Cohomological representations of quantum tau functions
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866913814400729088 |
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| author | Blot, Xavier Lewański, Danilo Shadrin, Sergey |
| author_facet | Blot, Xavier Lewański, Danilo Shadrin, Sergey |
| contents | In 2016, Buryak and Rossi introduced the quantum Double Ramification (DR) hierarchies which associate a quantum integrable hierarchy to any Cohomological Field Theory (CohFT). Shortly after, they introduced, in collaboration with Dubrovin and Guéré, the quantum tau functions of these hierarchies. In this work, we study quantum tau functions associated to a specific solution called the topological solution. We provide two cohomological representations for the correlators of these tau functions. The first representation involves an analog in the quantum setting of the $A$-class of the DR-DZ equivalence. The second representation, valid for CohFT of low degree, involves the so-called $Ω$-classes. Furthermore, we establish the string and dilaton equations for these tau functions, and present certain vanishing of their correlators. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2411_03499 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Cohomological representations of quantum tau functions Blot, Xavier Lewański, Danilo Shadrin, Sergey Algebraic Geometry In 2016, Buryak and Rossi introduced the quantum Double Ramification (DR) hierarchies which associate a quantum integrable hierarchy to any Cohomological Field Theory (CohFT). Shortly after, they introduced, in collaboration with Dubrovin and Guéré, the quantum tau functions of these hierarchies. In this work, we study quantum tau functions associated to a specific solution called the topological solution. We provide two cohomological representations for the correlators of these tau functions. The first representation involves an analog in the quantum setting of the $A$-class of the DR-DZ equivalence. The second representation, valid for CohFT of low degree, involves the so-called $Ω$-classes. Furthermore, we establish the string and dilaton equations for these tau functions, and present certain vanishing of their correlators. |
| title | Cohomological representations of quantum tau functions |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2411.03499 |