Twisted Hilbert spaces of 3d supersymmetric gauge theories

DOI10.1007/JHEP08(2018)018zbMATH Open1396.81196arXiv1802.10120OpenAlexW2789031118WikidataQ129406391 ScholiaQ129406391MaRDI QIDQ1783765

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Publication date: 21 September 2018

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Abstract: We study aspects of 3d $mathcalN=2$ 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.

Full work available at URL: https://arxiv.org/abs/1802.10120

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