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Chiral anomalies in even and odd dimensions. (English) Zbl 1223.81143

Summary: Odd dimensional Yang-Mills theories with an extra “topological mass” term, defined by the Chern-Simons secondary characteristic, are discussed. It is shown in detail how the topological mass affects the equal time charge commutation relations and how the modified commutation relations are related to non-abelian chiral anomalies in even dimensions. We also study the \(\mathrm{SU}(3)\) chiral model (Wess-Zumino model) in four dimensions, and we show how a gauge invariant interaction with an external \(\mathrm{SU}(3)\) vector potential can be defined with the help of the Chern-Simons characteristic in five dimensions.

MSC:

81T20 Quantum field theory on curved space or space-time backgrounds
53C80 Applications of global differential geometry to the sciences
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