Definition:Yang-Mills Theory

Definition
Yang-Mills theory is a gauge theory based on a special unitary group $\map {SU} N$, or more generally any compact, reductive Lie algebra.

Yang–Mills theory seeks to describe the behavior of elementary particles using these non-abelian Lie groups, and is at the core of the unification of the electromagnetic force and weak forces, that is $\map U 1 \times \map {SU} 2$, as well as quantum chromodynamics, the theory of the strong force (based on $\map {SU} 3$).

Thus it forms the basis of our understanding of the Standard Model of particle physics.