标题： 非阿贝尔杨-米尔斯格点上的对偶计算 显示英文标题

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

摘要： 在过去几十年里，人们提出了许多关于在格点上用非阿贝尔杨-米尔斯理论的对偶形式进行计算的方法。 受对偶模型提供的规范不变、几何直观以及U(1)情形下对偶应用的成功启发，我们重新审视了使用非阿贝尔对偶模型进行数值计算是否可行这一问题。 具体来说，我们考虑三维SU(2)纯杨-米尔斯理论作为一个既可及又非平凡的情况，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起来的方法，我们推导出一种高效计算对偶振幅的算法，并描述了用于抽样的梅特罗波利斯移动方法。 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中的先前工作联系起来，解决了遗留的一些问题。 我们报告了在不同大小和耦合强度的格点上的自旋期望值计算结果，这些结果与我们常规的格点计算一致。 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的问题中的应用。 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 derive an algorithm for efficiently computing the dual amplitude and describe Metropolis moves for sampling the dual ensemble. We relate our algorithms to prior work in non-abelian dual computations of Hari Dass and his collaborators, addressing several problems that have 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.