Yangian algebra and correlation functions in planar Gauge theories

Abstract

In this work we consider colour-ordered correlation functions of the fields in integrable planar gauge theories such as \superN=4 supersymmetric Yang–Mills theory with the aim to establish Ward–Takahashi identities corresponding to Yangian symmetries. To this end, we discuss the Yangian algebra relations and discover a novel set of bi-local gauge symmetries for planar gauge theories. We fix the gauge, introduce local and bi-local BRST symmetries and propose Slavnov–Taylor identities corresponding to the various bi-local symmetries. We then verify the validity of these identities for several correlation functions at tree and loop level. Finally, we comment on the possibility of quantum anomalies for Yangian symmetry.