Three-Loop Color-Kinematics Duality: A 24-Dimensional Solution Space Induced by New Generalized Gauge Transformations.

Guanda Lin,Gang Yang,Siyuan Zhang

doi:10.1103/physrevlett.127.171602

Abstract

We obtain full-color three-loop, three-point form factors of the stress-tensor supermultiplet and also of a length-3 half-Bogomol'nyi-Prasad-Sommerfield operator in N=4 supersymmetric Yang-Mills (SYM) theory based on the color-kinematics duality and on-shell unitarity. The integrand results are verified by all planar and nonplanar unitarity cuts, and they satisfy the minimal power counting of loop momenta and diagrammatic symmetries. Interestingly, these three-loop solutions, while manifesting all dual Jacobi relations, contain a large number of free parameters; in particular, there are 24 free parameters for the form factor of the stress-tensor supermultiplet. Such degrees of freedom are due to a new type of generalized gauge transformation associated with the operator insertion for form factors. We also perform numerical integration and obtain consistent full-color infrared divergences and the known planar remainder. The form factors we obtain can be understood as the N=4 SYM counterparts of three-loop Higgs plus three-gluon amplitudes in QCD and are expected to provide the maximally transcendental parts of the latter.

Highlights

We obtain full-color three-loop, three-point form factors of the stress-tensor supermultiplet and of a length-3 half–Bogomol’nyi-Prasad-Sommerfield operator in N 1⁄4 4 supersymmetric Yang-Mills (SYM) theory based on the color-kinematics duality and on-shell unitarity
These three-loop solutions, while manifesting all dual Jacobi relations, contain a large number of free parameters; in particular, there are 24 free parameters for the form factor of the stress-tensor supermultiplet. Such degrees of freedom are due to a new type of generalized gauge transformation associated with the operator insertion for form factors
The form factors we obtain can be understood as the N 1⁄4 4 SYM counterparts of three-loop Higgs plus three-gluon amplitudes in QCD and are expected to provide the maximally transcendental parts of the latter

Summary

Introduction

Three-Loop Color-Kinematics Duality: A 24-Dimensional Solution Space Induced by New Generalized Gauge Transformations We obtain full-color three-loop, three-point form factors of the stress-tensor supermultiplet and of a length-3 half–Bogomol’nyi-Prasad-Sommerfield operator in N 1⁄4 4 supersymmetric Yang-Mills (SYM) theory based on the color-kinematics duality and on-shell unitarity. These three-loop solutions, while manifesting all dual Jacobi relations, contain a large number of free parameters; in particular, there are 24 free parameters for the form factor of the stress-tensor supermultiplet.

Results

Conclusion