Summary
Zamolodchikov's c-theorem showed how flows of couplings under renormalisation in two-dimensional quantum field theories are constrained by a gradient flow equation with a positive definite "metric", leading to a "c-function" monotonically increasing with energy. The a-theorem is the extension of this result to four dimensions; in fact it is now well-established that similar results hold, at least perturbatively, in all even dimensions. In this talk we discuss the possibility of an exact a-function in 4-d supersymmetric gauge theories; and also present "experimental" evidence for an a-function in three-dimensional theories.
