SO(N) Lattice Gauge Theory, planar and beyond
SO(N) Lattice Gauge Theory, planar and beyond
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SO(N) 晶格规范理论，平面及其他
DOI：
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发表时间：
2016
影响因子：
3
通讯作者：
S. Ganguly
中科院分区：
文献类型：
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作者：
Riddhipratim Basu;S. Ganguly
长期以来，物理文献中一直将格子规范理论作为量子杨-米尔斯理论的离散近似进行研究。这些模型中感兴趣的主要统计数据是所谓的威尔逊循环变量的期望。在本文中，我们继续Chatterjee [3]发起的项目，通过规范弦对偶性在一定限度内理解格子规范理论中的威尔逊环期望。本文的目的是通过给出涉及与装饰树和非交叉分区等对象对应的弦轨迹的更具几何性的图像，更好地理解强耦合机制中的基础组合学。利用与自由概率论的联系，我们提供了平面环境中循环期望的详细描述，这也为高维轨迹的结构提供了一定的见解。利用这一点，我们构建了一个示例，表明在任何维度中，威尔逊环面积定律下界都不具有完全的普遍性。 © 2018 Wiley 期刊公司。
Lattice gauge theories have been studied in the physics literature as discrete approximations to quantum Yang‐Mills theory for a long time. Primary statistics of interest in these models are expectations of the so‐called Wilson loop variables. In this article we continue the program initiated by Chatterjee [3] to understand Wilson loop expectations in lattice gauge theories in a certain limit through gauge‐string duality. The objective in this paper is to better understand the underlying combinatorics in the strong coupling regime by giving a more geometric picture of string trajectories involving correspondence to objects such as decorated trees and noncrossing partitions. Using connections with free probability theory, we provide an elaborate description of loop expectations in the planar setting, which provides certain insights into structures of higher‐dimensional trajectories as well. Exploiting this, we construct an example showing that in any dimension, the Wilson loop area law lower bound does not hold in full generality. © 2018 Wiley Periodicals, Inc.