The Classical r-Matrix of AdS/CFT and its Lie Bialgebra Structure
Abstract
In this paper we investigate the algebraic structure of AdS/CFT in the strong-coupling limit. We propose an expression for the classical r-matrix with (deformed) $${\mathfrak{u}(2|2)}$$ symmetry, which leads to a quasi-triangular Lie bialgebra as the underlying symmetry algebra. On the fundamental representation our r-matrix coincides with the classical limit of the quantum R-matrix.
- Publication:
-
Communications in Mathematical Physics
- Pub Date:
- January 2009
- DOI:
- 10.1007/s00220-008-0578-2
- arXiv:
- arXiv:0708.1762
- Bibcode:
- 2009CMaPh.285..537B
- Keywords:
-
- Central Charge;
- Hopf Algebra;
- Classical Limit;
- Evaluation Representation;
- Loop Algebra;
- High Energy Physics - Theory;
- Mathematics - Quantum Algebra;
- Nonlinear Sciences - Exactly Solvable and Integrable Systems
- E-Print:
- 31 pages, v2: added comment on classical double structure in 4.5. new section 5 on relation to other algebras (from old appendix and new results). fixed typos and mathematical inaccuracies, added references, v3: improved mathematical presentation, to appear in CMP