Non-conformality of gamma_i-deformed N=4 SYM theory
Jan Fokken, Christoph Sieg, Matthias Wilhelm
TL;DR
The paper demonstrates that the three-parameter gamma_i deformation of N=4 SYM is not conformally invariant, due to a running double-trace coupling whose beta-function is generically nonzero in the 't Hooft limit. By systematically introducing and classifying tree-level and multi-trace couplings consistent with renormalizability and planarity, the authors show that conformality cannot be restored by such deformations. They explicitly compute the one-loop running of a key double-trace coupling, finding a nonzero beta-function unless the deformation angles coincide in a specific way, and discuss implications for the integrability-based finite-size problem and potential tachyonic instabilities in the dual string background. The work suggests that the gamma_i-deformed background may lack a conformal Lagrangian dual with the same field content as N=4 SYM, or that the AdS5 factor acquires corrections that destabilize the background. A concrete test is proposed to clarify the origin of observed divergences in integrability-based descriptions and to distinguish between potential scenarios for the dual theory.
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.