| A remark on Schwarz's topological eld theory (2007) | |||||||||||||
Abstract | |||||||||||||
| The standard evaluation of the partition function Z of Schwarz's topological eld 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 dierential forms which is formally equal to 1 by Hodge duality. An analogous result for Reidemeister combinatorial torsion is also obtained. 1 Introduction Analytic torsion [1] arises in a quantum eld theoretic context as (the square of) the partition function of Schwarz's topological eld theory [2, 3, 4]. This has turned out to be an important result in topological quantum eld theory; for example it is used to evaluate the semiclassical approximation for the Chern{Simons partition function [5, 6], which gives a QFT-predicted formula for an asymptotic limit of the Witten{Reshetikhin{Turaev 3-manifold invariant [7] since this invariant arises as the partit... | |||||||||||||
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