  Basis tensor gauge theory is a vierbein analog reformulation of ordinary
gauge theories in which the difference of local field degrees of freedom has
the interpretation of an object similar to a Wilson line. Here we present a
non-Abelian basis tensor gauge theory formalism. Unlike in the Abelian case,
the map between the ordinary gauge field and the basis tensor gauge field is
nonlinear. To test the formalism, we compute the beta function and the
two-point function at the one-loop level in non-Abelian basis tensor gauge
theory and show that it reproduces the well-known results from the usual
formulation of non-Abelian gauge theory.
