Analytic two-loop form factors in N=4 SYM

TL;DR

This paper derives a compact two-loop expression for three-point MHV form factors in N=4 SYM, confirming expected divergence behavior and constructing a simplified analytic remainder function with potential QCD connections.

Contribution

It provides the first compact analytic expression for the two-loop remainder function of form factors in N=4 SYM using advanced unitarity and symbol techniques.

Findings

Infrared divergences exponentiate as expected.

The remainder function is uniquely determined and expressed with classical polylogarithms.

The remainder matches the maximally transcendental part of a related QCD amplitude.

Abstract

We derive a compact expression for the three-point MHV form factors of half-BPS operators in N=4 super Yang-Mills at two loops. The main tools of our calculation are generalised unitarity applied at the form factor level, and the compact expressions for supersymmetric tree-level form factors and amplitudes entering the cuts. We confirm that infrared divergences exponentiate as expected, and that collinear factorisation is entirely captured by an ABDK/BDS ansatz. Next, we construct the two-loop remainder function obtained by subtracting this ansatz from the full two-loop form factor and compute it numerically. Using symbology, combined with various physical constraints and symmetries, we find a unique solution for its symbol. With this input we construct a remarkably compact analytic expression for the remainder function, which contains only classical polylogarithms, and compare it to our numerical results. Furthermore, we make the surprising observation that our remainder is equal to the maximally transcendental piece of a closely related two-loop amplitude in QCD.