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Twisted indices of 3d N = 4 gauge theories and enumerative geometry of quasi-maps.

Bullimore, Mathew and Ferrari, Andrea and Kim, Heeyeon (2019) 'Twisted indices of 3d N = 4 gauge theories and enumerative geometry of quasi-maps.', Journal of high energy physics., 2019 (7). 014.


We explore the geometric interpretation of the twisted index of 3d N = 4 gauge theories on S 1 × Σ where Σ is a closed Riemann surface. We focus on a rich class of supersymmetric quiver gauge theories that have isolated vacua under generic mass and FI parameter deformations. We show that the path integral localises to a moduli space of solutions to generalised vortex equations on Σ, which can be understood algebraically as quasi-maps to the Higgs branch. We show that the twisted index reproduces the virtual Euler characteristic of the moduli spaces of twisted quasi-maps and demonstrate that this agrees with the contour integral representation introduced in previous work. Finally, we investigate 3d N = 4 mirror symmetry in this context, which implies an equality of enumerative invariants associated to mirror pairs of Higgs branches under the exchange of equivariant and degree counting parameters.

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Publisher statement: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:26 June 2019
Date deposited:24 July 2019
Date of first online publication:03 July 2019
Date first made open access:No date available

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