Non-conformality of gamma_i-deformed N=4 SYM theory

TL;DR

This paper demonstrates that the gamma_i-deformation of N=4 SYM theory is not conformally invariant due to a running double-trace coupling, challenging its candidacy as a non-supersymmetric AdS/CFT dual and linking to divergences in integrability calculations.

Contribution

It provides the first analysis showing non-conformality of the gamma_i-deformation and explores its implications for the AdS/CFT correspondence and integrability.

Findings

Gamma_i-deformation is not conformally invariant.

Adding multi-trace couplings does not restore conformality.

Potential link between non-conformality and divergences in integrability calculations.

Abstract

We show that the gamma_i-deformation, which was proposed as candidate gauge theory for a non-supersymmetric three-parameter deformation of the AdS/CFT 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.