Strongly γ-deformed N=4 SYM as an integrable CFT

TL;DR

This work shows that γ-deformed planar N=4 SYM, supplemented with double-trace counter-terms, has two nontrivial fixed points in the double-scaling limit where $g\to 0$ and twists become large with finite $\xi_j$, yielding a non-unitary 4D CFT. The authors derive seven-loop beta-functions and prove conformality in this limit, computing an exact four-point function of protected operators and extracting the full conformal data for twist-2 and twist-4 operators via a conformal partial-wave analysis governed by an integrable fishnet kernel. The exact data are encoded in a pole structure at $h_{\Delta,S}=\xi^4$ and a closed-form expression for OPE coefficients, with results consistent with the γ-deformed quantum spectral curve (QSC$_{\gamma}$). Together, these findings support the view that both conformal symmetry and integrability survive for arbitrary deformation parameters in the planar limit and highlight the bi-scalar theory as a tractable non-unitary CFT with rich integrable structure. The work also points toward potential holographic and higher-dimensional extensions of fishnet-type integrable CFTs.

Abstract

We demonstrate by explicit multi-loop calculation that γ-deformed planar N=4 SYM, supplemented with a set of double-trace counter-terms, has two nontrivial fixed points in the recently proposed double scaling limit, combining vanishing 't Hooft coupling and large imaginary deformation parameter. We provide evidence that, at the fixed points, the theory is described by an integrable non-unitary four-dimensional CFT. We find a closed expression for the four-point correlation function of the simplest protected operators and use it to compute the exact conformal data of operators with arbitrary Lorentz spin. We conjecture that both conformal symmetry and integrability should survive in γ-deformed planar N=4 SYM for arbitrary values of the deformation parameters.

Figures (1)

• Figure 1: Feynman diagrams contributing to two-point correlation functions $G_2, G_3$ (left) and $G_1$ (right) in the planar limit. Interaction vertices in the left diagram describe either the single-trace coupling $\xi^2$ or the double-trace coupling $\alpha_i^2$ (with $i=2,3$) depending on the choice of $G_i$. The right diagram consists of the chain of scalar loops joined together through the double-trace coupling $\alpha_1^2$. Each internal scalar loop is built using the single-trace coupling $\xi^2$.