Integrable Spin Chains with U(1)^3 symmetry and generalized Lunin-Maldacena backgrounds

Abstract

We consider the most general three-state spin chain with U(1)^3 symmetry and nearest neighbour interaction. Our model contains as a special case the spin chain describing the holomorphic three scalar sector of the three parameter complex deformation of N=4 SYM, dual to type IIB string theory in the generalized Lunin-Maldacena backgrounds discovered by Frolov. We formulate the coordinate space Bethe ansatz, calculate the S-matrix and determine for which choices of parameters the S-matrix fulfills the Yang-Baxter equations. For these choices of parameters we furthermore write down the R-matrix. We find in total four classes of integrable models. In particular, each already known model of the above type is nothing but one in a family of such models.

16 pages, 3 figures, references corrected

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• The general Leigh-Strassler deformation and integrability
• Integrable twists in AdS/CFT
• Finite-Size Effects for Multi-Magnon States
• On the perturbative chiral ring for marginally deformed N=4 SYM theories
• The Leigh-Strassler Deformation and the Quest for Integrability
• Quantum Symmetries and Marginal Deformations
• Probing Universality in the Gravity Duals of N=1 SYM by gamma-deformations
• 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
• Anomalous Dimensions of Heavy Operators from Magnon Energies
• Is there a tower of charges to be discovered?
• Star product and the general Leigh-Strassler deformation
• A novel quasi-exactly solvable spin chain with nearest-neighbors interactions