2018/12/31 by Mathew Bullimore, Andrea E. V. Ferrari, Heeyeon Kim · 28 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Compact Riemann surface #Context (archaeology) #Equivariant map #Euler characteristic #Gauge theory #Geometry #Homotopy and Cohomology in Algebraic Topology #Mathematical physics #Mathematics #Moduli space #Physics #Pure mathematics #Quiver #Riemann surface #Supersymmetric gauge theory #Surface (topology) #hep-th #math.AG
paper · pdf · doi:10.1007/jhep07(2019)014
published in Journal of High Energy Physics 2019(7) (Springer Nature) · 65 pages, 2 figures, minor corrections, version to appear in JHEP
openalex created_date 2018/12/22 · openalex publication_date 2019/07/01 · arxiv created 2019/07/02 · arxiv updated 2020/01/08 · openalex updated_date 2026/08/06
A bstract We explore the geometric interpretation of the twisted index of 3d N <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 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.