Integrability of Type II Superstrings on Ramond-Ramond Backgrounds in Various Dimensions

Abstract

We consider type II superstrings on AdS backgrounds with Ramond-Ramond flux in various dimensions. We realize the backgrounds as supercosets and analyze explicitly two classes of models: non-critical superstrings on AdS_{2d} and critical superstrings on AdS_p\times S^p\times CY. We work both in the Green--Schwarz and in the pure spinor formalisms. We construct a one-parameter family of flat currents (a Lax connection) leading to an infinite number of conserved non-local charges, which imply the classical integrability of both sigma-models. In the pure spinor formulation, we use the BRST symmetry to prove the quantum integrability of the sigma-model. We discuss how classical κ-symmetry implies one-loop conformal invariance. We consider the addition of space-filling D-branes to the pure spinor formalism.

LaTeX2e, 56 pages, 1 figure, JHEP style; v2: references added, typos fixed in some equations; v3: typos fixed to match the published version

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• Beta Function of k Deformed AdS_5 x S^5 String Theory
• Integrable Deformations of Sigma Models
• Finite-gap equations for strings on AdS_3 x S^3 x T^4 with mixed 3-form flux
• On Integrable Backgrounds Self-dual under Fermionic T-duality
• Integrability of Green-Schwarz Sigma Models with Boundaries
• Comment on Strings in AdS3 x S3 x S3 x S1 at One Loop
• The Classical Exchange Algebra of AdS5 x S5 String Theory
• Self-Duality of Green-Schwarz Sigma-Models
• Classical Integrability of the Squashed Three-sphere, Warped AdS3 and Schroedinger Spacetime via T-Duality
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• Superstrings in AdS
• 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
• Algebraic Curves for Factorized String Solutions
• Integrable Superstrings on the Squashed Three-sphere
• On the Non-renormalization of the AdS Radius
• Integrable supersymmetric deformations of $\mathrm{Ad}{\mathrm{S}}_3\times {\mathrm{S}}^3\times {\mathrm{T}}^4$
• Exploring The Lambda Model Of The Hybrid Superstring
• The Pure Spinor Formulation of Superstrings
• Note About Redefinition of BRST Operator for Pure Spinor String in General Background
• On the Relation between Hybrid and Pure Spinor String Theory
• Lagrangian mechanics of massless superparticle on AdS_4 x CP^3 superbackground