INTEGRABILITY CONDITIONS FOR POTENTIAL FLOW OF THE RENORMALIZATION-GROUP

The renormalisation group (RG) flow for a quantum field theory in flat D dimensional space is considered. Some conditions are derived which ensure that the beta-functions are derivable from a potential on the s pace of couplings. This requires introducing a metric on the space of interactions and two possibilities are considered. Assuming positive d efiniteness of the metric the potential provides a function on the spa ce of couplings which is non-increasing along the RG trajectories. Thu s any theory which satisfies the integrability conditions also satisfi es a c-theorem in D dimensions.