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arXiv 1010.4240hep-lathep-th
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三维格点引力的超对称杨-米尔斯理论

Three dimensional lattice gravity as supersymmetric Yang-Mills theory

Simon Catterall

摘要:

我们证明了具有规范群SU(2)的三维扭曲超对称Yang-Mills理论具有一组拓扑观测量,其期望值可以在相关的Chern Simons理论中计算。这个陈-西蒙斯理论是作为三维欧几里德量子引力的定义而提出的。由于YM理论允许保持拓扑观测值的离散化,我们推测它可以作为量子引力理论的非微扰定义。

英文摘要:

We argue that a certain twisted supersymmetric Yang-Mills theory in three dimensions with gauge group SU(2) possesses a set of topological observables whose expectation values can be computed in a related Chern Simons theory. This Chern Simons theory has been proposed as a definition of three dimensional Euclidean quantum gravity. Since the YM theory admits a discretization which preserves the values of topological observables we conjecture that it can be used as a non-perturbative definition of the quantum gravity theory.

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