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Classical Lie Bialgebras for AdS/CFT Integrability by Contraction and Reduction

by Niklas Beisert, Egor Im

This Submission thread is now published as

Submission summary

Authors (as registered SciPost users): Niklas Beisert · Egor Im
Submission information
Preprint Link:  (pdf)
Date accepted: 2023-04-11
Date submitted: 2023-02-16 17:39
Submitted by: Beisert, Niklas
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • High-Energy Physics - Theory
  • Mathematical Physics
Approach: Theoretical


Integrability of the one-dimensional Hubbard model and of the factorised scattering problem encountered on the worldsheet of AdS strings can be expressed in terms of a peculiar quantum algebra. In this article, we derive the classical limit of these algebraic integrable structures based on established results for the exceptional simple Lie superalgebra d(2,1;epsilon) along with standard sl(2) which form supersymmetric isometries on 3D AdS space. The two major steps in this construction consist in the contraction to a 3D Poincar\'e superalgebra and a certain reduction to a deformation of the u(2|2) superalgebra. We apply these steps to the integrable structure and obtain the desired Lie bialgebras with suitable classical r-matrices of rational and trigonometric kind. We illustrate our findings in terms of representations for on-shell fields on AdS and flat space.

Author comments upon resubmission

We thank the referees for their reports and we have adressed their remarks and suggestions as listed below (see also the immediate replies to the reports).

List of changes

* below (3.27): reference to (3.19) added
* above (4.9): explanation added and reference to (3.27) corrected
* in (5.14), (5.19): sign corrected
* above (5.23): reference to (3.27) corrected
* paragraph below (6.14): added reference [33]
* conclusions 4th paragraph: added "It is also interesting ..."

Published as SciPost Phys. 14, 157 (2023)

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