A remark on Schwarz's topological field theory

Abstract

The standard evaluation of the partition function $Z$ of Schwarz's topological field theory results in the Ray--Singer analytic torsion. Here we present an alternative evaluation which results in Z=1. Mathematically, this amounts to a novel perspective on analytic torsion: it can be formally written as a ratio of volumes of spaces of differential forms which is formally equal to 1 by Hodge duality. An analogous result for Reidemeister combinatorial torsion is also obtained.

9 pages, latex, to appear in Lett. Math. Phys

References in corpus (2)

• A doubled discretisation of abelian Chern-Simons theory
• Ray-Singer Torsion for a Hyperbolic 3-Manifold and Asymptotics of Chern-Simons-Witten Invariant