The algebra of anomaly interplay
arXiv:2011.10102 · doi:10.21468/SciPostPhys.10.3.074
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.
55 pages, 10 figures. Added figure illustrating the construction of a nullbordism for the U(2) mapping torus; added explicit computations of the generators of various groups classifying local anomalies (for all 4d examples), together with the 6d bordism generators to which they are dual; other minor corrections and added references