Boundaries & localisation with a topological twist

Journal article

We study the partition functions of topologically twisted 3d N = 2 gauge theories on a hemisphere spacetime with boundary HS2 × S1. We show that the partition function may be localised to either the Higgs branch or the Coulomb branch where the contributions to the path integral are vortex or monopole configurations respectively. Turning to N = 4 supersymmetry, we consider partition functions for exceptional Dirichlet boundary conditions that yield a complete set of ‘IR holomorphic blocks’. We demonstrate that these correspond to vertex functions: equivariant Euler characteristics of quasimap moduli spaces. In this context, we explore the geometric interpretation of both the Higgs and Coulomb branch localisation schemes in terms of the enumerative geometry of quasimaps and discuss the action of mirror symmetry.

Authors: Crew, S; Zhang, D; Zhao, B

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Springer
• Journal: Journal of High Energy Physics
• Volume: 2023
• Issue: 10
• Pages: 93
• Article number: 93
• Publication date: 2023-10-16
• Acceptance date: 2023-09-27
• DOI: 10.1007/jhep10(2023)093
• EISSN: 1029-8479
• ISSN: 1126-6708
• Language: English
• Keywords: Supersymmetric Gauge Theory; Solitons Monopoles and Instantons; Differential and Algebraic Geometry