A more general definition of anomaly: *A QFT that has no UV completion in the same dimension is anomalous.*

In other words, a QFT that has no well defined short distance regularization in the same dimension is anomalous.

Example: A 1+1D QFT with only one right moving fermion mode is anomalous.

We conjectured that an anomalous QFT, although not well defined in the same dimension, can always be realized as a boundary of a well-defined STP state (for gauge anormaly) or a well-defined topologically ordered state (for gravitational anomaly) in one higher dimension. This leads to a classification of gauge and gravitational anomalies (see arXiv:1303.1803 ) . The above UV completion definition of anomaly and the above classification include the usual ABJ chiral anomalies, global gauge anormalies, gravitational anomalies, and global gravitational anomalies. Most of the global gauge/gravitational anomalies are new.

This post imported from StackExchange Physics at 2014-04-05 04:42 (UCT), posted by SE-user Xiao-Gang Wen