Abstract loop equations, topological recursion and new applications
Abstract loop equations, topological recursion and new applications
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抽象循环方程、拓扑递归及新应用
DOI：
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
N. Orantin
中科院分区：
文献类型：
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作者：
G. Borot;B. Eynard;N. Orantin
本文提出了“抽象回路方程”的概念，并证明了在某些假设下，它们的解是由拓扑递归给出的，特别是结果具有普遍形式。一个和两个厄米矩阵模型的Schwinger-Dyson方程，以及Opnq模型的Schwinger-Dyson方程作为特例出现。我们研究排斥粒子系统的应用，并解释我们的循环方程的概念是如何与Virasoro约束。然后，作为一个特殊的情况下，我们详细研究了应用程序枚举问题的一般类的非相交的循环模型的随机格的所有拓扑结构，SUpNq陈-西蒙斯不变量的环面结在大N扩展。我们还提到了Liouville理论在正亏格曲面上的应用，提出了“抽象回路方程”的概念，并证明了在某些假设下，它们的解是由拓扑递归提供的，特别是结果具有普遍形式。一个和两个厄米矩阵模型的Schwinger-Dyson方程，以及Opnq模型的Schwinger-Dyson方程作为特例出现。我们研究排斥粒子系统的应用，并解释我们的循环方程的概念是如何与Virasoro约束。然后，作为一个特殊的情况下，我们详细研究了应用程序枚举问题的一般类的非相交的循环模型的随机格的所有拓扑结构，SUpNq陈-西蒙斯不变量的环面结在大N扩展。我们还提到了应用刘维理论的表面上的积极属。
loop equations, topological recursion and applications Gaetan Borot, Bertrand Eynard, Nicolas Orantin Abstract We formulate a notion of ”abstract loop equations”, and show that their solution is provided by a topological recursion under some assumptions, in particular the result takes a universal form. The Schwinger-Dyson equation of the one and two hermitian matrix models, and of the Opnq model appear as special cases. We study applications to repulsive particles systems, and explain how our notion of loop equations are related to Virasoro constraints. Then, as a special case, we study in detail applications to enumeration problems in a general class of non-intersecting loop models on the random lattice of all topologies, to SUpNq Chern-Simons invariants of torus knots in the large N expansion. We also mention an application to Liouville theory on surfaces of positive genus.We formulate a notion of ”abstract loop equations”, and show that their solution is provided by a topological recursion under some assumptions, in particular the result takes a universal form. The Schwinger-Dyson equation of the one and two hermitian matrix models, and of the Opnq model appear as special cases. We study applications to repulsive particles systems, and explain how our notion of loop equations are related to Virasoro constraints. Then, as a special case, we study in detail applications to enumeration problems in a general class of non-intersecting loop models on the random lattice of all topologies, to SUpNq Chern-Simons invariants of torus knots in the large N expansion. We also mention an application to Liouville theory on surfaces of positive genus.
排斥粒子系统和随机矩阵的局部普遍性
影响因子：
2.3
作者：
F. Götze;M. Venker
通讯作者：
M. Venker