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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2504.19403 |
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| _version_ | 1866916946488852480 |
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| author | Herrera, Rafael Cardona, Sergio A. Holguin Velez, Alexander Quintero |
| author_facet | Herrera, Rafael Cardona, Sergio A. Holguin Velez, Alexander Quintero |
| contents | We construct a topological quantum field theory based on the moduli space of $\mathrm{Spin}(7)$-instantons on 8-dimensional manifolds. Using the Mathai-Quillen formalism, we derive the action of the theory in purely geometric terms, which coincides with prior results in the literature. We then reformulate the theory within the AKSZ formalism, obtaining a Batalin-Vilkovisky action that, after gauge fixing, matches our Mathai-Quillen construction while making the BRST symmetry explicit and providing a natural framework for classical observables. We also show that the Batalin-Vilkovisky action can be elegantly recast as a Chern-Simons type theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_19403 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A topological quantum field theory for $\mathrm{Spin}(7)$-instantons Herrera, Rafael Cardona, Sergio A. Holguin Velez, Alexander Quintero High Energy Physics - Theory Mathematical Physics Differential Geometry We construct a topological quantum field theory based on the moduli space of $\mathrm{Spin}(7)$-instantons on 8-dimensional manifolds. Using the Mathai-Quillen formalism, we derive the action of the theory in purely geometric terms, which coincides with prior results in the literature. We then reformulate the theory within the AKSZ formalism, obtaining a Batalin-Vilkovisky action that, after gauge fixing, matches our Mathai-Quillen construction while making the BRST symmetry explicit and providing a natural framework for classical observables. We also show that the Batalin-Vilkovisky action can be elegantly recast as a Chern-Simons type theory. |
| title | A topological quantum field theory for $\mathrm{Spin}(7)$-instantons |
| topic | High Energy Physics - Theory Mathematical Physics Differential Geometry |
| url | https://arxiv.org/abs/2504.19403 |