Non-planar form factors of generic local operators via on-shell unitarity and color-kinematics duality

TL;DR

This paper develops a systematic approach to compute full color-dependent form factors for local operators in N=4 SYM, including non-planar two-loop results and color-kinematics duality, revealing new transcendental structures.

Contribution

It introduces a method for constructing full color form factors beyond the planar limit and finds explicit color-kinematics dual representations at two loops.

Findings

Computed full two-loop non-planar form factors for BPS and non-BPS operators.

Established color-kinematics duality for high-length operators at two loops.

Reproduced the two-loop non-planar dilatation operator and identified new transcendental parts.

Abstract

Form factors, as quantities involving both local operators and asymptotic particle states, contain information of both the spectrum of operators and the on-shell amplitudes. So far the studies of form factors have been mostly focused on the large Nc planar limit, with a few exceptions of Sudakov form factors. In this paper, we discuss the systematical construction of full color dependent form factors with generic local operators. We study the color decomposition for form factors and discuss the general strategy of using on-shell unitarity cut method. As concrete applications, we compute the full two-loop non-planar minimal form factors for both half-BPS operators and non-BPS operators in SU(2) sector in N=4 SYM. Another important aspect is to investigate the color-kinematics (CK) duality for form factors with high-length operators. Explicit CK dual representation is found for the two-loop half-BPS minimal form factors with arbitrary number of external legs. The full-color two-loop form factor results provide an independent check of the infrared dipole formula for two-loop n-point amplitudes. By extracting the UV divergence, we also reproduce the known two-loop non-planar SU(2) dilatation operator. As for the finite remainder function, interestingly, the non-planar part is found to contain a new maximally transcendental part beyond the known planar result.