Minitwistors and 3d Yang-Mills-Higgs theory

TL;DR

This paper develops a minitwistor action for 3D Yang-Mills-Higgs theory, enabling a new formula for tree amplitudes and connecting to four-dimensional RSVW results, advancing understanding of perturbation theory in gauge theories.

Contribution

It introduces a minitwistor action for 3D Yang-Mills-Higgs theory and derives a novel formula for all tree amplitudes, linking 3D and 4D twistor approaches.

Findings

Constructed a minitwistor action for 3D YMH theory.

Derived a new formula for all tree amplitudes in YMH theory.

Showed the formula's consistency with known MHV amplitudes and factorization.

Abstract

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.