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 Web site:||https://doi.org/10.1007/JHEP07(2019)014|
|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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