An Extension of Pohlmeyer's Theorem

Abstract

Applying the Exact Renormalization Group to scalar field theory in Euclidean space of general (not necessarily integer) dimension, it is proven that the only fixed-point with vanishing anomalous dimension is the Gaussian one. The proof requires positivity of the two-point connected correlation function together with a technical assumption concerning solutions of the flow equation. The method, in which the representation of the flow equation as a heat equation plays a central role, extends directly to non-gauge theories with arbitrary matter content (though non-linear sigma models are beyond the scope of the current method).

Comments: v1: 29 pages; v2: 30 pages, minor tweaks; v3: published with very minor changes