SciPost logo

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:
  • High-Energy Physics - Theory
  • Mathematical Physics

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

With this resubmission we address the points raised by the referees. In particular, we add some context and emphasize the relation of our prescription to the previous JK prescription. We acknowledge the fact that subtleties remain for non-Abelian gauge groups at higher genus due to the presence of additional poles; this was already pointed out in section 3.1, page 10 and in footnote 9, page 34.

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)


Reports on this Submission

Report #2 by Anonymous (Referee 1) on 2022-5-2 (Invited Report)

Report

This paper is now suitable for publication

  • validity: -
  • significance: -
  • originality: -
  • clarity: -
  • formatting: -
  • grammar: -

Report #1 by Anonymous (Referee 2) on 2022-5-2 (Invited Report)

Report

I support the resubmitted manuscript with the described modifications for publication.

  • validity: -
  • significance: -
  • originality: -
  • clarity: -
  • formatting: -
  • grammar: -

Login to report or comment