Minitwistors and 3d Yang-Mills-Higgs theory

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.

29 pages, 1 figure. v2: references added, published version

References in corpus (10)

• The Complete Planar S-matrix of N=4 SYM as a Wilson Loop in Twistor Space
• From Twistor Actions to MHV Diagrams
• Dual Superconformal Symmetry of N=6 Chern-Simons Theory
• Amplitudes of 3D and 6D Maximal Superconformal Theories in Supertwistor Space
• Holomorphic Linking, Loop Equations and Scattering Amplitudes in Twistor Space
• A Direct Proof of BCFW Recursion for Twistor-Strings
• Resultants and Gravity Amplitudes
• Manifest SO(N) invariance and S-matrices of three-dimensional N=2,4,8 SYM
• The Construction of Monopoles
• On the Berezinian of a moduli space of curves in P^{n|n+1}

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• Graviton scattering in self-dual radiative space-times
• Twistors, the ASD Yang-Mills equations, and 4d Chern-Simons theory
• Higher-spin Yang-Mills, amplitudes and self-duality
• Twistor fishnets
• Twistor action for general relativity
• Integrable models from 4d holomorphic BF theory