Pions and generalized cohomology

Daniel S. Freed University of Texas

Differential Geometry mathscidoc:1609.10078

Journal of Differential Geometry, 80, (1), 45-77, 2008
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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@inproceedings{daniel2008pions,
  title={PIONS AND GENERALIZED COHOMOLOGY },
  author={Daniel S. Freed},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160909134918542932735},
  booktitle={Journal of Differential Geometry},
  volume={80},
  number={1},
  pages={45-77},
  year={2008},
}
Daniel S. Freed. PIONS AND GENERALIZED COHOMOLOGY . 2008. Vol. 80. In Journal of Differential Geometry. pp.45-77. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160909134918542932735.
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