MHV Vertices and Scattering Amplitudes in Gauge Theory

TL;DR

This work strengthens the CSW (MHV-diagram) program for perturbative gauge theory by deriving the generic googly amplitudes from off-shell MHV vertices and verifying key symmetries such as parity, charge conjugation, and the dual Ward identity. It extends the CSW rules to gauge theories with fermions, obtaining googly amplitudes for a single quark-anti-quark pair, and investigates the prospects for a gravity analogue, finding that naive extensions fail and that gravity requires new ingredients. The results provide strong support for CSW’s applicability to pure gauge theory amplitudes while clarifying the barriers to a straightforward gravity generalization. Overall, the paper offers a cohesive framework for computing tree-level amplitudes via MHV vertices, discusses symmetry properties rigorously, and outlines directions for future extensions to fermions and gravity.

Abstract

The generic googly amplitudes in gauge theory are computed by using the Cachazo-Svrcek-Witten approach to perturbative calculation in gauge theory and the results are in agreement with the previously well-known ones. Within this approach we also discuss the parity transformation, charge conjugation and the dual Ward identity. We also extend this calculation to include fermions and the googly amplitudes with a single quark-anti-quark pair are obtained correctly from fermionic MHV vertices. At the end we briefly discuss the possible extension of this approach to gravity.

Figures (15)

• Figure 1: The diagram decomposition for the generic googly amplitude. We note that there is only one 4 gluon vertex.
• Figure 2: The diagram decomposition for the generic googly amplitude when $(i+1)\le r\le j$.
• Figure 3: The diagram decomposition for the generic googly amplitude when $(j+1)\le r\le k$.
• Figure 4: The diagram decomposition for the generic googly amplitude when $(k+1)\le r\le l$.
• Figure 5: The diagram decomposition for the gauge amplitude $A(1,\cdots,n)$.