The Constraints of Conformal Symmetry on RG Flows

Understand

If the coupling constants in QFT are promoted to functions of space-time, the dependence of the path integral on these couplings is highly constrained by conformal symmetry.

• We begin the present note by showing that this idea leads to a new proof of Zamolodchikov's theorem.
• We then review how this simple observation also leads to a derivation of the a-theorem.
• We exemplify the general procedure in some interacting theories in four space-time dimensions.