Notes on fast moving strings

Abstract

We review the recent work on the mechanics of fast moving strings in anti-de Sitter space times a sphere and discuss the role of conserved charges. An interesting relation between the local conserved charges of rigid solutions was found in the earlier work. We propose a generalization of this relation for arbitrary solutions, not necessarily rigid. We conjecture that an infinite combination of local conserved charges is an action variable generating periodic trajectories in the classical string phase space. It corresponds to the length of the operator on the field theory side.

arXiv commentv2: added Section 4.4; v3: added references, expanded review section, small corrections in Section 4, added Section 4.6; v4: added conclusion

References in corpus (27)

• The Bethe-Ansatz for N=4 Super Yang-Mills
• Hidden Symmetries of the AdS_5 x S^5 Superstring
• Semiclassical quantization of rotating superstring in AdS_5 x S^5
• Classical/quantum integrability in AdS/CFT
• Multi-spin string solutions in AdS_5 x S^5
• The su(2|3) Dynamic Spin Chain
• Spin chains and string theory
• Spinning strings in AdS_5 x S^5: new integrable system relations
• The Algebraic Curve of Classical Superstrings on AdS_5xS^5
• Aspects of Semiclassical Strings in AdS${}_5$
• Large spin limit of AdS_5 x S^5 string theory and low energy expansion of ferromagnetic spin chains
• Matching Higher Conserved Charges for Strings and Spins
• Integrable Hamiltonian for Classical Strings on AdS_5 x S^5
• Quantizing three-spin string solution in AdS_5 x S^5
• Semiclassical relativistic strings in S^5 and long coherent operators in N=4 SYM theory
• On Integrability of Classical SuperStrings in AdS_5 x S^5
• On one-loop correction to energy of spinning strings in S^5
• Semiclassical quantization of superstrings: AdS_5 x S^5 and beyond
• Anomalous dimensions in gauge theories from rotating strings in $Ad{S}_5\times S^5$
• Speeding Strings
• Higher Loops Beyond the SU(2) Sector
• Non-local charges on AdS_5 x S^5 and PP-waves
• Higher Conserved Charges and Integrability for Spinning Strings in AdS_5 x S^5
• Supersymmetric null-surfaces
• Slow evolution of nearly-degenerate extremal surfaces
• Quantum string integrability and AdS/CFT
• Plane wave limit of local conserved charges

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• Matching quantum strings to quantum spins: one-loop vs. finite-size corrections
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• An action variable of the sine-Gordon model
• 1/J corrections to semiclassical AdS/CFT states from quantum Landau-Lifshitz model
• Super spin chain coherent state actions and $Ad{S}_5\times S^5$ superstring
• Linking Backlund and Monodromy Charges for Strings on AdS_5 x S^5
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• On the propagator of a scalar field in AdS x S and in its plane wave limit
• Anomalous dimension and local charges
• Plane wave limit of local conserved charges
• On Singleton Composites in Non-compact WZW Models
• Spin chain from membrane and the Neumann-Rosochatius integrable system
• The SU(1|2) and SU(2|2) Sectors from Superstrings in AdS5 x S5
• Renormalization group flow of reduced string actions
• String Solutions in General Backgrounds