The Algebra of Transition Matrices for the AdS_5 x S^5 Superstring

Abstract

We consider integrability properties of the superstring on $Ad{S}_5\times S^5$ background and construct a new one parameter family of currents which satisfies the vanishing curvature condition. We present the Hamiltonian analysis for the sigma model action and determine the Poisson algebra of the transition matrices. We reveal the generalization of the ${\mathbb{Z}}_4$ automorphism analogous to the sigma models defined on a symmetric space coset. A possible regularization scheme for the ambiguities present, which respects the generalized automorphism, is also discussed.

24 pages, Latex, jhep style; references added

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Cited by in corpus (50)

• Foundations of the AdS_5 x S^5 Superstring. Part I
• The Algebraic Curve of Classical Superstrings on AdS_5xS^5
• Superstrings on AdS_4 x CP^3 as a Coset Sigma-model
• Finite-size Effects from Giant Magnons
• The Off-shell Symmetry Algebra of the Light-cone AdS_5 x S^5 Superstring
• Uniform Light-Cone Gauge for Strings in AdS_5 x S^5: Solving su(1|1) Sector
• On Integrability of Classical SuperStrings in AdS_5 x S^5
• Bethe Ansatz for a Quantum Supercoset Sigma Model
• Non-local charges, Zm gradings and coset space actions
• New Integrable System of 2dim Fermions from Strings on AdS_5 x S^5
• On Drinfeld's second realization of the AdS/CFT su(2|2) Yangian
• The classical R-matrix of AdS/CFT and its Lie dialgebra structure
• A Secret Symmetry of the AdS/CFT S-matrix
• The Classical Exchange Algebra of AdS5 x S5 String Theory
• The algebra of flat currents for the string on AdS_5 x S^5 in the light-cone gauge
• Yangians, S-matrices and AdS/CFT
• Algebra of transfer-matrices and Yang-Baxter equations on the string worldsheet in AdS(5) x S(5)
• A Yangian Double for the AdS/CFT Classical r-matrix
• Flat Currents of the Green-Schwarz Superstrings in AdS_5 x S^1 and AdS_3 x S^3 backgrounds
• Linking Backlund and Monodromy Charges for Strings on AdS_5 x S^5
• Giant Magnon in NS5-brane Background
• Hamiltonian dynamics and the hidden symmetries of the AdS_5 x S^5 superstring
• Current Algebra of the Pure Spinor Superstring in AdS(5) x S(5)
• Review of AdS/CFT Integrability, Chapter II.3: Sigma Model, Gauge Fixing
• Open Spinning Strings and AdS/dCFT Duality
• The U(N) chiral model and exact multi-solitons
• Notes on Collective Field Theory of Matrix and Spin Calogero Models
• Integrability and Higher Loops in AdS/dCFT Correspondence
• BPS Operators in N=4 SYM: Calogero Models and 2D Fermions
• Pulsating Strings With Angular Momenta
• Structure of the string R-matrix
• Current Algebra and Integrability of Principal Chiral Model on the World-sheet with General Metric
• Lambda Models From Chern-Simons Theories
• Pure Spinor Strings in TsT Deformed Background
• On S-Matrix factorization of the Landau-Lifshitz model
• Nonlocal charges of T-dual strings
• Note About Integrability and Gauge Fixing for Bosonic String on AdS(5)xS(5)
• Sugawara form for AdS superstring
• The S-matrix of the Faddeev-Reshetikhin Model, Diagonalizability and PT Symmetry
• Review of AdS/CFT Integrability, Chapter VI.2: Yangian Algebra
• Hamiltonian Analysis of Non-Linear Sigma Model on Supercoset Target
• Reduced Sigma-Model on O(N): Hamiltonian Analysis and Poisson Bracket of Lax Connection
• BRST Invariance of Non-local Charges and Monodromy Matrix of Bosonic String on AdS(5)xS(5)
• Bihamiltonian structure of the classical superstring in AdS_5 x S**5
• Conserved Charges in the Principal Chiral Model on a Supergroup
• The tetrahedral Zamolodchikov algebra for the fermionic Bazhanov-Stroganov R-operator
• Exact Results in Supersymmetric Gauge Theories
• The SU(1|2) and SU(2|2) Sectors from Superstrings in AdS5 x S5
• String Solutions in General Backgrounds
• Solution Transformations for GS String in AdS_5 x S^5 by Conserved Quantities