Spin chain sigma models with fermions

Abstract

The complete one-loop planar dilatation operator of N=4 supersymmetric Yang-Mills is isomorphic to the hamiltonian of an integrable PSU(2,2|4) quantum spin chain. We construct the non-linear sigma models describing the continuum limit of the SU(1|3) and SU(2|3) sectors of the complete N=4 chain. We explicitely identify the spin chain sigma model with the one for a superstring moving in AdS_5xS^5 with large angular momentum along the five-sphere.

16 pages. Latex. v2: Misprints corrected and references added

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• Bethe Ansatz for Quantum Strings
• Large spin limit of AdS_5 x S^5 string theory and low energy expansion of ferromagnetic spin chains
• Deformations of N=4 SYM and integrable spin chain models
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Cited by in corpus (40)

• The Factorized S-Matrix of CFT/AdS
• Lax Pair for Strings in Lunin-Maldacena Background
• The Algebraic Curve of Classical Superstrings on AdS_5xS^5
• Finite-size Effects from Giant Magnons
• Integrability and the AdS(3)/CFT(2) correspondence
• Integrable Hamiltonian for Classical Strings on AdS_5 x S^5
• Spinning strings and integrable spin chains in the AdS/CFT correspondence
• Spiky strings and single trace operators in gauge theories
• Algebraic Curve for the SO(6) sector of AdS/CFT
• Uniform Light-Cone Gauge for Strings in AdS_5 x S^5: Solving su(1|1) Sector
• On Integrability of Classical SuperStrings in AdS_5 x S^5
• Matching quantum strings to quantum spins: one-loop vs. finite-size corrections
• Complete Spectrum of Long Operators in N=4 SYM at One Loop
• Quantum corrections to spinning strings in AdS(5)xS(5) and Bethe ansatz: a comparative study
• Semiclassical strings in Sasaki-Einstein manifolds and long operators in N=1 gauge theories
• New Integrable System of 2dim Fermions from Strings on AdS_5 x S^5
• Finite size effects in ferromagnetic spin chains and quantum corrections to classical strings
• 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
• Wound and Rotating Strings in AdS_5 x S^5
• Anisotropic Landau-Lifshitz sigma models from q-deformed AdS_5 x S^5 superstrings
• Asymptotic Bethe Ansatz S-matrix and Landau-Lifshitz type effective 2-d actions
• The SU(2) sector in AdS/CFT
• Landau-Lifshitz sigma-models, fermions and the AdS/CFT correspondence
• An exactly solvable supersymmetric spin chain of BC_N type
• Superstring sigma models from spin chains: the SU(1,1|1) case
• Sigma model from SU(1,1|2) spin chain
• Rational three-spin string duals and non-anomalous finite size effects
• Systematic classical continuum limits of integrable spin chains and emerging novel dualities
• More Pendants for Polya: Two loops in the SU(2) sector
• Chaotic spin chains in AdS/CFT
• Spin chains of Haldane-Shastry type and a generalized central limit theorem
• $1/f^{\alpha }$ noise and integrable systems
• Three-parameter deformation of $\mathbb{R}\times S^3$ in the Landau-Lifshitz limit
• BMN operators with a scalar fermion pair and operator mixing in N=4 Super Yang-Mills Theory
• The $\mathrm{SL}(2,\mathbb{R})$ Wess-Zumino-Novikov-Witten spin-chain $\sigma$-model
• The $SU(2)$ Wess-Zumino-Witten spin chain sigma model
• The SU(1|2) and SU(2|2) Sectors from Superstrings in AdS5 x S5
• Renormalization group flow of reduced string actions
• An integrable deformed Landau-Lifshitz model with particle production?