Thermodynamic limit of random partitions and dispertionless Todahierarchy
Thermodynamic limit of random partitions and dispertionless Todahierarchy
复制标题
随机分区和无色散托达层次结构的热力学极限
DOI：
10.1088/1751-8113/45/2/025403
复制
发表时间：
2012
期刊：
影响因子：
--
通讯作者：
中津了勇
中科院分区：
文献类型：
--
作者：
高崎金久;中津了勇
研究了4维和5维超对称U(1)规范理论的瞬子和的随机配分模型的热力学极限。在统计模型中，物理可观量对应于外部势。根据Maya图的密度函数重新定义了配分函数。热力学极限由与配分函数中的主导项相关联的杨图的极限形状所支配。将极限形状转化为一个变分问题，进而转化为标量Riemann-Hilbert问题。这个Riemann-Hilbert问题借助于一条复曲线来求解，它可以被认为是变形U(1)规范理论的Seiberg-Witten曲线。Riemann-Hilbert问题的这个解被证明为满足一对广义弦方程的无色散Toda族的一个特解。结果表明，5D规范理论的广义弦方程与统计模型的隐对称性有关。文中还考虑了前势和Seiberg-Witten微分。
We study the thermodynamic limit of random partition models for the instanton sum of 4D and 5D supersymmetric U (1) gauge theories deformed by some physical observables. The physical observables correspond to external potentials in the statistical model. The partition function is reformulated in terms of the density function of Maya diagrams. The thermodynamic limit is governed by a limit shape of Young diagrams associated with dominant terms in the partition function. The limit shape is characterized by a variational problem, which is further converted to a scalar-valued Riemann–Hilbert problem. This Riemann–Hilbert problem is solved with the aid of a complex curve, which may be thought of as the Seiberg–Witten curve of the deformed U (1) gauge theory. This solution of the Riemann–Hilbert problem is identified with a special solution of the dispersionless Toda hierarchy that satisfies a pair of generalized string equations. The generalized string equations for the 5D gauge theory are shown to be related to hidden symmetries of the statistical model. The prepotential and the Seiberg–Witten differential are also considered.