Triviality from the Exact Renormalization Group

Abstract

Using the exact renormalization group, it is shown that no physically acceptable non-trivial fixed points, with positive anomalous dimension, exist for (i) O(N) scalar field theory in four or more dimensions, (ii) non-compact, pure Abelian gauge theory in any dimension. It is then shown, for both theories in any dimension, that otherwise physically acceptable non-trivial fixed points with negative anomalous dimension are non-unitary. In addition, a very simple demonstration is given, directly from the exact renormalization group, that should a critical fixed point exist for either theory in any dimension, then the n-point correlation functions exhibit the expected behaviour.

14 pages, 6 figures; v2: Important addition - negative anomalous dimensions now treated; v3: error in treatment of negative anomalous dimension corrected and some clarifications added; v4: published in JHEP; very minor changes

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