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arXiv · 2301.01131

BKP-Affine Coordinates and Emergent Geometry of Generalized Br\'ezin-Gross-Witten Tau-Functions

Zhiyuan Wang·Chenglang Yang·Qingsheng Zhang
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Abstract

Following Zhou's framework, we consider the emergent geometry of the generalized Br\'ezin-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-Su{\l}kowski emerges from the BKP-affine coordinates and Eynard-Orantin topological recursion.

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Zhiyuan Wang, Chenglang Yang, Qingsheng Zhang. 2023-01-03. BKP-Affine Coordinates and Emergent Geometry of Generalized Br\'ezin-Gross-Witten Tau-Functions. https://arxiv.org/abs/2301.01131

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