A geometric discretisation scheme applied to the Abelian Chern-Simons theory

Details A geometric discretisation scheme applied to the Abelian Chern-Simons theory A geometric discretisation scheme applied to the Abelian Chern-Simons theory

2000-01-07

arxiv.org/abs/hep-th/0001030v1

Phys.Rev. E61 (2000) 3174-3185

Physics

High Energy Physics

High Energy Physics - Theory

27 pages, 5 figures, 6 tables. in latex

Scientific paper

10.1103/PhysRevE.61.3174

We give a detailed general description of a recent geometrical discretisation scheme and illustrate, by explicit numerical calculation, the scheme's ability to capture topological features. The scheme is applied to the Abelian Chern-Simons theory and leads, after a necessary field doubling, to an expression for the discrete partition function in terms of untwisted Reidemeister torsion and of various triangulation dependent factors. The discrete partition function is evaluated computationally for various triangulations of $S^3$ and of lens spaces. The results confirm that the discretisation scheme is triangulation independent and coincides with the continuum partition function

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