Bootstrapping a Two-Loop Four-Point Form Factor

TL;DR

This paper introduces a new bootstrap method to compute a complex two-loop four-point form factor in N=4 SYM, leveraging physical constraints and unitarity cuts to achieve an analytic result.

Contribution

A novel bootstrapping strategy for calculating two-loop form factors using physical constraints and unitarity cuts in planar N=4 SYM.

Findings

Analytic expressions in terms of symbol and Goncharov polylogarithms.

Effective fixing of ansatz coefficients through physical constraints.

Complete two-loop four-point form factor in N=4 SYM obtained.

Abstract

We compute the two-loop four-point form factor of a length-3 half-BPS operator in planar N=4 SYM, which belongs to the class of two-loop five-point scattering observables with one off-shell color-singlet leg. A new bootstrapping strategy is developed to obtain this result by starting with an ansatz expanded in terms of master integrals and then solving the master coefficients via various physical constraints. We find that consistency conditions of infrared divergences and collinear limits, together with the cancellation of spurious poles, can fix a significant part of the ansatz. The remaining degrees of freedom can be fixed by one simple type of two-double unitarity cut. Full analytic results in terms of both symbol and Goncharov polylogarithms are provided.