Affine Classical Lie Bialgebras for AdS/CFT Integrability
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866917570481750016 |
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| author | Beisert, Niklas Im, Egor |
| author_facet | Beisert, Niklas Im, Egor |
| contents | In this article we continue the classical analysis of the symmetry algebra underlying the integrability of the spectrum in the AdS_5/CFT_4 and in the Hubbard model. We extend the construction of the quasi-triangular Lie bialgebra gl(2|2) by contraction and reduction studied in the earlier work to the case of the affine algebra sl(2)^(1) times d(2,1;alpha)^(1). The reduced affine derivation naturally measures the deviation of the classical r-matrix from the difference form. Moreover, it implements a Lorentz boost symmetry, originally suggested to be related to a q-deformed 2D Poincare algebra. We also discuss the classical double construction for the bialgebra of interest and comment on the representation of the affine structure. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_10327 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Affine Classical Lie Bialgebras for AdS/CFT Integrability Beisert, Niklas Im, Egor High Energy Physics - Theory Mathematical Physics Quantum Algebra In this article we continue the classical analysis of the symmetry algebra underlying the integrability of the spectrum in the AdS_5/CFT_4 and in the Hubbard model. We extend the construction of the quasi-triangular Lie bialgebra gl(2|2) by contraction and reduction studied in the earlier work to the case of the affine algebra sl(2)^(1) times d(2,1;alpha)^(1). The reduced affine derivation naturally measures the deviation of the classical r-matrix from the difference form. Moreover, it implements a Lorentz boost symmetry, originally suggested to be related to a q-deformed 2D Poincare algebra. We also discuss the classical double construction for the bialgebra of interest and comment on the representation of the affine structure. |
| title | Affine Classical Lie Bialgebras for AdS/CFT Integrability |
| topic | High Energy Physics - Theory Mathematical Physics Quantum Algebra |
| url | https://arxiv.org/abs/2401.10327 |