In the glossary of the AMS book on Quantum Fields and Strings it is stated that

An anomalous theory does not make sense quantum mechanically, so anomaly cancellation is a fundamental requirement of quantum theories.

However, from what I understand, a chiral anomaly means that quantum fluctuations destroy the axial symmetry of the classical theory, whose reality is an observed fact.

Are these two different kinds of anomalies?


1 Answer 1


A theory with an anomalous global symmetry, like chiral symmetry, is not problematic. Global symmetries are physical, and we can break them. Breaking gauge symmetry is a problem, because gauge symmetry is just a redundancy in labelling things. A $d$-dimensional theory with an anomalous gauge symmetry is telling us that it can't exist in just $d$ dimensions, but it could exist as the boundary of a $d+1$ dimensional theory. (See Wen, arXiv:1303.1803)

Some more details on anomalies in global vs. gauge symmetries are in this answer by Luboš Motl.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.