Cookies

We use cookies to ensure that we give you the best experience on our website. You can change your cookie settings at any time. Otherwise, we'll assume you're OK to continue.

Durham University

Research & business

View Profile

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

Abstract

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.