A Remark on Schwarz's Topological Field Theory

Source: https://www.maths.tcd.ie/report_series/abstracts/tcdm9917.html Parent: https://www.maths.tcd.ie/research/papers/

A Remark on Schwarz's Topological Field Theory

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 formaly 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.