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Durham University

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Publication details for Mathew Bullimore

Bullimore, Mathew, Ferrari, Andrea & Kim, Heeyeon (2019). Twisted indices of 3d N = 4 gauge theories and enumerative geometry of quasi-maps. Journal of High Energy Physics 2019(7): 14.

Author(s) from Durham


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.