Dual of 3-dimensional pure SU (2) lattice gauge theory and the Ponzano-Regge model
Dual of 3-dimensional pure SU (2) lattice gauge theory and the Ponzano-Regge model
复制标题
3 维纯 SU (2) 晶格规范理论与 Ponzano-Regge 模型的对偶
DOI：
10.1016/0370-2693(93)91254-k
复制
发表时间：
1992
期刊：
影响因子：
--
通讯作者：
Manu Mathur
中科院分区：
文献类型：
--
作者：
R. Anishetty;S. Cheluvaraja;H. Sharatchandra;Manu Mathur
通过对所有链变量进行特征展开和积分，将三维纯SU(2)格点规范理论的配分函数改写为6J符号。其结果是三维引力的Pozano-Regge模型，其中的一个项明确地打破了一般的坐标不变性。相反，我们证明了Ponzano-Regge模型的对偶是一个SU(2)格点规范理论，其中所有的斑点变量都被限制到单位矩阵，因此该模型不需要进一步的正则化。我们的方法适用于其他具有任意维非阿贝尔对称性的模型，并提供了配分函数的对偶变换。
By carrying out a character expansion and integration over all link variables, the partition function of 3-dimensional pure SU (2) lattice gauge theory is rewritten in terms of 6j symbols. The results is the Pozano-Regge model of 3-dimensional gravity with a term that explicitly breaks general coordinate invariance. Conversely, we show that the dual of the Ponzano-Regge model is an SU (2) lattice gauge theory where all plaquette variables are constrained to the identity matrix and therefore the model needs no further regularization. Our techniques are applicable to other models with non-abelian symmetries in any dimension and provide a duality transform for the partition function.