Finite size effects in ferromagnetic spin chains and quantum corrections to classical strings

Abstract

N=4 supersymmetric Yang-Mills operators carrying large charges are dual to semiclassical strings in AdS_5xS^5. The spectrum of anomalous dimensions of very large operators has been calculated solving the Bethe ansatz equations in the thermodynamic limit, and matched to energies of string solitons. We have considered finite size corrections to the Bethe equations, that should correspond to quantum effects on the string side.

18 pages. Latex. v2: Misprints corrected, expanded discussions with comments on end point effects, and updated reference

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• Foundations of the AdS_5 x S^5 Superstring. Part I
• The Algebraic Curve of Classical Superstrings on AdS_5xS^5
• Quantum corrections to the string Bethe ansatz
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• Quantum spinning strings in AdS_4 x CP^3: testing the Bethe Ansatz proposal
• Green-Schwarz Strings in TsT-transformed backgrounds
• Matching quantum strings to quantum spins: one-loop vs. finite-size corrections
• The Strong Coupling Limit of the Scaling Function from the Quantum String Bethe Ansatz
• Quantum corrections to spinning strings in AdS(5)xS(5) and Bethe ansatz: a comparative study
• Complete 1-loop test of AdS/CFT
• A Universality Test of the Quantum String Bethe Ansatz
• Semiclassical strings in Sasaki-Einstein manifolds and long operators in N=1 gauge theories
• Stringy sums and corrections to the quantum string Bethe ansatz
• Tailoring Three-Point Functions and Integrability III. Classical Tunneling
• Bethe Ansatz for a Quantum Supercoset Sigma Model
• Exact expressions for quantum corrections to spinning strings
• How Accurate is the Quantum String Bethe Ansatz?
• Y-system and Quasi-Classical Strings
• Constructing the AdS/CFT dressing factor
• Strings as Multi-Particle States of Quantum Sigma-Models
• PSU(2,2|4) Character of Quasiclassical AdS/CFT
• Long-Range GL(n) Integrable Spin Chains and Plane-Wave Matrix Theory
• 1/J corrections to semiclassical AdS/CFT states from quantum Landau-Lifshitz model
• Double Scaling and Finite Size Corrections in sl(2) Spin Chain
• Integrable Open Spin Chains and the Doubling Trick in N = 2 SYM with Fundamental Matter
• Semiclassical strings in Lunin-Maldacena background
• On the finite size corrections of anti-ferromagnetic anomalous dimensions in $\mathcal{N}=4$ SYM
• Wound and Rotating Strings in AdS_5 x S^5
• Quantum Stability for the Heisenberg Ferromagnet
• Quantum Scattering of Giant Magnons
• Hubbard's Adventures in $\mathcal{N}=4$ SYM-land? Some non-perturbative considerations on finite length operators
• Local correlations in the attractive 1D Bose gas: from Bethe ansatz to the Gross-Pitaevskii equation
• Generalizations of Lunin-Maldacena transformation on the $AdSsub5xSsup5$ background
• Superstring sigma models from spin chains: the SU(1,1|1) case
• Semiclassical Strings, Dipole Deformations of N=1 SYM and Decoupling of KK Modes
• Sigma model from SU(1,1|2) spin chain
• Aspects of Integrability in AdS/CFT Duality
• Review of AdS/CFT Integrability, Chapter II.2: Quantum Strings in AdS5xS5
• Finite-size corrections to the rotating string and the winding state
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• Quantum fluctuations of rotating strings in AdS_5 x S^5
• Strong coupling anomalous dimensions of $\mathcal{N}=4$ super Yang-Mills
• Semi-classical quantisation of magnetic solitons in the anisotropic Heisenberg quantum chain
• Renormalization group flow of reduced string actions
• Integrability and scattering of the boson field theory on a lattice
• String Solutions in General Backgrounds