Hamiltonian dynamics and the hidden symmetries of the AdS_5 x S^5 superstring

Abstract

We construct the Lax connection of the Green-Schwarz superstring in AdS_5 x S^5 within the Hamiltonian formalism and obtain precisely that used in 0810.4136. It differs in a crucial way from the Bena-Polchinski-Roiban connection by terms proportional to the Hamiltonian constraints. These extra terms ensure firstly that the integrals of motion are all first class and secondly that the Lax connection is flat in the strong sense.

21 pages, 1 figure

References in corpus (6)

• Foundations of the AdS_5 x S^5 Superstring. Part I
• The Classical Exchange Algebra of AdS5 x S5 String Theory
• Algebra of transfer-matrices and Yang-Baxter equations on the string worldsheet in AdS(5) x S(5)
• Perturbative study of the transfer matrix on the string worldsheet in AdS(5)xS(5)
• Current Algebra and Integrability of Principal Chiral Model on the World-sheet with General Metric
• Note About Integrability and Gauge Fixing for Bosonic String on AdS(5)xS(5)

Cited by in corpus (23)

• On classical q-deformations of integrable sigma-models
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• The classical R-matrix of AdS/CFT and its Lie dialgebra structure
• 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
• Review of AdS/CFT Integrability, Chapter II.3: Sigma Model, Gauge Fixing
• Local charges in involution and hierarchies in integrable sigma-models
• First-principles derivation of the AdS/CFT Y-systems
• Yang-Baxter deformations of the AdS${}_5\times$S${}^5$ supercoset sigma model from 4D Chern-Simons theory
• Integrable Lambda Models And Chern-Simons Theories
• Ultralocal Lax connection for para-complex ${\mathbb{Z}}_T$-cosets
• Coset space actions for nonrelativistic strings
• Lambda Models From Chern-Simons Theories
• Strong integrability of $\lambda$-deformed models
• Review of AdS/CFT Integrability, Chapter VI.2: Yangian Algebra
• On semiclassical analysis of pure spinor superstring in an AdS_5 x S^5 background
• Yang-Baxter deformations of the $Ad{S}_4\times {\mathbb{CP}}^3$ superstring sigma model
• $\lambda$-Deformation Of The $Ad{S}_5\times S^5$ Pure Spinor Superstring
• The Hirota equation for string theory in AdS5xS5 from the fusion of line operators
• Super Yangian of superstring on AdS5xS5 revisited
• Classical Spectral Curve of the AdS_5 x S^5 Lambda Superstring