Twisted indices of 3d N = 4 gauge theories and enumerative geometry of quasi-maps
We explore the geometric interpretation of the twisted index of 3d N = 4 gauge theories on S1 × 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...
| Main Authors: | , , |
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| Format: | Journal article |
| Language: | English |
| Published: |
Springer Verlag
2019
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| Summary: | We explore the geometric interpretation of the twisted index of 3d N = 4 gauge theories on S1 × 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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