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September 2008 Pions and generalized cohomology
D. S. Freed
J. Differential Geom. 80(1): 45-77 (September 2008). DOI: 10.4310/jdg/1217361066


The Wess-Zumino-Witten term was first introduced in the low energy σ-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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D. S. Freed. "Pions and generalized cohomology." J. Differential Geom. 80 (1) 45 - 77, September 2008.


Published: September 2008
First available in Project Euclid: 29 July 2008

zbMATH: 1146.81050
MathSciNet: MR2434259
Digital Object Identifier: 10.4310/jdg/1217361066

Rights: Copyright © 2008 Lehigh University


Vol.80 • No. 1 • September 2008
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