Minitwistors and 3d Yang-Mills-Higgs theory

Understand

We construct a minitwistor action for Yang--Mills--Higgs theory in three dimensions.

• The Feynman diagrams of this action will construct perturbation theory around solutions of the Bogomolny equations in much the same way that MHV diagrams describe perturbation theory around the self--dual Yang Mills equations in four dimensions.
• We also provide a new formula for all tree amplitudes in YMH theory (and its maximally supersymmetric extension) in terms of degree d maps to minitwistor space.
• We demonstrate its relationship to the RSVW formula in four dimensions and show that it generates the correct MHV amplitudes at d=1 and factorizes correctly in all channels for all degrees.