Tropological Sigma Models
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866913398884663296 |
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| author | Albrychiewicz, Emil Ellers, Kai-Isaak Valiente, Andrés Franco Hořava, Petr |
| author_facet | Albrychiewicz, Emil Ellers, Kai-Isaak Valiente, Andrés Franco Hořava, Petr |
| contents | With the use of mathematical techniques of tropical geometry, it was shown by Mikhalkin some twenty years ago that certain Gromov-Witten invariants associated with topological quantum field theories of pseudoholomorphic maps can be computed by going to the tropical limit of the geometries in question. Here we examine this phenomenon from the physics perspective of topological quantum field theory in the path integral representation, beginning with the case of the topological sigma model before coupling it to topological gravity. We identify the tropicalization of the localization equations, investigate its geometry and symmetries, and study the theory and its observables using the standard cohomological BRST methods. We find that the worldsheet theory exhibits a nonrelativistic structure, similar to theories of the Lifshitz type. Its path-integral formulation does not require a worldsheet complex structure; instead, it is based on a worldsheet foliation structure. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_00745 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Tropological Sigma Models Albrychiewicz, Emil Ellers, Kai-Isaak Valiente, Andrés Franco Hořava, Petr High Energy Physics - Theory Mathematical Physics Algebraic Geometry Differential Geometry With the use of mathematical techniques of tropical geometry, it was shown by Mikhalkin some twenty years ago that certain Gromov-Witten invariants associated with topological quantum field theories of pseudoholomorphic maps can be computed by going to the tropical limit of the geometries in question. Here we examine this phenomenon from the physics perspective of topological quantum field theory in the path integral representation, beginning with the case of the topological sigma model before coupling it to topological gravity. We identify the tropicalization of the localization equations, investigate its geometry and symmetries, and study the theory and its observables using the standard cohomological BRST methods. We find that the worldsheet theory exhibits a nonrelativistic structure, similar to theories of the Lifshitz type. Its path-integral formulation does not require a worldsheet complex structure; instead, it is based on a worldsheet foliation structure. |
| title | Tropological Sigma Models |
| topic | High Energy Physics - Theory Mathematical Physics Algebraic Geometry Differential Geometry |
| url | https://arxiv.org/abs/2311.00745 |