 Yang-Mills theta term

In four dimensions the Yang-Mills theta term is proportional to $\theta \mathrm{Tr}(F_{\mu \nu }{}^{\star }{F}^{\mu \nu })$. Its density is a total derivative, but nontrivial gauge-field topology can make its spacetime integral physically relevant in the quantum theory.

The term weights topological sectors and supplies the angle labeling a theta vacuum.