SciPost Submission Page
The 3d Twisted Index and Wall-Crossing
by Mathew Bullimore, Andrea E.V. Ferrari, Heeyeon Kim
This Submission thread is now published as
Submission summary
| Authors (as registered SciPost users): | Andrea Ferrari · Heeyeon Kim |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202201_00022v2 (pdf) |
| Date accepted: | 2022-05-10 |
| Date submitted: | 2022-04-28 09:54 |
| Submitted by: | Ferrari, Andrea |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
|
Abstract
We study the twisted index of 3d $\mathcal{N}=2$ supersymmetric gauge theories on $S^1 \times \Sigma$ 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 wall-crossing 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 $\mathcal{N}=4$ supersymmetry and in a non-abelian example that reproduces wall-crossing phenomena associated to moduli spaces of stable pairs.
Author comments upon resubmission
List of changes
We added some context and motivation in the introduction and emphasized the relation to the previous prescription in subsection 3.4.
Published as SciPost Phys. 12, 186 (2022)