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Pions and Generalized Cohomology

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arxiv hep-th/0607134 v2 pith:WDGNYU4Q submitted 2006-07-19 hep-th math.AT

Pions and Generalized Cohomology

Daniel S. Freed This is my paper
classification hep-th math.AT
keywords cohomologytheoryarbitrarybackgroundsflavorgeneralizedgravitationalpions
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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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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