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arXiv · 2408.05805

Supersymmetric brick wall diagrams and the dynamical fishnet

Moritz Kade·Matthias Staudacher
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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.

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Moritz Kade, Matthias Staudacher. 2024-08-11. Supersymmetric brick wall diagrams and the dynamical fishnet. https://arxiv.org/abs/2408.05805

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