Cut-and-join description of generalized Brezin–Gross–Witten model
Aug 4, 2016
53 pages
Published in:
- Adv.Theor.Math.Phys. 22 (2018) 1347-1399
- Published: 2018
e-Print:
- 1608.01627 [math-ph]
Report number:
- ITEP/TH-18/16,
- ITEP-TH-18-16
View in:
Citations per year
Abstract: (International Press)
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. Explicit expressions for the coefficients of the tau-function and the free energy are derived, and a compact formula for the genus zero contribution is conjectured. A family of polynomial solutions of the KdV hierarchy, given by the Schur functions, is obtained for the half-integer values of the parameter. The quantum spectral curve and its classical limit are discussed.Note:
- 45 pages
- Korteweg-de Vries equation: hierarchy
- constraint: Virasoro
- Korteweg-de Vries equation: solution
- approximation: classical
- tau-function
- correlation function
- partition function
- loop equation
- free energy
- deformation
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