Conformal invariance in gauge theories II. Yang–Mills theory

The results of Part I are generalized to the non-Abelian ease. By analogy with conformal QED, in which interaction with a matter field is realized by means of a four-vector potential that transforms in accordance with a direct sum of two nonprincipal representations, the first step in the present paper is the construction of a new formulation of quantum eleetrodynamics, in which the four-vector potential is regarded as an independent variable. Although the potential as a whole transforms in accordance with a principal representation, the corresponding conformally invariant two-point functions have a nonzero transverse part, and the Lagrangian is nondegenerate. In the non-Abelian case, one manifestly conformally invariant gauge condition is found, and the corresponding functional determinant is calculated. It is shown that in the gauge-invariant sector this theory is equivalent to the ordinary theory with conformally noninvariant gauge condition. A local effective Lagrangian is constructed, the Faddeev–Popov “ghost” fields having in this case scale dimension zero. It is shown that this effective Lagrangian has a residual global supersymmetry of Becchi–Rouet–Stora type.