Twisted Hilbert Spaces of 3d Supersymmetric Gauge Theories

Abstract

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.

arXiv comment49 + 11 pages, 6 figures. v2: clarifications and corrections added

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• Factorisation of 3d $\mathcal{N}=4$ Twisted Indices and the Geometry of Vortex Moduli Space
• Boundary vertex algebras for 3d $\mathcal{N}=4$ rank-0 SCFTs
• Monopole Operators and Bulk-Boundary Relation in Holomorphic Topological Theories
• Twisted indices, Bethe ideals and 3d $\mathcal{N}=2$ infrared dualities
• Supersymmetric Ground States of 3d $\mathcal{N}=4$ Gauge Theories on a Riemann Surface
• Remarks on Berry Connection in QFT, Anomalies, and Applications
• On the Witten index of 3d $\mathcal{N}=2$ unitary SQCD with general CS levels
• (0,2) Dualities and the 4-Simplex
• Vortex counting and the quantum Hall effect
• Supersymmetric ground states of 3d $\mathcal{N}=4$ SUSY gauge theories and Heisenberg Algebras
• The colored Jones polynomials as vortex partition functions