Abstract. We show that the γ 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 couplingnot 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.

In the non-supersymmetric γ i -deformed N = 4 SYM theory, the scaling dimensions of the operators tr[Z L ] composed of L scalar fields Z receive finite-size wrapping and prewrapping corrections in the 't Hooft limit. In this paper, we calculate these scaling dimensions to leading wrapping order directly from Feynman diagrams. For L ≥ 3, the result is proportional to the maximally transcendental 'cake' integral. It matches with an earlier result obtained from the integrability-based Lüscher corrections, TBA and Y-system equations. At L = 2, where the integrability-based equations yield infinity, we find a finite rational result. This result is renormalization-scheme dependent due to the non-vanishing β-function of an induced quartic scalar double-trace coupling, on which we have reported earlier. This explicitly shows that conformal invariance is broken -even in the 't Hooft limit.

Abstract:We determine the missing finite-size corrections to the asymptotic one-loop dilatation operator of the real β-deformed N = 4 SYM theory for the gauge groups U(N ) and SU(N ) in the 't Hooft limit. In the SU(N ) case, the absence of the U(1) field components leads to a new kind of finite-size effect, which we call prewrapping. We classify which states are potentially affected by prewrapping at generic loop orders and comment on the necessity to include it into the integrability-based description. As a further result, we identify classes of n-point correlation functions which at all loop orders in the planar theory are given by the values of their undeformed counterparts. Finally, we determine the superconformal multiplet structure and one-loop anomalous dimensions of all single-trace states with classical scaling dimension ∆ 0 ≤ 4.5.

We study the thermodynamic behaviour of the real β-and γ i -deformation of N = 4 Super Yang-Mills theory on R×S 3 in the planar limit. These theories were shown to be the most general asymptotically integrable supersymmetric and non-supersymmetric field-theory deformations of N = 4 Super Yang-Mills theory, respectively. We calculate the first loop correction to their partition functions using an extension of the dilatation-operator and Pólya-counting approach. In particular, we account for the oneloop finite-size effects which occur for operators of length one and two. Remarkably, we find that the O(λ) correction to the Hagedorn temperature is independent of the deformation parameters, although the partition function depends on them in a nontrivial way.