Algebraic Curve for the SO(6) sector of AdS/CFT

Abstract

We construct the general algebraic curve of degree four solving the classical sigma model on RxS5. Up to two loops it coincides with the algebraic curve for the dual sector of scalar operators in N=4 SYM, also constructed here. We explicitly reproduce some particular solutions.

58 pages, v2: minor changes, references added, v3: "length" identified in sigma model, comparison of curves improved, minor changes, v4: references added, to appear in Commun. Math. Phys

References in corpus (17)

• Bethe Ansatz for Quantum Strings
• The Dilatation Operator of N=4 Super Yang-Mills Theory and Integrability
• Integrability in QCD and beyond
• Introduction to Yangian symmetry in integrable field theory
• Semiclassical relativistic strings in S^5 and long coherent operators in N=4 SYM theory
• Large spin limits of AdS/CFT and generalized Landau-Lifshitz equations
• Classical/quantum integrability in non-compact sector of AdS/CFT
• A three-loop test of the dilatation operator in N=4 SYM
• Higher Impurity AdS/CFT Correspondence in the Near-BMN Limit
• Spin chain sigma models with fermions
• Yangian Symmetries of Matrix Models and Spin Chains: The Dilatation Operator of $\mathcal{N}$$=4$ SYM
• Higher-Loop Integrability in N=4 Gauge Theory
• The Circular, Elliptic Three Spin String from the SU(3) Spin Chain
• Spin Chain for Quantum Strings
• Semiclassical strings in AdS_5 x S^5 and scalar operators in N=4 SYM theory
• Notes on fast moving strings
• Lattice Super Yang-Mills: A Virial Approach to Operator Dimensions

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