Geometric discretization scheme applied to the Abelian Chern-Simons theory

We give a detailed general description of a recent geometrical discretization 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 S³ and of lens spaces. The results confirm that the discretization scheme is triangulation independent and coincides with the continuum partition function.