Topological quantum field theory
type: Item
instance of: scholarly article
title: Topological quantum field theory
zbMATH Open document ID: 0656.53078
DOI: 10.1007/BF01223371
published in: Communications in Mathematical Physics
publication date: 1988-01-01T00:00:00Z
review text: A twisted version of four dimensional supersymmetric gauge theory is formulated. The starting point is the connection between the Floer and Donaldson theories which has led to the conjecture that the ``Morse theory'' interpretation of Floer homology must be an approximation to a relativistic quantum field theory. It is shown that the Donaldson polynomial invariants of four manifolds and the Floer groups of three manifolds appear naturally. The Floer theory is generalized to the relativistic case and then the formula for the supersymmetry current and the energy-momentum tensor are obtained. The most important result of the paper is the assertion that the stress tensor is a ``BRST'' commutator \(T_{\alpha \beta}=\{Q,\lambda_{\alpha \beta}\},\) where Q is a linear transformation of the space of all functionals of the field variables, and \(\lambda_{\alpha \beta}^ a \)tensor field characteristic for the model. Finally, the possible physical interpretation of the model is presented. It is pointed out that the model is in a sense a generally covariant quantum theory in which general covariance is unbroken, there are no gravitons, and the only excitations are topological.
Mathematics Subject Classification ID: 53C80
Mathematics Subject Classification ID: 81T60
Mathematics Subject Classification ID: 81T08
zbMATH DE Number: 4071872
zbMATH Keywords: twistor
zbMATH Keywords: supersymmetric gauge theory
zbMATH Keywords: Floer homology
zbMATH Keywords: Donaldson polynomial invariants
zbMATH Keywords: Floer theory
zbMATH Keywords: stress tensor
Wikidata QID: Q55880680
reviewed by: Gheorghe Zet
MaRDI profile type: Publication
cites work: Q5185713
cites work: Self-dual Yang-Mills connections on non-self-dual 4-manifolds
cites work: Connections with \(L^ p \)bounds on curvature
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cites work: Floer homology groups for homology three-spheres
cites work: Supersymmetry and Morse theory
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cites work: Q3756080
cites work: Manifestly covariant canonical formulation of the Yang-Mills field theories. I. General formalism.
cites work: Topological sigma models
author: Edward Witten
description: scientific article; zbMATH DE number 4071872