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Twisted Hilbert spaces of 3d supersymmetric gauge theories.

Bullimore, Mathew and Ferrari, Andrea (2018) 'Twisted Hilbert spaces of 3d supersymmetric gauge theories.', Journal of high energy physics., 2018 (08). 018.


We study aspects of 3d 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.

Item Type:Article
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Publisher statement:© The Author(s) 2018 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.
Date accepted:30 July 2018
Date deposited:16 August 2018
Date of first online publication:07 August 2018
Date first made open access:16 August 2018

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