From Yang-Mills Lagrangian to MHV Diagrams

TL;DR

The authors address how the CSW/MHV diagram formulation for Yang–Mills can be derived from the standard YM theory by a formally non-local change of variables in the light-cone formulation, using a self-dual perturbiner background to generate the off-shell continuation. They provide explicit formulas for the transformation that maps the YM Lagrangian to the CSW (MHV) Lagrangian, recover the correct tree-level MHV vertices and propagators, and discuss the potential one-loop completion via the Jacobian of the transformation. The approach connects the off-shell MHV structure to a self-dual sector and suggests a twistor-theoretic interpretation, with several generalizations and open questions left for future work. Key ingredients include the off-shell continuation $\lambda_a = p_{a\dot{a}} \eta^{\dot{a}}$, the perturbiner-based group element $g_{ptb}$, and the non-local mapping $\Phi_{+}=F(\phi_{+})$, $\Phi_{-}=\partial_{+}^{-4}F'(\phi_{+},\partial_{+}^{4}\phi_{-})$ guiding the CSW reformulation.

Abstract

We prove the equivalence of a recently suggested MHV-formalism to the standard Yang-Mills theory. This is achieved by a formally non-local change of variables. In this note we present the explicit formulas while the detailed proofs are postponed to a future publication.