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Yangian Algebra and Correlation Functions in Planar Gauge Theories

by Niklas Beisert, Aleksander Garus

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Submission summary

Authors (as registered SciPost users): Niklas Beisert
Submission information
Preprint Link:  (pdf)
Date accepted: 2018-07-16
Date submitted: 2018-07-03 02:00
Submitted by: Beisert, Niklas
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • Quantum Algebra
  • High-Energy Physics - Theory
  • Mathematical Physics
Approach: Theoretical


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.

List of changes

below (2.1) added:
"This means that in the planar limit N_c->infty all monomials are independent and form a basis for polynomials."

section 2.2 and following:
changed J^1,2 to J^a,b

above (2.12):
changed "Yangian algebra" to "Yangian quantum algebra"

below (2.13) added:
"Furthermore, the Yangian algebra contains infinitely many higher-level generators. However, we can ignore these because their algebraic relations are fully determined by the above relations involving only level-zero and level-one generators."

minor changes of wording:

first paragraph on page 13:
after "The above bi-local action (2.46) was derived" added "in [5]".
before "Let us comment on these conditions." added "The superconformal symmetries J^a and the action S of integrable planar gauge theories such as N=4 sYM satisfy these requirements."

added below (2.48):
Allowing for a_n,m != 0 will turn out unnecessary in our analysis.

expanded text around (2.49)

section 6.2, first sentence:
added "planar" to "correlators"

fixed the labels on one diagram

below (6.32), above (7.1):
added "planar" to "diagrams"

section 7.4 between (7.10) and (7.15):
various minor changes and additions to make arguments more self-contained

conclusions, first paragraph:
some changes of words. added remark on planar limit:
"Importantly, these identities, tools and verifications crucially rely on the planar limit. This further justifies the relevance of the planar limit for integrability and Yangian symmetry to apply for the considered models."

Published as SciPost Phys. 5, 018 (2018)

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