BKP-Affine Coordinates and Emergent Geometry of Generalized Brézin-Gross-Witten Tau-Functions

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.