R-torsion and linking numbers from simplicial abelian gauge theories
R-torsion and linking numbers from simplicial abelian gauge theories
复制标题
R 扭转和单纯阿贝尔规范理论中的连接数
DOI：
--
复制
发表时间：
1996
期刊：
影响因子：
--
通讯作者：
D. Adams
中科院分区：
文献类型：
--
作者：
D. Adams
Simplicial versions of topological abelian gauge theories are constructed which reproduce the continuum expressions for the partition function and Wilson expectation value of linked loops, expressible in terms of R-torsion and linking numbers respectively. The new feature which makes this possible is the introduction of simplicial fields (cochains) associated with the dual triangulation of the background manifold, as well as with the triangulation itself. This doubling of fields, reminiscent of lattice fermion doubling, is required because the natural simplicial analogue of the Hodge star operator maps between cochains of a triangulation and cochains of the dual triangulation. The simplicial analogue of Hodge-de Rham theory is developed, along with a natural simplicial framework for considering linking numbers of framed loops. When the loops represent torsion elements of the homology of the manifold then Q/Z-valued torsion pairings appear in place of linking numbers for certain discrete values of the coupling parameter of the theory.
