Long-range deformations of arbitrary homogeneous Yang-Baxter integrable spin chains are realized as twists of the quantum group, with the Drinfeld associator encoding the long-range interaction terms up to first order in the deformation parameter.
The Bethe ansatz for N=4 superYang-Mills
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abstract
We derive the one loop mixing matrix for anomalous dimensions in N=4 Super Yang-Mills. We show that this matrix can be identified with the Hamiltonian of an integrable SO(6) spin chain with vector sites. We then use the Bethe ansatz to find a recipe for computing anomalous dimensions for a wide range of operators. We give exact results for BMN operators with two impurities and results up to and including first order 1/J corrections for BMN operators with many impurities. We then use a result of Reshetikhin's to find the exact one-loop anomalous dimension for an SO(6) singlet in the limit of large bare dimension. We also show that this last anomalous dimension is proportional to the square root of the string level in the weak coupling limit.
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A Groenewold-Moyal twist deforms an integrable sl(2) spin-chain whose spectrum is computed perturbatively via the Baxter equation and matched at order J^{-3} to a non-local charge of a deformed BMN string in AdS.
Generalizes the BIZZ recursive procedure and provides sufficient conditions under which auxiliary field deformations of integrable sigma models retain classical Yangian symmetry and Maillet bracket structure.
Holographic probe-brane calculations produce defect one- and two-point functions of heavy scalars that match OPE and BOE limits.
citing papers explorer
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The quantum group structure of long-range integrable deformations
Long-range deformations of arbitrary homogeneous Yang-Baxter integrable spin chains are realized as twists of the quantum group, with the Drinfeld associator encoding the long-range interaction terms up to first order in the deformation parameter.
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Groenewold-Moyal twists, integrable spin-chains and AdS/CFT
A Groenewold-Moyal twist deforms an integrable sl(2) spin-chain whose spectrum is computed perturbatively via the Baxter equation and matched at order J^{-3} to a non-local charge of a deformed BMN string in AdS.
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The classical Yangian symmetry of Auxiliary Field Sigma Models
Generalizes the BIZZ recursive procedure and provides sufficient conditions under which auxiliary field deformations of integrable sigma models retain classical Yangian symmetry and Maillet bracket structure.
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Heavy holographic correlators in defect conformal field theories
Holographic probe-brane calculations produce defect one- and two-point functions of heavy scalars that match OPE and BOE limits.