Algebra of transfer-matrices and Yang-Baxter equations on the string worldsheet in AdS(5) x S(5)

Abstract

Integrability of the string worldsheet theory in AdS(5) x S(5) is related to the existence of a flat connection depending on the spectral parameter. The transfer matrix is the open-ended Wilson line of this flat connection. We study the product of transfer matrices in the near-flat space expansion of the AdS(5) x S(5) string theory in the pure spinor formalism. The natural operations on Wilson lines with insertions are described in terms of r- and s-matrices satisfying a generalized classical Yang-Baxter equation. The formalism is especially transparent for infinite or closed Wilson lines with simple gauge invariant insertions.

LaTeX, 47 pp; v2: clarified the relation to the calculation of Poisson bracket (Section 2.2.2); added example in Section 7

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• The Classical Exchange Algebra of AdS5 x S5 String Theory
• Yangians, S-matrices and AdS/CFT
• UV finiteness of Pohlmeyer-reduced form of the AdS_5xS^5 superstring theory
• Superstrings in AdS
• Fusion of Critical Defect Lines in the 2D Ising Model
• GGI Lectures on the Pure Spinor Formalism of the Superstring
• An Exceptional Algebraic Origin of the AdS/CFT Yangian Symmetry
• Hamiltonian dynamics and the hidden symmetries of the AdS_5 x S^5 superstring
• Symmetries of massless vertex operators in AdS(5) x S(5)
• Review of AdS/CFT Integrability, Chapter II.3: Sigma Model, Gauge Fixing
• Fusion of line operators in conformal sigma-models on supergroups, and the Hirota equation
• First-principles derivation of the AdS/CFT Y-systems
• Structure of the string R-matrix
• On S-Matrix factorization of the Landau-Lifshitz model
• Strong integrability of $\lambda$-deformed models
• Quantum Current Algebra for the $Ad{S}_5\times S^5$ Superstring
• $Ad{S}_5\times S^5$ supergravity vertex operators
• The r-matrix of the Alday-Arutyunov-Frolov model
• The Hirota equation for string theory in AdS5xS5 from the fusion of line operators
• Note About Redefinition of BRST Operator for Pure Spinor String in General Background
• Vertex operators for the plane wave pure spinor string
• Master symmetry in the $Ad{S}_5\times S^5$ pure spinor string
• Integrability of the Gauged Linear Sigma Model for AdS_5xS^5
• Quantum corrections to $Ad{S}_5\times S^5$ left-invariant superstring current algebra
• Algebra of Lax Connection for T-Dual Models