Bootstrapping a Two-Loop Four-Point Form Factor

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 colorsinglet 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.

Full-color three-loop three-point form factors in N=4 SYM

“…Symbol bootstrap method has also been used to compute form factors at two loops [23] and recently to much higher loops in [31] with the help of the form factor operator product expansion (OPE) [32,33]. A new bootstrap strategy based on the master-integral ansatz has been applied to compute a two-loop four-point BPS form factor in [34]. See also some other studies in [35][36][37][38][39][40][41][42][43].…”