Gradient flows in three dimensions

Abstract

The a-function is a proposed quantity defined for quantum field theories which has a monotonic behaviour along renormalisation group flows, being related to the beta-functions via a gradient flow equation involving a positive definite metric. We demonstrate the existence of a candidate a-function for renormalisable Chern-Simons theories in three dimensions, involving scalar and fermion fields, in both non-supersymmetric and supersymmetric cases.

15 pages, 2 figures, uses axodraw. Revised with minor corrections; also additional clarifications and references included

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Cited by in corpus (2)

• The a-function in three dimensions: beyond leading order
• Gradient flows for $\beta$ functions via multi-scale renormalization group equations