Non-conformality of γ ᵢ-deformed 𝒩 = 4 SYM theory

We show that the γ i -deformation, which was proposed as candidate gauge theory for a non-supersymmetric three-parameter deformation of the anti-de Sitter / conformal field theory correspondence, is not conformally invariant due to a running double-trace coupling—not even in the ’t Hooft limit. Moreover, this non-conformality cannot be cured when we extend the theory by adding at tree-level arbitrary multi-trace couplings that obey certain minimal consistency requirements. Our findings suggest a possible connection between this breakdown of conformal invariance and a puzzling divergence recently encountered in the integrability-based descriptions of two-loop finite-size corrections for the single-trace operator of two identical chiral fields. We propose a test to clarify this.