The Classical Exchange Algebra of AdS5 x S5 String Theory

Abstract

The classical exchange algebra satisfied by the monodromy matrix of AdS5 x S5 string theory in the Green-Schwarz formulation is determined by using a first-order Hamiltonian formulation and by adding to the Bena-Polchinski-Roiban Lax connection terms proportional to constraints. This enables in particular to show that the conserved charges of this theory are in involution. This result is obtained for a general world-sheet metric. The same exchange algebra is obtained within the pure spinor description of AdS5 x S5 string theory. These results are compared to the one obtained by A. Mikhailov and S. Schaefer-Nameki for the pure spinor formulation.

37 pages; v2: Result on Jacobi identity and Yang-Baxter equation added in section 3.3; v3: References added; v4: Comparison with ref [12] clarified in section 3.3

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Cited by in corpus (33)

• Foundations of the AdS_5 x S^5 Superstring. Part I
• An integrable deformation of the AdS_5 x S^5 superstring action
• Derivation of the action and symmetries of the q-deformed AdS_5 x S^5 superstring
• Integrable Deformations of Sigma Models
• The classical R-matrix of AdS/CFT and its Lie dialgebra structure
• Supergravity backgrounds of the eta-deformed AdS2 x S2 x T6 and AdS5 x S5 superstrings
• Quantum integrability and functional equations
• Yangians, S-matrices and AdS/CFT
• Alleviating the non-ultralocality of coset sigma models through a generalized Faddeev-Reshetikhin procedure
• On the Hamiltonian integrability of the bi-Yang-Baxter sigma-model
• Alleviating the non-ultralocality of the AdS_5 x S^5 superstring
• Hamiltonian dynamics and the hidden symmetries of the AdS_5 x S^5 superstring
• Review of AdS/CFT Integrability, Chapter II.3: Sigma Model, Gauge Fixing
• Local charges in involution and hierarchies in integrable sigma-models
• Three-parameter integrable deformation of Z_4 permutation supercosets
• Fusion of line operators in conformal sigma-models on supergroups, and the Hirota equation
• First-principles derivation of the AdS/CFT Y-systems
• Integrable Lambda Models And Chern-Simons Theories
• A lattice Poisson algebra for the Pohlmeyer reduction of the AdS_5 x S^5 superstring
• Ultralocal Lax connection for para-complex ${\mathbb{Z}}_T$-cosets
• Coset space actions for nonrelativistic strings
• Lambda Models From Chern-Simons Theories
• Exploring The Lambda Model Of The Hybrid Superstring
• Yang-Baxter deformations of the $Ad{S}_4\times {\mathbb{CP}}^3$ superstring sigma model
• On semiclassical analysis of pure spinor superstring in an AdS_5 x S^5 background
• $\lambda$-Deformation Of The $Ad{S}_5\times S^5$ Pure Spinor Superstring
• Symmetric space $\lambda$-model exchange algebra from 4d holomorphic Chern-Simons theory
• The Hirota equation for string theory in AdS5xS5 from the fusion of line operators
• PSU(2,2|4) Exchange Algebra of N=4 Superconformal Multiplets
• Classical Spectral Curve of the AdS_5 x S^5 Lambda Superstring
• Super Yangian of superstring on AdS5xS5 revisited
• Killing scalar of non-linear sigma models on G/H realizing the classical exchange algebra
• Constrained WZWN Models on G/{S x U(1)^n} and Exchange Algebra of G-Primaries