Cut-and-join description of generalized Brezin-Gross-Witten model
Cut-and-join description of generalized Brezin-Gross-Witten model
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DOI：
10.4310/atmp.2018.v22.n6.a1
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发表时间：
2016-08
期刊：
影响因子：
--
通讯作者：
A. Alexandrov
中科院分区：
文献类型：
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作者：
A. Alexandrov
研究了KdV族的τ函数Brezin-Gross-维滕模型及其自然单参数变形广义Brezin-Gross-维滕τ函数.特别是，我们推导出Virasoro约束，它完全指定的分区函数。我们用切割和连接算子来解决它们。Virasoro约束导致回路方程，我们解决的相关函数。导出了τ函数系数和自由能的显式表达式，并给出了亏格零贡献的简洁公式。一个家庭的多项式解决方案的KdV族，给出的舒尔功能，获得的参数的半整数值。讨论了量子谱曲线及其经典极限。
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.