nLab
Yang-Mills theory

Yang–Mills theory is a gauge theory on 4-dimensional (pseudo)Riemannian manifold $X$ whose field is the Yang–Mills field – a cocycle $\hat{F}\in H(X,\overline{B}U(n))$ in differential nonabelian cohomology represented by a vector bundle with connection – and whose action functional is

$$\hat{F}\mapsto {\int }_{X}F\wedge \star F+\theta {\int }_{X}F\wedge F$$\hat F \mapsto \int_X F \wedge \star F + \theta \int_X F \wedge F

for some real number $\theta$.

All gauge fields in the standard model of particle physics? as well as in GUT models are Yang–Mills fields.