Twisted Hilbert spaces of 3d supersymmetric gauge theories

  • Mathew BullimoreEmail author
  • Andrea Ferrari
Open Access
Regular Article - Theoretical Physics


We study aspects of 3d \( \mathcal{N}=2 \) supersymmetric gauge theories on the product of a line and a Riemann surface. Performing a topological twist along the Riemann surface leads to an effective supersymmetric quantum mechanics on the line. We propose a construction of the space of supersymmetric ground states as a graded vector space in terms of a certain cohomology of generalized vortex moduli spaces on the Riemann surface. This exhibits a rich dependence on deformation parameters compatible with the topological twist, including superpotentials, real mass parameters, and background vector bundles associated to flavour symmetries. By matching spaces of supersymmetric ground states, we perform new checks of 3d abelian mirror symmetry.


Supersymmetric Gauge Theory Supersymmetry and Duality Duality in Gauge Field Theories 


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.


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Copyright information

© The Author(s) 2018

Authors and Affiliations

  1. 1.Mathematics Department, Durham University, Science LaboratoriesDurhamU.K.
  2. 2.Mathematical InstituteUniversity of OxfordOxfordU.K.

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