Twisted indices of 3d \( \mathcal{N}=4 \) gauge theories and enumerative geometry of quasi-maps

DOI10.1007/JHEP07(2019)014zbMATH Open1418.81073arXiv1812.05567MaRDI QIDQ2317716

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Publication date: 12 August 2019

Published in: (Search for Journal in Brave)

Abstract: We explore the geometric interpretation of the twisted index of 3d $mathcalN=4$ gauge theories on $S^{1}imesSigma$ where $Sigma$ 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 generalised vortex equations on $Sigma$, 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 $mathcalN=4$ 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.

Full work available at URL: https://arxiv.org/abs/1812.05567

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