Cut-and-join description of generalized Brezin-Gross-Witten model

Understand

We investigate the Brezin-Gross-Witten model, a tau-function of the KdV hierarchy, and its natural one-parameter deformation, the generalized Brezin-Gross-Witten tau-function.

• In particular, we derive the Virasoro constraints, which completely specify the partition function.
• We solve them in terms of the cut-and-join operator.
• The Virasoro constraints lead to the loop equations, which we solve in terms of the correlation functions.