Geometric discretization scheme applied to the Abelian Chern-Simons theory

• Main Authors: Sen, Samik, Sen, Siddhartha, Sexton, James, Adams, David H.
• Other Authors: School of Physical and Mathematical Sciences
• Format: Article
• Language: English
• Published: 2013
• Subjects: Physical and Mathematical Sciences
• Online Access: https://hdl.handle.net/10356/100977; http://hdl.handle.net/10220/18277
• Institution: Nanyang Technological University

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 S 3 and of lens spaces. The results confirm that the discretization scheme is triangulation independent and coincides with the continuum partition function.