Long-range deformations of homogeneous Yang-Baxter integrable spin chains are generated by a twist of the quantum group that produces a non-associative algebra whose Drinfeld associator encodes the long-range terms up to first order.
Thesu(2|3) dynamic spin chain
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abstract
The complete one-loop, planar dilatation operator of the N=4 superconformal gauge theory was recently derived and shown to be integrable. Here, we present further compelling evidence for a generalisation of this integrable structure to higher orders of the coupling constant. For that we consider the su(2|3) subsector and investigate the restrictions imposed on the spin chain Hamiltonian by the symmetry algebra. This allows us to uniquely fix the energy shifts up to the three-loop level and thus prove the correctness of a conjecture in hep-th/0303060. A novel aspect of this spin chain model is that the higher-loop Hamiltonian, as for N=4 SYM in general, does not preserve the number of spin sites. Yet this dynamic spin chain appears to be integrable.
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A non-Lorentzian scalar QFT with SU(1,1) symmetry obtained from N=4 SYM is finite at all orders in perturbation theory.
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The quantum group structure of long-range integrable deformations
Long-range deformations of homogeneous Yang-Baxter integrable spin chains are generated by a twist of the quantum group that produces a non-associative algebra whose Drinfeld associator encodes the long-range terms up to first order.
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Finite scalar field theory with SU(1,1) spacetime symmetry from near-BPS limits of $\mathcal{N}=4$ SYM
A non-Lorentzian scalar QFT with SU(1,1) symmetry obtained from N=4 SYM is finite at all orders in perturbation theory.