How instantons solve the U(1) problem.

Abstract

The gauge theory for strong interactions, QCD, has an apparent U(1) symmetry that is not realized in the real world. The violation of the U(1) symmetry can be attributed to a well-known anomaly in the regularization of the theory, which in field configurations called 'instantons' can be seen to give rise to interactions that explicitly break the symmetry. A simple polynomial effective Lagrangian describes these effects qualitatively very well. In particular it is seen that no unwanted Goldstone bosons appear and the eta particle owes a large fraction of its mass to instantons. There is no need for field configurations with fractional winding numbers and it is explained how a spurious U(1) symmetry that remains in QCD even after introducing instantons, does not affect these results.