BKP-Affine Coordinates and Emergent Geometry of Generalized Brézin-Gross-Witten Tau-Functions
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866915103369068544 |
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| author | Wang, Zhiyuan Yang, Chenglang Zhang, Qingsheng |
| author_facet | Wang, Zhiyuan Yang, Chenglang Zhang, Qingsheng |
| contents | Following Zhou's framework, we consider the emergent geometry of the generalized Brézin-Gross-Witten models whose partition functions are known to be a family of tau-functions of the BKP hierarchy. More precisely, we construct a spectral curve together with its special deformation, and show that the Eynard-Orantin topological recursion on this spectral curve emerges naturally from the Virasoro constraints for the generalized BGW tau-functions. Moreover, we give the explicit expressions for the BKP-affine coordinates of these tau-functions and their generating series. The BKP-affine coordinates and the topological recursion provide two different approaches towards the concrete computations of the connected $n$-point functions. Finally, we show that the quantum spectral curve of type $B$ in the sense of Gukov-Sułkowski emerges from the BKP-affine coordinates and Eynard-Orantin topological recursion. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_01131 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | BKP-Affine Coordinates and Emergent Geometry of Generalized Brézin-Gross-Witten Tau-Functions Wang, Zhiyuan Yang, Chenglang Zhang, Qingsheng Mathematical Physics High Energy Physics - Theory Exactly Solvable and Integrable Systems Following Zhou's framework, we consider the emergent geometry of the generalized Brézin-Gross-Witten models whose partition functions are known to be a family of tau-functions of the BKP hierarchy. More precisely, we construct a spectral curve together with its special deformation, and show that the Eynard-Orantin topological recursion on this spectral curve emerges naturally from the Virasoro constraints for the generalized BGW tau-functions. Moreover, we give the explicit expressions for the BKP-affine coordinates of these tau-functions and their generating series. The BKP-affine coordinates and the topological recursion provide two different approaches towards the concrete computations of the connected $n$-point functions. Finally, we show that the quantum spectral curve of type $B$ in the sense of Gukov-Sułkowski emerges from the BKP-affine coordinates and Eynard-Orantin topological recursion. |
| title | BKP-Affine Coordinates and Emergent Geometry of Generalized Brézin-Gross-Witten Tau-Functions |
| topic | Mathematical Physics High Energy Physics - Theory Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/2301.01131 |