Twistor-Space Recursive Formulation of Gauge-Theory Amplitudes

TL;DR

This paper presents explicit non-MHV vertices in a twistor-inspired gauge-theory framework, building them from stripped CSW diagrams (skeletons) and organizing amplitudes via MHV skeletons. It introduces a recursive formulation that expresses higher-degree non-MHV vertices in terms of lower-degree ones connected by propagators, enabling efficient computation of tree-level amplitudes with any number of negative-helicity gluons. The authors also derive and analyze alternative representations and establish a direct correspondence between skeleton diagrams and degenerations of twistor-space curves, clarifying combinatorial factors and intermediate prescriptions. The work highlights a practical duality between field-theory and twistor-string perspectives and points to potential extensions to loop amplitudes using unitarity-based approaches.

Abstract

Using twistor space intuition, Cachazo, Svrcek and Witten presented novel diagrammatic rules for gauge-theory amplitudes, expressed in terms of maximally helicity-violating (MHV) vertices. We define non-MHV vertices, and show how to use them to give a recursive construction of these amplitudes. We also use them to illustrate the equivalence of various twistor-space prescriptions, and to determine the associated combinatoric factors.

Figures (13)

• Figure 1: A term in the CSW representation of an NMHV amplitude. The black dot represents the multiparticle pole multiplying the two on-shell amplitudes. The '1' inside the vertex signifies that it is a basic MHV vertex corresponding to a degree 1 curve in twistor space.
• Figure 2: Examples of diagrams for the seven-point NMHV amplitude $A_7(1^-,2^-,3^+,4^-,5^+,6^+,7^+)$.
• Figure 3: The stripped diagrams for amplitudes with three negative-helicity gluons.
• Figure 4: The lone MHV skeleton diagram for amplitudes with three negative-helicity gluons.
• Figure 5: The skeleton diagrams with up to six external negative-helicity legs. The numbers inside the circles give the degree of the associated curves in twistor space.