Algebraic Curves for Integrable String Backgrounds

Abstract

Many Ramond-Ramond backgrounds which arise in the AdS/CFT correspondence are described by integrable sigma-models. The equations of motion for classical spinning strings in these backgrounds are exactly solvable by finite-gap integration techniques. We review the finite-gap integral equations and algebraic curves for coset sigma-models, and then apply the results to the AdS(d+1) backgrounds with d=4,3,2,1.

33 pages, 8 figures, talk at "Gauge Fields. Yesterday, Today, Tomorrow", Moscow, 19-24.01.2010; v2: misprints in (4.8), (4.13) corrected, discussion of the quantum Bethe equations expanded

References in corpus (5)

• The AdS_5xS^5 superstring worldsheet S-matrix and crossing symmetry
• The AdS4/CFT3 algebraic curve
• Non-local charges, Zm gradings and coset space actions
• A Symplectic Structure for String Theory on Integrable Backgrounds
• S-matrix for magnons in the D1-D5 system

Cited by in corpus (7)

• Quantum corrections to spinning superstrings in AdS_3 x S^3 x M^4: determining the dressing phase
• Evidence for the classical integrability of the complete AdS(4) x CP(3) superstring
• $Ad{S}_3/CF{T}_2$, finite-gap equations and massless modes
• Generalized unitarity and the worldsheet S matrix in AdS_n x S^n x M^(10-2n)
• Fusion of line operators in conformal sigma-models on supergroups, and the Hirota equation
• Extended systems of Baxter Q-functions and fused flags I: simply-laced case
• On the algebraic curves for circular and folded strings in ${\text{AdS}}_5\times S^5$