On the Factorisation of the Connected Prescription for Yang-Mills Amplitudes
C. Vergu
TL;DR
The paper addresses factorisation in the connected prescription for Yang-Mills amplitudes and introduces a contour-based interpretation of delta functions as holomorphic objects to reveal the multi-particle pole. It employs a Berkovits-inspired scaling limit to separate amplitudes into left and right sectors connected by an on-shell internal line, producing the expected $1/P^2$ pole, with explicit gauge-fixing and contour tests supporting the approach. While not a rigorous proof due to contour ambiguities, the results align with known factorisation properties and suggest avenues for extending the framework to loops and other theories such as conformal or Einstein supergravity. Overall, the work elucidates how factorisation can emerge in the on-shell connected prescription and clarifies the role of delta-function interpretation and contour choice in this context.
Abstract
We examine factorisation in the connected prescription of Yang-Mills amplitudes. The multi-particle pole is interpreted as coming from representing delta functions as meromorphic functions. However, a naive evaluation does not give a correct result. We give a simple prescription for the integration contour which does give the correct result. We verify this prescription for a family of gauge-fixing conditions.