Color-kinematic Duality for Form Factors

TL;DR

This paper extends the color-kinematic duality from scattering amplitudes to form factors in gauge theories, demonstrating its validity at multi-loop levels in supersymmetric Yang-Mills theory and deriving a simplified four-loop integrand.

Contribution

It introduces the extension of the color-kinematic duality to form factors and verifies it through multi-loop examples in supersymmetric gauge theories.

Findings

Duality verified at two- and three-loop levels in N=4 SYM.

Derived a simple four-loop two-point form factor integrand.

The duality reproduces known results transparently.

Abstract

Recently a powerful duality between color and kinematics has been proposed for integrands of scattering amplitudes in quite general gauge theories. In this paper the duality proposal is extended to the more general class of gauge theory observables formed by form factors. After a discussion of the general setup the existence of the duality is verified in two- and three-loop examples in four dimensional maximally supersymmetric Yang-Mills theory which involve the stress energy tensor multiplet. In these cases the duality reproduces known results in a particularly transparent and uniform way. As a non-trivial application we obtain a very simple form of the integrand of the four-loop two-point (Sudakov) form factor which passes a large set of unitarity cut checks.