Deformations of Yang-Mills theory

TL;DR

This paper introduces a new class of non-renormalisable gauge theories in four dimensions, which share many properties with Yang-Mills theory and have improved ultraviolet behavior, with potential implications for gravity theories.

Contribution

It defines a novel class of gauge theories based on the self-dual field strength, analyzing their properties, amplitudes, and beta-function, revealing connections to deformations of General Relativity.

Findings

Theories have improved UV behavior with at most one derivative per internal line.

They share MHV amplitudes with Yang-Mills theory and are constructible via BCFW recursion.

The one-loop beta-function of the new coupling is positive, indicating UV significance.

Abstract

We introduce and study a new class of power-counting non-renormalisable gauge theories in four space-time dimensions. The Lagrangian is an arbitrary function of the self-dual part of the field strength. The resulting perturbation theory has the property that whenever two derivatives act on an internal line propagator, the result is a delta-function and the line collapses to a point. This means that there remains at most one derivative on each internal line, which gives improved ulta-violet behaviour. For many purposes, this class of theories behaves just like ordinary Yang-Mills theory. In particular, they all share the Yang-Mills theory MHV amplitudes. Moreover, these theories remain constructible in the sense that higher-point tree level scattering amplitudes can be obtained from the lower-point amplitudes using the BCFW recursion relations. Also, the square of these gauge-theory amplitudes gives the scattering amplitudes of "deformations" of General Relativity, at least for the low particle numbers that we checked. We compute the one-loop beta-function of the first new coupling constant, and find it to be positive, which signals the associated non-renormalisable interaction becoming important in the ulta-violet.