SU(2) gauge theory ($SU(2)$ gauge theory)

An SU(2) gauge theory is a Yang-Mills theory with gauge group $SU(2)$. In its defining representation the generators are $T^a={\sigma }^a/2$, and its structure constants are the Levi-Civita symbols ${ϵ}^{abc}$.

A real scalar field in the Adjoint representation can have a nonzero vacuum expectation value, leaving one massless and two massive gauge bosons. This breaking differs from electroweak symmetry breaking by a complex Higgs doublet.