论文标题
巨大的射线手扭转和路径积分
Massive Ray-Singer Torsion and Path Integrals
论文作者
论文摘要
零模式是拓扑字段理论的重要组成部分，但它们通常也是对相关路径积分进行明确评估的障碍。为了解决此问题的情况，在各种拓扑量学理论中出现的射线手扭转情况，我们引入了射线手扭转的大规模变体，涉及具有质量但没有零模式的扭曲的laplacian的决定因素。这具有允许一个人明确跟踪理论的零模式依赖性。我们建立了这种巨大的射线手扭转的许多一般特性。对于产品歧管，$ m = n \ times s^1 $，映射托里可以将质量术语解释为flat $ \ mathbb {r} _ {+} $连接，并且可以将大量的射线手扭转表示为schwarz类型拓扑仪的路径积分。使用路径积分技术，可以明智地选择代数量规固定条件和变量的变化，而变量会留下自由动作，我们可以以封闭形式评估扭转。我们讨论了许多应用程序，包括$ g = psl（2，r）$的$ s^1 $上的射线摩擦扭转的明确计算以及对有限订单映射托里（Tori）扭转的油炸公式的概括的路径积分。
Zero modes are an essential part of topological field theories, but they are frequently also an obstacle to the explicit evaluation of the associated path integrals. In order to address this issue in the case of Ray-Singer Torsion, which appears in various topological gauge theories, we introduce a massive variant of the Ray-Singer Torsion which involves determinants of the twisted Laplacian with mass but without zero modes. This has the advantage of allowing one to explicitly keep track of the zero mode dependence of the theory. We establish a number of general properties of this massive Ray-Singer Torsion. For product manifolds $M=N \times S^1$ and mapping tori one is able to interpret the mass term as a flat $\mathbb{R}_{+}$ connection and one can represent the massive Ray-Singer Torsion as the path integral of a Schwarz type topological gauge theory. Using path integral techniques, with a judicious choice of an algebraic gauge fixing condition and a change of variables which leaves one with a free action, we can evaluate the torsion in closed form. We discuss a number of applications, including an explicit calculation of the Ray-Singer Torsion on $S^1$ for $G=PSL(2,R)$ and a path integral derivation of a generalisation of a formula of Fried for the torsion of finite order mapping tori.
