N=1 Supersymmetric One-loop Amplitudes and the Holomorphic Anomaly of Unitarity Cuts

TL;DR

This paper explores the application of the holomorphic anomaly of unitarity cuts to compute N=1 supersymmetric one-loop amplitudes, extending methods previously used in N=4 super Yang-Mills theory.

Contribution

It demonstrates that the holomorphic anomaly approach can be applied to non-MHV N=1 amplitudes, revealing the need for differential equations in the evaluation process.

Findings

Holomorphic anomaly reproduces collinearity operators in twistor space.

Application requires solving differential equations, not algebraic.

Method extends to more general supersymmetric theories.

Abstract

Recently, it has been shown that the holomorphic anomaly of unitarity cuts can be used as a tool in determining the one-loop amplitudes in N=4 super Yang-Mills theory. It is interesting to examine whether this method can be applied to more general cases. We present results for a non-MHV N=1 supersymmetric one-loop amplitude. We show that the holomorphic anomaly of each unitarity cut correctly reproduces the action on the amplitude's imaginary part of the differential operators corresponding to collinearity in twistor space. We find that the use of the holomorphic anomaly to evaluate the amplitude requires the solution of differential rather than algebraic equations.