A new C-theorem in four dimensions

Spectral function methods are used to derive an n-dimensional formula describing the renormalisation group flow of a scalar function C(g) defined in terms of energy-momentum tensor Green functions. For n=2 the formula reduces to the Zamolodchikov theorem, while for n=4 it gives a new C-theorem whose physical interpretation, however, differs radically. The two- and four-dimensional C-theorems are investigated using renormalisation group ideas, and their relationship with the Osborn-Jack consistency conditions is discussed. It is speculated that this is the first of a family of similar C-theorems in four dimensions. (orig.)