Boundaries & localisation with a topological twist
Abstract We study the partition functions of topologically twisted 3d N $$ \mathcal{N} $$ = 2 gauge theories on a hemisphere spacetime with boundary HS 2 × S 1. We show that the partition function may be localised to either the Higgs branch or the Coulomb branch where the contributions to the path i...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2023-10-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP10(2023)093 |
| _version_ | 1797341372801351680 |
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| author | Samuel Crew Daniel Zhang Boan Zhao |
| author_facet | Samuel Crew Daniel Zhang Boan Zhao |
| author_sort | Samuel Crew |
| collection | DOAJ |
| description | Abstract We study the partition functions of topologically twisted 3d N $$ \mathcal{N} $$ = 2 gauge theories on a hemisphere spacetime with boundary HS 2 × S 1. 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 $$ \mathcal{N} $$ = 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. |
| first_indexed | 2024-03-08T10:18:05Z |
| format | Article |
| id | doaj.art-c87e5af150f34ef0b755c2c7af8ebf42 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-03-08T10:18:05Z |
| publishDate | 2023-10-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-c87e5af150f34ef0b755c2c7af8ebf422024-01-28T12:19:37ZengSpringerOpenJournal of High Energy Physics1029-84792023-10-0120231014610.1007/JHEP10(2023)093Boundaries & localisation with a topological twistSamuel Crew0Daniel Zhang1Boan Zhao2Faculty of Computer Science, Ruhr University BochumSt John’s College, University of OxfordDAMTP, Centre for Mathematical Sciences, University of CambridgeAbstract We study the partition functions of topologically twisted 3d N $$ \mathcal{N} $$ = 2 gauge theories on a hemisphere spacetime with boundary HS 2 × S 1. 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 $$ \mathcal{N} $$ = 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.https://doi.org/10.1007/JHEP10(2023)093Supersymmetric Gauge TheoryDifferential and Algebraic GeometrySolitons Monopoles and Instantons |
| spellingShingle | Samuel Crew Daniel Zhang Boan Zhao Boundaries & localisation with a topological twist Journal of High Energy Physics Supersymmetric Gauge Theory Differential and Algebraic Geometry Solitons Monopoles and Instantons |
| title | Boundaries & localisation with a topological twist |
| title_full | Boundaries & localisation with a topological twist |
| title_fullStr | Boundaries & localisation with a topological twist |
| title_full_unstemmed | Boundaries & localisation with a topological twist |
| title_short | Boundaries & localisation with a topological twist |
| title_sort | boundaries localisation with a topological twist |
| topic | Supersymmetric Gauge Theory Differential and Algebraic Geometry Solitons Monopoles and Instantons |
| url | https://doi.org/10.1007/JHEP10(2023)093 |
| work_keys_str_mv | AT samuelcrew boundarieslocalisationwithatopologicaltwist AT danielzhang boundarieslocalisationwithatopologicaltwist AT boanzhao boundarieslocalisationwithatopologicaltwist |