Supersymmetric brick wall diagrams and the dynamical fishnet

Abstract

We consider the double scaling limit of β-deformed planar $\mathcal{N}$ = 4 supersymmetric Yang-Mills theory (SYM), which has been argued to be conformal and integrable. It is a special point in the three-parameter space of double-scaled γ_i-deformed $\mathcal{N}$ = 4 SYM, preserving $\mathcal{N}$ = 1 supersymmetry. The Feynman diagrams of the general three-parameter models form a “dynamical fishnet” that is much harder to analyze than the original one-parameter fishnet, where major progress in uncovering the model’s integrable structure has been made in recent years. Here we show that by applying $\mathcal{N}$ = 1 superspace techniques to the β-deformed model the dynamical nature of its Feynman graph expansion disappears, and we recover a regular lattice structure of brick wall (honeycomb) type. As a first application, we compute the zero-mode-fixed thermodynamic free energy of this model by applying Zamolodchikov’s method of inversion to the supersymmetric brick wall diagrams.