The algebra of anomaly interplay
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.
Cite
@article{arxiv.2011.10102,
title = {The algebra of anomaly interplay},
author = {Joe Davighi and Nakarin Lohitsiri},
journal= {arXiv preprint arXiv:2011.10102},
year = {2021}
}
Comments
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