标题： 非交换杨-米尔斯在格点上的对偶计算 显示英文标题

标题： Dual Computations of Non-abelian Yang-Mills on the Lattice

摘要： 在过去几十年中，人们提出了许多在格点上计算非阿贝尔杨-米尔斯理论的对偶形式的方法。 受对偶模型提供的规范不变、几何图像以及在U(1)情况下对偶性的成功应用的启发，我们重新审视使用非阿贝尔对偶模型进行数值计算是否具有可行性。 具体而言，我们考虑三维SU(2)纯杨-米尔斯理论作为一个易于处理但又不平凡的案例，其中规范群是非阿贝尔的。 利用最近在自旋泡沫量子引力背景下发展出的方法，我们描述了一种用于采样对偶系综并高效计算对偶振幅的Metropolis算法。 我们将我们的算法与Hari Dass及其合作者在非阿贝尔对偶计算方面的先前工作联系起来，解决了几个（据我们所知）之前未解决的问题。 我们报告了在一系列格点大小和耦合常数下的自旋期望值计算结果，这些结果与传统的格点计算结果一致。 最后，我们展望了对偶方法的进一步发展及其在当前感兴趣问题中的应用。 显示英文摘要

摘要： In the past several decades there have been a number of proposals for computing with dual forms of non-abelian Yang-Mills theories on the lattice. Motivated by the gauge-invariant, geometric picture offered by dual models and successful applications of duality in the U(1) case, we revisit the question of whether it is practical to perform numerical computation using non-abelian dual models. Specifically, we consider three-dimensional SU(2) pure Yang-Mills as an accessible yet non-trivial case in which the gauge group is non-abelian. Using methods developed recently in the context of spin foam quantum gravity, we describe a Metropolis algorithm for sampling the dual ensemble and efficiently computing the dual amplitude. We relate our algorithms to prior work in non-abelian dual computations of Hari Dass and his collaborators, addressing several problems that have (to the best our knowledge) been left open. We report results of spin expectation value computations over a range of lattice sizes and couplings that are in agreement with our conventional lattice computations. We conclude with an outlook on further development of dual methods and their application to problems of current interest.