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 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.

arXiv comment56 pages, v2: minor changes to address issues raised at https://scipost.org/submission/1804.09110v1/

References in corpus (31)

• Review of AdS/CFT Integrability: An Overview
• Dual superconformal symmetry of scattering amplitudes in N=4 super-Yang-Mills theory
• The Complete One-Loop Dilatation Operator of N=4 Super Yang-Mills Theory
• The All-Loop Integrand For Scattering Amplitudes in Planar N=4 SYM
• Conformal Ward identities for Wilson loops and a test of the duality with gluon amplitudes
• Yangian symmetry of scattering amplitudes in N=4 super Yang-Mills theory
• Dual Superconformal Invariance, Momentum Twistors and Grassmannians
• A Relation Between Approaches to Integrability in Superconformal Yang-Mills Theory
• Scattering into the fifth dimension of N=4 super Yang-Mills
• New integrable non-gauge 4D QFTs from strongly deformed planar N=4 SYM
• Jumpstarting the all-loop S-matrix of planar N=4 super Yang-Mills
• Quantum Consistency of the Superstring in AdS_5 x S^5 Background
• Introduction to Yangian symmetry in integrable field theory
• All tree-level amplitudes in N=4 SYM
• Exacting N=4 Superconformal Symmetry
• An Introduction to Yangian Symmetries
• Yangians, Grassmannians and T-duality
• One-Loop Superconformal and Yangian Symmetries of Scattering Amplitudes in N=4 Super Yang-Mills
• Lectures on Yangian Symmetry
• Yangian Symmetry for Bi-Scalar Loop Amplitudes
• Yangian Symmetry of smooth Wilson Loops in N=4 super Yang-Mills Theory
• Bonus Yangian Symmetry for the Planar S-Matrix of N=4 Super Yang-Mills
• Alleviating the non-ultralocality of the AdS_5 x S^5 superstring
• Yangian Symmetry and Integrability of Planar N=4 Super-Yang-Mills Theory
• Review of AdS/CFT Integrability, Chapter II.3: Sigma Model, Gauge Fixing
• Yangian Symmetry for the Action of Planar N=4 Super Yang-Mills and N=6 Super Chern-Simons Theories
• Integrability of Smooth Wilson Loops in N=4 Superspace
• Nonlocal Charges for Bonus Yangian Symmetries of Super-Yang-Mills
• Bonus Symmetry for Super Wilson Loops
• Yangian Symmetry for the Tree Amplituhedron
• Yangians in Integrable Field Theories, Spin Chains and Gauge-String Dualities

Cited by in corpus (6)

• Yangian Symmetry for the Action of Planar N=4 Super Yang-Mills and N=6 Super Chern-Simons Theories
• Yangian Ward Identities for Fishnet Four-Point Integrals
• Properties of the Conformal Yangian in Scalar and Gauge Field Theories
• Marginal deformations and quasi-Hopf algebras
• On Exact Solvability of $\mathcal{N}$=4 super Yang-Mills
• Nonlocal charges from marginal deformations of 2D CFTs: Holographic $T\bar{T}$, $T\bar{J}$ and Yang-Baxter deformations