Pions and Generalized Cohomology

2006/07/19 by Daniel S. Freed, Freed, Daniel S. · 4 citations
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Algebraic Topology (math.AT) #Black Holes and Theoretical Physics #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.hep-th/0607134

openalex publication_date 2006/07/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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).

Citations

• Classical Chern-Simons on manifolds with spin structure
• Global aspects of current algebra

Cited by

• How to Build Anomalous (3+1)d Topological Quantum Field Theories
• Anomaly of Continuous Symmetries from Topological Defect Network
• The Classification of 3+1d Symmetry Enriched Topological Order
• Mutual Influence of Symmetries and Topological Field Theories

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