论文标题
2D U（1）符号理论的复杂Langevin分析具有$θ$项
Complex Langevin analysis of 2D U(1) gauge theory on a torus with a $θ$ term
论文作者
论文摘要
蒙特卡洛模拟具有$θ$项的仪表理论由于标志问题而非常困难。最近，基于使动力学变量复杂的想法解决此问题的主要进展。在这里，我们考虑了复杂的Langevin方法（CLM），这是其低计算成本的有希望的方法。但是，该方法的缺点是必须满足的条件的存在，以使结果正确。作为第一步，我们将方法应用于具有$θ$项的圆环上的2D U（1）量规理论，可以通过分析解决。我们发现，由于$θ$项的拓扑性质，该方法的幼稚实现失败了。为了避免此问题，我们在刺穿的圆环上模拟了相同的理论，该理论等同于$ |θ|的无限体积限制中的原始模型。 <π$。相当令人惊讶的是，我们发现CLM即使在大$θ$处的刺穿圆环的确切结果也可以重现，并在$θ$上进行刺穿的圆环，在该$θ$中，刺穿附近的链接变量远离统一。
Monte Carlo simulation of gauge theories with a $θ$ term is known to be extremely difficult due to the sign problem. Recently there has been major progress in solving this problem based on the idea of complexifying dynamical variables. Here we consider the complex Langevin method (CLM), which is a promising approach for its low computational cost. The drawback of this method, however, is the existence of a condition that has to be met in order for the results to be correct. As a first step, we apply the method to 2D U(1) gauge theory on a torus with a $θ$ term, which can be solved analytically. We find that a naive implementation of the method fails because of the topological nature of the $θ$ term. In order to circumvent this problem, we simulate the same theory on a punctured torus, which is equivalent to the original model in the infinite volume limit for $ |θ| < π$. Rather surprisingly, we find that the CLM works and reproduces the exact results for a punctured torus even at large $θ$, where the link variables near the puncture become very far from being unitary.
