A note on spin chain/string duality

Abstract

Recently a significant progress in matching the anomalous dimensions of certain class of operators in N=4 SYM theory and rotating strings was made. The correspondence was established mainly using Bethe ansatz technique applied to the spin s Heisenberg model. In a recent paper Kruczenski (hep-th/0311203) suggested to solve the Heisenberg model by using of sigme model approach. In this paper we generalize the solutions obtained by Kruczenski and comment on the dual string theory. It turns out that our solutions are related to the so called Neumann-Rosochatius integrable system. We comment on the spin chain solutions and on the string/gauge theory correspondence.

v.2 One reference added, typos corrected, 21 pages

References in corpus (1)

• Large spin limit of AdS_5 x S^5 string theory and low energy expansion of ferromagnetic spin chains

Cited by in corpus (36)

• Bethe Ansatz for Quantum Strings
• Spin chains and string theory
• Integrable Hamiltonian for Classical Strings on AdS_5 x S^5
• The SU(3) spin chain sigma model and string theory
• Yang-Mills Correlation Functions from Integrable Spin Chains
• Semiclassical strings in Sasaki-Einstein manifolds and long operators in N=1 gauge theories
• Semiclassical Bethe Ansatz and AdS/CFT
• Multispin Giant Magnons
• Finite size effects in ferromagnetic spin chains and quantum corrections to classical strings
• Pulsating Strings on AdS_5 x S^5
• Generalized pulsating strings
• Spin chain sigma models with fermions
• Finite-Size Corrections to Anomalous Dimensions in N=4 SYM Theory
• Spiky Strings, Giant Magnons and beta-deformations
• Integrable Open Spin Chains and the Doubling Trick in N = 2 SYM with Fundamental Matter
• Semiclassical strings in Lunin-Maldacena background
• Wound and Rotating Strings in AdS_5 x S^5
• Quantum Stability for the Heisenberg Ferromagnet
• N=2 Super Yang-Mills and the XXZ spin chain
• Dual Spikes; New Spiky String Solutions
• Generalizations of Lunin-Maldacena transformation on the $AdSsub5xSsup5$ background
• On the anatomy of multi-spin magnon and single spike string solutions
• Semiclassical Strings, Dipole Deformations of N=1 SYM and Decoupling of KK Modes
• Integrable Rosochatius deformations of higher-order constrained flows and the soliton hierarchy with self-consistent sources
• Magnon-Like Dispersion Relation from M-Theory
• Finite Density States in Integrable Conformal Field Theories
• Circular and Folded Multi-Spin Strings in Spin Chain Sigma Models
• The Anatomy of Gauge/String Duality in Lunin-Maldacena Background
• Giant Magnons under NS-NS and Melvin Fields
• Multispin magnons on deformed $Ad{S}_3\times S^3$
• gamma_i Deformed Lax Pair for Rotating Strings in the Fast Motion Limit
• Stringy correlations on deformed $Ad{S}_3\times S^3$
• Spin chain from membrane and the Neumann-Rosochatius integrable system
• Fast spinning strings on $\eta$ deformed $Ad{S}_5\times S^5$
• Renormalization group flow of reduced string actions
• String Solutions in General Backgrounds