The algebra of anomaly interplay
Joe Davighi, Nakarin Lohitsiri
Abstract
We give a general description of the interplay that can occur between local and global anomalies, in terms of (co)bordism. Mathematically, such an interplay is encoded in the non-canonical splitting of short exact sequences known to classify invertible field theories. We study various examples of the phenomenon in 2, 4, and 6 dimensions. We also describe how this understanding of anomaly interplay provides a rigorous bordism-based version of an old method for calculating global anomalies (starting from local anomalies in a related theory) due to Elitzur and Nair.
Topics & Concepts
Anomaly (physics)MathematicsInvertible matrixField (mathematics)PhenomenonAlgebra over a fieldTheoretical physicsPure mathematicsMixed anomalyClass (philosophy)Basis (linear algebra)Sequence (biology)PhysicsCovariant transformationBlack Holes and Theoretical PhysicsHomotopy and Cohomology in Algebraic TopologyAlgebraic and Geometric Analysis