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| Main Authors: | , , |
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| Format: | Preprint |
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2021
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2107.06734 |
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| _version_ | 1866913628106522624 |
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| author | Gwilliam, Owen Rabinovich, Eugene Williams, Brian R. |
| author_facet | Gwilliam, Owen Rabinovich, Eugene Williams, Brian R. |
| contents | In both mathematics and physics, topological field theories and holomorphic field theories appear naturally, but there are interesting theories that are hybrids -- looking topological in some directions and holomorphic in others -- such as twists of supersymmetric field theories or Costello's 4-dimensional Chern--Simons theory. In this paper we construct perturbative, one-loop quantizations rigorously on the model manifold $\mathbb{R}^m \times \mathbb{C}^n$, and find a remarkable vanishing result about anomalies: the one-loop obstruction to quantization on $\mathbb{R}^m\times \mathbb{C}^n$ vanishes when $m\geq 1$. A concrete consequence of our results is the existence of exact and finite quantizations at one-loop for twists of pure $\mathcal{N} =2$ four-dimensional supersymmetric Yang--Mills theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2107_06734 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Quantization of topological-holomorphic field theories: local aspects Gwilliam, Owen Rabinovich, Eugene Williams, Brian R. Mathematical Physics High Energy Physics - Theory Differential Geometry In both mathematics and physics, topological field theories and holomorphic field theories appear naturally, but there are interesting theories that are hybrids -- looking topological in some directions and holomorphic in others -- such as twists of supersymmetric field theories or Costello's 4-dimensional Chern--Simons theory. In this paper we construct perturbative, one-loop quantizations rigorously on the model manifold $\mathbb{R}^m \times \mathbb{C}^n$, and find a remarkable vanishing result about anomalies: the one-loop obstruction to quantization on $\mathbb{R}^m\times \mathbb{C}^n$ vanishes when $m\geq 1$. A concrete consequence of our results is the existence of exact and finite quantizations at one-loop for twists of pure $\mathcal{N} =2$ four-dimensional supersymmetric Yang--Mills theory. |
| title | Quantization of topological-holomorphic field theories: local aspects |
| topic | Mathematical Physics High Energy Physics - Theory Differential Geometry |
| url | https://arxiv.org/abs/2107.06734 |