Classical Integrability and Super Yangian of Superstring on AdS_5 x S^5

Abstract

We discuss a classical integrability in the type IIB string theory on the AdS_5 x S^5 background. By using the Roiban-Siegel formulation of the superstring on the AdS_5 x S^5, we carefully treat the Wess-Zumino term and the constraint conditions intrinsic to the supersymmetric case, and construct explicitly non-local charges for a hidden infinite-dimensional symmetry. The existence of the symmetry is shown by Bena-Polchinski-Roiban. Then the super Yangian algebra is calculated. We also show the Serre relation ensuring the structure of the Hopf algebra. In addition, the classical integrability is discussed by constructing the Lax pair and the transfer matrix.

arXiv comment24 pages, LaTeX, added r-matrix and comments, version to appear in Adv. Theor. Math. Phys

References in corpus (28)

• Strings in flat space and pp waves from $\mathcal{N}=4$ Super Yang Mills
• The Bethe-Ansatz for N=4 Super Yang-Mills
• Hidden Symmetries of the AdS_5 x S^5 Superstring
• Type IIB superstring action in AdS_5 x S^5 background
• The N=4 SYM Integrable Super Spin Chain
• Semiclassical quantization of rotating superstring in AdS_5 x S^5
• Bethe Ansatz for Quantum Strings
• The Complete One-Loop Dilatation Operator of N=4 Super Yang-Mills Theory
• Spinning strings in AdS_5 x S^5 and integrable systems
• Spinning strings in AdS_5 x S^5: new integrable system relations
• Aspects of Semiclassical Strings in AdS${}_5$
• Superstring Theory on AdS_2 x S^2 as a Coset Supermanifold
• Matching Higher Conserved Charges for Strings and Spins
• $PSL(n|n)$ Sigma Model as a Conformal Field Theory
• Superstrings on AdS_5 x S^5 supertwistor space
• Conformal Fixed Points of Unidentified Gauge Theories
• Two-loop commuting charges and the string/gauge duality
• The gl(M|N) Super Yangian and Its Finite Dimensional Representations
• Yangian Symmetry in Conformal Field Theory
• Classical AdS Superstring Mechanics
• Conserved Charges and Supersymmetry in Principal Chiral Models
• A new holographic limit of AdS5 x S5
• Wess-Zumino terms for AdS D-branes
• AdS and pp-wave D-particle superalgebras
• Lattice quantization of Yangian charges
• Algebra of Non-Local Charges in Supersymmetric Non-Linear Sigma Models
• The Affine Hidden Symmetry and Integrability of Type IIB Superstring in $Ad{S}_5\times S^5$
• The affine ambitwistor space as the moduli space of SUYM in $Ad{S}_5\otimes S^5$

Cited by in corpus (14)

• Bethe Ansatz for a Quantum Supercoset Sigma Model
• The classical R-matrix of AdS/CFT and its Lie dialgebra structure
• Yangians, S-matrices and AdS/CFT
• Integrable Open Spin Chains and the Doubling Trick in N = 2 SYM with Fundamental Matter
• Giant Magnon in NS5-brane Background
• Ramond-Ramond gauge fields in superspace with manifest T-duality
• Open Semiclassical Strings and Long Defect Operators in AdS/dCFT Correspondence
• Integrability and Higher Loops in AdS/dCFT Correspondence
• Structure of the string R-matrix
• Higher-spin conserved currents in supersymmetric sigma models on symmetric spaces
• Sugawara form for AdS superstring
• BRST Invariance of Non-local Charges and Monodromy Matrix of Bosonic String on AdS(5)xS(5)
• Kappa symmetric OSp(2|2) WZNW model
• PSU(2,2|4) Exchange Algebra of N=4 Superconformal Multiplets