Color-kinematic duality for form factors

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 twoand 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.

Note on symmetric BCJ numerator

“…(1.2) This duality between the color and kinematic factors was later found to be present in a variety of Yang-Mills theories [2][3][4][5][6][7][8][9][10] and, perhaps most surprisingly, was shown to be valid at least for the first few loop levels [2,3,[5][6][7][8][9][11][12][13][14][15][16][17][18][19]. The apparently symmetrical structure also suggests mirror versions of the existing color decomposition formulations.…”

The kinematic algebras from the scattering equations

“…At loop level, the colour-kinematics duality remains conjectural. However, it has been verified in various examples [21,22,[42][43][44][45][46][47][48][49][50].…”

On three-algebra and bi-fundamental matter amplitudes and integrability of supergravity

“…[13][14][15]). The conjecture has been extended to loop level [16], where duality satisfying numerators has been found for various amplitudes in different theories [16,18,[46][47][48][49][50][51] and used in gravity constructions [19,20,52,53], though a formal proof is still an open problem.…”