Yangian symmetry holds classically in fishnet models under restricted evaluation parameters but does not extend to generic quantum correlators in the bi-scalar model, with counterexamples indicating that non-zero dual Coxeter number blocks full quantum Yangian invariance.
On a CFT limit of planar $\gamma_i$-deformed $\mathcal{N}=4$ SYM theory
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abstract
We show that an integrable four-dimensional non-unitary field theory that was recently proposed as a certain limit of the $\gamma_i$-deformed $\mathcal{N}=4$ SYM theory is incomplete and not conformal -- not even in the planar limit. We complete this theory by double-trace couplings and find conformal one-loop fix-points when admitting respective complex coupling constants. These couplings must not be neglected in the planar limit, as they can contribute to planar multi-point functions. Based on our results for certain two-loop planar anomalous dimensions, we propose tests of integrability.
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Yangian Symmetry Escapes from the Fishnet
Yangian symmetry holds classically in fishnet models under restricted evaluation parameters but does not extend to generic quantum correlators in the bi-scalar model, with counterexamples indicating that non-zero dual Coxeter number blocks full quantum Yangian invariance.