Yangian Algebra and Correlation Functions in Planar Gauge Theories

TL;DR

This paper explores Yangian symmetries in planar gauge theories, establishing Ward-Takahashi identities, discovering new bi-local gauge symmetries, and verifying these identities for correlation functions at various loop levels.

Contribution

It introduces a novel set of bi-local gauge symmetries in planar gauge theories and formulates corresponding Slavnov-Taylor identities, advancing understanding of Yangian symmetry in these theories.

Findings

Verified identities for correlation functions at tree level

Extended identities to loop level calculations

Identified potential quantum anomalies in Yangian symmetry

Abstract

In this work we consider colour-ordered correlation functions of the fields in integrable planar gauge theories such as N=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.