Deformations of Yang-Mills theory

We introduce and study a new class of power-counting nonrenormalizable 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 ultra-violet behavior. 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 generalized sense), with the higher-point tree-level scattering amplitudes obtainable from the lower-point amplitudes using the BCFW recursion relations, and adding new amplitudes at every particle number. 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 nonrenormalizable interaction becoming important in the ultraviolet.