Supersymmetric brick wall diagrams and the dynamical fishnet

TL;DR

This paper demonstrates that superspace techniques simplify the complex dynamical fishnet diagrams in a specific supersymmetric Yang-Mills theory, revealing a regular lattice structure and enabling the computation of thermodynamic free energy.

Contribution

It introduces a method to transform complex dynamical fishnet diagrams into regular lattice structures using superspace techniques in a supersymmetric gauge theory.

Findings

Superspace techniques reveal a regular brick wall lattice structure.

The thermodynamic free energy is computed using Zamolodchikov's inversion method.

The dynamical fishnet diagrams become more tractable with supersymmetry.

Abstract

We consider the double scaling limit of $\beta$-deformed planar 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 $\gamma_i$-deformed N = 4 SYM, preserving 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 N = 1 superspace techniques to the $\beta$-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.