标题： 模拟非对易场理论 显示英文标题

标题： Simulating non-commutative field theory

摘要： 非交换（NC）场论可以映射到扭曲的矩阵模型。 这种映射使得它们能够进行蒙特卡洛模拟，其中矩阵模型的大N极限描述了NC场论的连续极限。 首先我们给出二维秩1 NC规范理论的数值结果，结果表明它是可重整化的。 在小面积下，威尔逊环的面积定律成立，但在大面积下我们观察到一个旋转相，这对应于阿哈罗诺夫-玻姆效应。 接下来我们研究d=3中的NC φ^4模型并探索其相图。 我们的结果与古伯瑟和桑迪在d=4中的猜想一致，他们预测有序区域会分裂成均匀相和由条纹图案主导的相。 显示英文摘要

摘要： Non-commutative (NC) field theories can be mapped onto twisted matrix models. This mapping enables their Monte Carlo simulation, where the large N limit of the matrix models describes the continuum limit of NC field theory. First we present numeric results for 2d NC gauge theory of rank 1, which turns out to be renormalizable. The area law for the Wilson loop holds at small area, but at large area we observe a rotating phase, which corresponds to an Aharonov-Bohm effect. Next we investigate the NC phi^4 model in d=3 and explore its phase diagram. Our results agree with a conjecture by Gubser and Sondhi in d=4, who predicted that the ordered regime splits into a uniform phase and a phase dominated by stripe patterns.