The Algebraic Curve of Classical Superstrings on AdS_5xS^5

Abstract

We investigate the monodromy of the Lax connection for classical IIB superstrings on AdS_5xS^5. For any solution of the equations of motion we derive a spectral curve of degree 4+4. The curve consists purely of conserved quantities, all gauge degrees of freedom have been eliminated in this form. The most relevant quantities of the solution, such as its energy, can be expressed through certain holomorphic integrals on the curve. This allows for a classification of finite gap solutions analogous to the general solution of strings in flat space. The role of fermions in the context of the algebraic curve is clarified. Finally, we derive a set of integral equations which reformulates the algebraic curve as a Riemann-Hilbert problem. They agree with the planar, one-loop N=4 supersymmetric gauge theory proving the complete agreement of spectra in this approximation.

56 pages, v2: first local charge derived, minor improvements, references added, v3: minor corrections, reference added, to appear in Commun. Math. Phys

References in corpus (28)

• Bethe Ansatz for Quantum Strings
• A Novel Long Range Spin Chain and Planar N=4 Super Yang-Mills
• The Factorized S-Matrix of CFT/AdS
• The Dilatation Operator of N=4 Super Yang-Mills Theory and Integrability
• Integrable Hamiltonian for Classical Strings on AdS_5 x S^5
• Spinning strings and AdS/CFT duality
• Quantum Consistency of the Superstring in AdS_5 x S^5 Background
• Holography Beyond the Penrose Limit
• Algebraic Curve for the SO(6) sector of AdS/CFT
• Classical/quantum integrability in non-compact sector of AdS/CFT
• Matching quantum strings to quantum spins: one-loop vs. finite-size corrections
• The Algebraic Curve of 1-loop Planar N=4 SYM
• Complete Spectrum of Long Operators in N=4 SYM at One Loop
• Higher Impurity AdS/CFT Correspondence in the Near-BMN Limit
• Semiclassical Bethe Ansatz and AdS/CFT
• The Algebra of Transition Matrices for the AdS_5 x S^5 Superstring
• Two-loop commuting charges and the string/gauge duality
• Finite size effects in ferromagnetic spin chains and quantum corrections to classical strings
• N-Impurity Superstring Spectra Near the pp-Wave Limit
• Spin chain sigma models with fermions
• BRST Cohomology and Nonlocal Conserved Charges
• Supersymmetric null-surfaces
• Higher-Loop Integrability in N=4 Gauge Theory
• Quantum string integrability and AdS/CFT
• Semiclassical strings in AdS_5 x S^5 and scalar operators in N=4 SYM theory
• Spin Chain for Quantum Strings
• Notes on fast moving strings
• Plane wave limit of local conserved charges

Cited by in corpus (219)

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• Comment on Strings in AdS3 x S3 x S3 x S1 at One Loop
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• Algebraic Curves for Factorized String Solutions
• Giant Magnons and Singular Curves
• Integrability and Higher Loops in AdS/dCFT Correspondence
• Constant mean curvature surfaces in AdS_3
• Integrable Superstrings on the Squashed Three-sphere
• Homogeneous Yang-Baxter deformations as undeformed yet twisted models
• Aspects of Integrability in AdS/CFT Duality
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• TBA for non-perturbative moduli spaces
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