Simple loop integrals and amplitudes in N=4 SYM

TL;DR

This paper employs momentum twistors and a novel AdS-inspired mass regulator to evaluate planar loop integrals in N=4 SYM, simplifying the computation of two-loop amplitudes and confirming their relation to Wilson loops.

Contribution

It introduces a basis of twistor numerator integrals for two-loop amplitudes in N=4 SYM, demonstrating their simplicity over traditional methods.

Findings

Analytical results for the two-loop six-point MHV amplitude's remainder function.

Agreement with Wilson loop computations in a specific kinematic limit.

Evidence that the logarithm of MHV amplitudes can be expressed with simple twistor integrals.

Abstract

We use momentum twistors to evaluate planar loop integrals. Infrared divergences are regulated by the recently proposed AdS-inspired mass regulator. We show that two-loop amplitudes in N=4 super Yang-Mills can be expanded in terms of basis integrals having twistor numerators. We argue that these integrals are considerably simpler compared to the ones conventionally used. Our case in point is the two-loop six-point MHV amplitude. We present analytical results for the remainder function in a kinematical limit, and find agreement with a recent Wilson loop computation. We also provide two-loop evidence that the logarithm of MHV amplitudes can be written in terms of simple twistor space integrals.