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Classical Lie Bialgebras for AdS/CFT Integrability by Contraction and Reduction
by Niklas Beisert, Egor Im
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Submission summary
| Authors (as registered SciPost users): | Niklas Beisert · Egor Im |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2210.11150v2 (pdf) |
| Date accepted: | 2023-04-11 |
| Date submitted: | 2023-02-16 17:39 |
| Submitted by: | Beisert, Niklas |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
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
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)