Two-loop conformal generators for leading-twist operators in QCD

Understand

QCD evolution equations in minimal subtraction schemes have a hidden symmetry: One can construct three operators that commute with the evolution kernel and form an $SL(2)$ algebra, i.e.

• they satisfy (exactly) the $SL(2)$ commutation relations.
• In this paper we find explicit expressions for these operators to two-loop accuracy going over to QCD in non-integer $d=4-2\epsilon$ space-time dimensions at the intermediate stage.
• In this way conformal symmetry of QCD is restored on quantum level at the specially chosen (critical) value of the coupling, and at the same time the theory is regularized allowing one to use the standard renormalization procedure for the relevant Feynman diagrams.