The classical R-matrix of AdS/CFT and its Lie dialgebra structure

Abstract

The classical integrable structure of Z_4-graded supercoset sigma-models, arising in the AdS/CFT correspondence, is formulated within the R-matrix approach. The central object in this construction is the standard R-matrix of the Z_4-twisted loop algebra. However, in order to correctly describe the Lax matrix within this formalism, the standard inner product on this twisted loop algebra requires a further twist induced by the Zhukovsky map, which also plays a key role in the AdS/CFT correspondence. The non-ultralocality of the sigma-model can be understood as stemming from this latter twist since it leads to a non skew-symmetric R-matrix.

22 pages, 2 figures

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• Assembling integrable sigma-models as affine Gaudin models
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• Alleviating the non-ultralocality of coset sigma models through a generalized Faddeev-Reshetikhin procedure
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• Alleviating the non-ultralocality of the AdS_5 x S^5 superstring
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• Review of AdS/CFT Integrability, Chapter II.3: Sigma Model, Gauge Fixing
• Local charges in involution and hierarchies in integrable sigma-models
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• Integrable deformations of coupled sigma-models
• First-principles derivation of the AdS/CFT Y-systems
• Holomorphic Chern-Simons theory and affine Gaudin models
• A lattice Poisson algebra for the Pohlmeyer reduction of the AdS_5 x S^5 superstring
• Strong integrability of $\lambda$-deformed models
• Integrability vs Supersymmetry: Poisson Structures of The Pohlmeyer Reduction
• Constrained affine Gaudin models and diagonal Yang-Baxter deformations
• Geometry of the spectral parameter and renormalisation of integrable $\sigma$-models
• Review of AdS/CFT Integrability, Chapter VI.2: Yangian Algebra
• Integrable deformation of ${\mathbb{CP}}^n$ and generalised Kaehler geometry
• The Hirota equation for string theory in AdS5xS5 from the fusion of line operators
• Classical Spectral Curve of the AdS_5 x S^5 Lambda Superstring
• Generalized sine-Gordon models and quantum braided groups
• Integrable models based on non-semi-simple groups and plane wave target spacetimes
• Splitting strings on integrable backgrounds
• Towards a quadratic Poisson algebra for the subtracted classical monodromy of Symmetric Space Sine-Gordon theories