Heat kernel and moduli space
type: Item
instance of: scholarly article
title: Heat kernel and moduli space
zbMATH Open document ID: 0871.58014
published in: Mathematical Research Letters
publication date: 1997-09-08T00:00:00Z
review text: The author describes a proof of the formulas of \textit{E. Witten} [Commun. Math. Phys. 141, No. 1, 153-209 (1991; Zbl 0762.53063); J. Geom. Phys. 9, No. 4, 303-368 (1992; Zbl 0768.53042)] about the symplectic volumes and the intersection numbers of the moduli spaces of principal bundles on a compact Riemann surface. It is known that these formulas give all the information needed for the Verlinde formula. The main idea of the proof is to use the heat kernel on compact Lie groups, in a way very similar to the heat kernel proof of the Atiyah-Singer index formula and the Atiyah-Bott fixed point formula. The Reidemeister torsion comes into the picture, through a beautiful observation of Witten, as the symplectic volume of the moduli space. It plays the role similar to that played by the Ray-Singer torsion in the path-integral computations on the space of connections.
Mathematics Subject Classification ID: 58D27
Mathematics Subject Classification ID: 14J60
Mathematics Subject Classification ID: 81T13
Mathematics Subject Classification ID: 81T40
zbMATH DE Number: 991911
zbMATH Keywords: symplectic volumes
zbMATH Keywords: intersection numbers
zbMATH Keywords: moduli spaces
zbMATH Keywords: principal bundles
zbMATH Keywords: compact Riemann surface
zbMATH Keywords: heat kernel on compact Lie groups
zbMATH Keywords: heat equation method
author: Kefeng Liu
MaRDI profile type: Publication
DOI: 10.4310/MRL.1996.V3.N6.A3
description: scientific article; zbMATH DE number 991911