On spin chains and field theories

Abstract

We point out that the existence of global symmetries in a field theory is not an essential ingredient in its relation with an integrable model. We describe an obvious construction which, given an integrable spin chain, yields a field theory whose 1-loop scale transformations are generated by the spin chain Hamiltonian. We also identify a necessary condition for a given field theory to be related to an integrable spin chain. As an example, we describe an anisotropic and parity-breaking generalization of the XXZ Heisenberg spin chain and its associated field theory. The system has no nonabelian global symmetries and generally does not admit a supersymmetric extension without the introduction of more propagating bosonic fields. For the case of a 2-state chain we find the spectrum and the eigenstates. For certain values of its coupling constants the field theory associated to this general type of chain is the bosonic sector of the Leigh-Strassler deformation of N=4 SYM theory.

22 pages, Latex; v2. typos corrected

References in corpus (12)

• Hidden Symmetries of the AdS_5 x S^5 Superstring
• The N=4 SYM Integrable Super Spin Chain
• The Complete One-Loop Dilatation Operator of N=4 Super Yang-Mills Theory
• Stringing Spins and Spinning Strings
• Spinning strings in AdS_5 x S^5 and integrable systems
• Spinning strings in AdS_5 x S^5: new integrable system relations
• A Relation Between Approaches to Integrability in Superconformal Yang-Mills Theory
• Matching Higher Conserved Charges for Strings and Spins
• Gauge/string duality for QCD conformal operators
• Yang-Mills Duals for Semiclassical Strings
• Superconformal operators in N=4 super-Yang-Mills theory
• Integrable Spin Chain and Operator Mixing in N=1,2 Supersymmetric Theories

Cited by in corpus (65)

• Deforming field theories with $U(1)\times U(1)$ global symmetry and their gravity duals
• Lax Pair for Strings in Lunin-Maldacena Background
• Gauge-string duality for superconformal deformations of N=4 Super Yang-Mills theory
• Beauty and the Twist: The Bethe Ansatz for Twisted N=4 SYM
• Spinning strings and integrable spin chains in the AdS/CFT correspondence
• Quantum Deformations of the One-Dimensional Hubbard Model
• Green-Schwarz Strings in TsT-transformed backgrounds
• Gauge-string duality for (non)supersymmetric deformations of N=4 Super Yang-Mills theory
• Long-Range Deformations for Integrable Spin Chains
• Review of AdS/CFT Integrability, Chapter IV.2: Deformations, Orbifolds and Open Boundaries
• Magnons, Classical Strings and beta-Deformations
• On Marginal Deformations and Non-Integrability
• Integrability and non-Integrability in N=2 SCFTs and their Holographic Backgrounds
• 1/J corrections to semiclassical AdS/CFT states from quantum Landau-Lifshitz model
• The Bethe Ansatz for Z_S Orbifolds of N=4 Super Yang-Mills Theory
• Y-system and beta-deformed N=4 Super-Yang-Mills
• Integrability in dipole-deformed N=4 super Yang-Mills
• The general Leigh-Strassler deformation and integrability
• Emergent geometry from q-deformations of N=4 super Yang-Mills
• Integrable Open Spin Chains and the Doubling Trick in N = 2 SYM with Fundamental Matter
• Integrable twists in AdS/CFT
• Single impurity operators at critical wrapping order in the beta-deformed N=4 SYM
• On the finite size corrections of anti-ferromagnetic anomalous dimensions in $\mathcal{N}=4$ SYM
• On the perturbative chiral ring for marginally deformed N=4 SYM theories
• A piece of cake: the ground-state energies in gamma_i-deformed N=4 SYM theory
• Marginal and non-commutative deformations via non-abelian T-duality
• N=2 Super Yang-Mills and the XXZ spin chain
• Integrable Spin Chains with U(1)^3 symmetry and generalized Lunin-Maldacena backgrounds
• Conformal invariance of the planar beta-deformed N=4 SYM theory requires beta real
• The Leigh-Strassler Deformation and the Quest for Integrability
• On wrapping corrections to GKP-like operators
• Unstable Giants
• Effective action of beta-deformed N=4 SYM theory and AdS/CFT
• A supersymmetric matrix model: III. Hidden SUSY in statistical systems
• Quantum Symmetries and Marginal Deformations
• Real versus complex beta-deformation of the N=4 planar super Yang-Mills theory
• Rotating Strings with Two Unequal Spins in Lunin-Maldacena Background
• Strings on conifolds from strong coupling dynamics, part I
• Electric/Magnetic Field Deformed Giant Gravitons in Melvin Geometry
• The Anatomy of Gauge/String Duality in Lunin-Maldacena Background
• Chaotic spin chains in AdS/CFT
• Worldsheet S-matrix of beta-deformed SYM
• Pure Spinor Strings in TsT Deformed Background
• Dynamical Spin Chains in 4D $\mathcal{N}=2$ SCFTs
• Gravity duals for the Coulomb branch of marginally deformed N=4 Yang-Mills
• Note on Integrability of Marginally Deformed ABJ(M) Theories
• Holographic Cusped Wilson loops in $q$-deformed $Ad{S}_5\times S^5$ Spacetime
• One-Loop Non-Planar Anomalous Dimensions in Super Yang-Mills Theory
• Is there a tower of charges to be discovered?
• Y-system for $\gamma$-deformed ABJM Theory
• The dual string sigma-model of the SU_q(3) sector
• Thermal Giant Graviton with Non-commutative Dipole Field
• Yangians in Deformed Super Yang-Mills Theories
• Integrability of Orbifold ABJM Theories
• The fate of the Konishi multiplet in the β-deformed Quantum Spectral Curve
• Evidence for a $4$-dimensional $\mathcal{N}=1$ integrable quiver in massive type IIA
• Pulsating Strings in Lunin-Maldacena Backgrounds
• Wrapping effects in supersymmetric gauge theories
• Three Spin Spiky Strings in beta-deformed Background
• Contour deformation trick in hybrid NLIE
• One-point functions in $\beta$-deformed N = 4 SYM with defect
• Multi-Spin Strings in AdS_4*CP^3 and its β-deformation
• Supergraphs and the cubic Leigh-Strassler model
• Large N anomalous dimensions for large operators in Leigh-Strassler deformed SYM
• Tunnelling of Pulsating Strings in Deformed Minkowski Spacetime