Foams and KZ-equations in Rozansky-Witten theories
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866916338712182784 |
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| author | Gukov, Sergei Haghighat, Babak Reshetikhin, Nicolai |
| author_facet | Gukov, Sergei Haghighat, Babak Reshetikhin, Nicolai |
| contents | In this paper, we present a geometric description of foams, which are prevalent in topological quantum field theories (TQFTs) based on quantum algebra, and reciprocally explore the geometry of Rozansky-Witten (RW) theory from an algebraic perspective. This approach illuminates various aspects of decorated TQFTs via geometry of the target space $X$ of RW theory. Through the formulation of the Knizhnik-Zamolodchikov (KZ) equation within this geometric framework, we derive the corresponding braiding and associator morphisms. We discuss applications where the target space of RW theory emerges as the Coulomb branch of a compactified 6d SCFT or Little String Theory, with the latter being particularly intriguing as it results in a compact $X$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2407_19757 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Foams and KZ-equations in Rozansky-Witten theories Gukov, Sergei Haghighat, Babak Reshetikhin, Nicolai High Energy Physics - Theory In this paper, we present a geometric description of foams, which are prevalent in topological quantum field theories (TQFTs) based on quantum algebra, and reciprocally explore the geometry of Rozansky-Witten (RW) theory from an algebraic perspective. This approach illuminates various aspects of decorated TQFTs via geometry of the target space $X$ of RW theory. Through the formulation of the Knizhnik-Zamolodchikov (KZ) equation within this geometric framework, we derive the corresponding braiding and associator morphisms. We discuss applications where the target space of RW theory emerges as the Coulomb branch of a compactified 6d SCFT or Little String Theory, with the latter being particularly intriguing as it results in a compact $X$. |
| title | Foams and KZ-equations in Rozansky-Witten theories |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2407.19757 |