Pions and Generalized Cohomology

Details Pions and Generalized Cohomology Pions and Generalized Cohomology

2006-07-19

arxiv.org/abs/hep-th/0607134v2

Physics

High Energy Physics

High Energy Physics - Theory

29 pages, minor changes and added Proposition 4.4

Scientific paper

The Wess-Zumino-Witten term was first introduced in the low energy sigma-model which describes pions, the Goldstone bosons for the broken flavor symmetry in quantum chromodynamics. We introduce a new definition of this term in arbitrary gravitational backgrounds. It matches several features of the fundamental gauge theory, including the presence of fermionic states and the anomaly of the flavor symmetry. To achieve this matching we use a certain generalized differential cohomology theory. We also prove a formula for the determinant line bundle of special families of Dirac operators on 4-manifolds in terms of this cohomology theory. One consequence is that there are no global anomalies in the Standard Model (in arbitrary gravitational backgrounds).

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