Planar zeros in gauge theories and gravity

• Published in: The journal of high energy physics Vol. 2016; no. 9; pp. 1 - 20
• Main Authors: Jiménez, Diego Medrano, Vera, Agustín Sabio, Vázquez-Mozo, Miguel Á.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.09.2016; Springer Nature B.V
• Subjects: Bosons; Classical and Quantum Gravitation; Color; Elementary Particles; Gages; Gauge theory; Gauges; Gravitation; High energy physics; Labelling; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; Scattering amplitude; String Theory; Scattering Amplitudes; Models of Quantum Gravity; Perturbative QCD
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP09(2016)006

A bstract 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.