attribution 4.0 International License.<br /> Published by the SciPost Foundation.

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