Remarks on exact RG equations

Exact RG equations are discussed with emphasis on the role of the anomalous dimension ηη. For the Polchinski equation, this may be introduced as a free parameter reflecting the freedom of such equations up to contributions which vanish in the functional integral. The exact value of ηη is only determined by the requirement that there should exist a well defined nontrivial limit at an IR fixed point. The determination of ηη is related to the existence of an exact marginal operator, for which an explicit form is given. The results are extended to the exact Wetterich RG equation for the one particle irreducible action ΓΓ by a Legendre transformation. An alternative derivation of the derivative expansion is described. An application to N=2N=2 supersymmetric theories in three dimensions is described where if an IR fixed point exists then ηη is not small.

► Derivation and analysis of exact RG equations including anomalous dimension. ► Analysis of reparameterisation invariance and associated zero mode. ► Role of zero mode in determining anomalous dimension. ► Derivation of a modified derivative expansion in accord with reparameterisation invariance. ► Application to supersymmetric models in three dimensions.