Topological field theory and physics

Abstract

Topological Yang-Mills theory with the Belavin-Polyakov-Schwarz-Tyupkin $SU(2)$ instanton is solved completely, revealing an underlying multi-link intersection theory. Link invariants are also shown to survive the coupling to a certain kind of matter (hyperinstantons). The physical relevance of topological field theory and its invariants is discovered. By embedding topological Yang-Mills theory into pure Yang-Mills theory, it is shown that the topological version TQFT of a quantum field theory QFT allows us to formulate consistently the perturbative expansion of QFT in the topologically nontrivial sectors. In particular, TQFT classifies the set of good measures over the instanton moduli space and solves the inconsistency problems of the previous approaches. The qualitatively new physical implications are pointed out. Link numbers in QCD are related to a non abelian analogoue of the Aharonov-Bohm effect.

23 pages, 1 figure. Revision: additional explanations

References in corpus (6)

• Twisted N=2 Supergravity as Topological Gravity in Four Dimensions
• Topological Sigma-Models in Four Dimensions and Triholomorphic Maps
• Topological Twist in Four Dimensions, R-Duality and Hyperinstantons
• Gauged Hyperinstantons and Monopole Equations
• The Donaldson-Witten Invariants in Pure QCD with Order and Disorder 't Hooft-like Operators
• Anomalies in Instanton Calculus

Cited by in corpus (12)

• Generating branes via sigma-models
• Topological field theory and computing with instantons
• The BF Formalism for QCD and Quark Confinement
• Digital Memcomputing: from Logic to Dynamics to Topology
• On the variational principle for dust shells in General Relativity
• Non-extremal Localised Branes and Vacuum Solutions in M-Theory
• Topological Yang-Mills cohomology in pure Yang-Mills Theory
• Dimension of the moduli space and Hamiltonian analysis of BF field theories
• On field theory quantization around instantons
• Topological Yang-Mills Theory with Two Fermionic Charges. A Superfield Approach on Kähler Manifolds
• Quantum Topological Invariants, Gravitational Instantons and the Topological Embedding
• Topological Field Theory and Stochastic Dynamics