On a CFT limit of planar $\gamma_i$-deformed $\mathcal{N}=4$ SYM theory

TL;DR

This paper demonstrates that a proposed integrable limit of the gamma-deformed N=4 SYM theory is incomplete without double-trace couplings, which are essential for achieving conformality and maintaining integrability in the planar limit.

Contribution

It completes the non-unitary theory by including double-trace couplings, establishing conformal fixed points, and proposing tests for integrability based on two-loop anomalous dimensions.

Findings

The original theory is incomplete and not conformal without double-trace couplings.

Conformal fixed points are found at one-loop with complex couplings.

Proposes tests of integrability using two-loop planar anomalous dimensions.

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.