Planar Zeros in Gauge Theories and Gravity

TL;DR

This paper investigates planar zeros in five-point scattering amplitudes for gauge bosons and gravitons, revealing algebraic conditions in gauge theories and that graviton amplitudes vanish in planar configurations, linked to color-kinematics duality.

Contribution

It introduces the algebraic characterization of planar zeros in gauge theories and demonstrates the vanishing of five-graviton amplitudes in planar configurations.

Findings

Planar zeros in gauge theories are described by algebraic curves depending on color structures.

Five-graviton amplitudes vanish when the process is planar, explained via color-kinematics duality.

Abstract

Planar zeros are studied in the context of the five-point scattering amplitude for gauge bosons and gravitons. In the case of gauge theories, it is found that planar zeros are determined by an algebraic curve in the projective plane spanned by the three stereographic coordinates labelling the direction of the outgoing momenta. This curve depends on the values of six independent color structures. Considering the gauge group SU(N) with N=2,3,5 and fixed color indices, the class of curves obtained gets broader by increasing the rank of the group. For the five-graviton scattering, on the other hand, we show that the amplitude vanishes whenever the process is planar, without imposing further kinematic conditions. A rationale for this result is provided using color-kinematics duality.