The three-dimensional $\mathcal{N} = 2$ superfishnet theory

TL;DR

This paper introduces a new superconformal, integrable superfishnet theory derived from a double-scaling limit of $eta$-deformed ABJM theory, providing exact calculations of free energy, critical coupling, and operator dimensions.

Contribution

It develops a novel superfishnet theory in three-dimensional $ ext{N}=2$ superspace and applies integrability techniques to compute key physical quantities.

Findings

Exact all-loop scaling dimensions of operators

Calculated thermodynamic free energy and critical coupling

Confirmed results through supersymmetric dynamical fishnet theory

Abstract

We propose a double-scaling limit of $\beta$-deformed ABJM theory in three-dimensional $\mathcal{N} = 2$ superspace, and a non-local deformation thereof. Due to the regular appearance of the theory's Feynman supergraphs, we refer to this superconformal and integrable theory as the superfishnet theory. We use techniques inspired by the integrability of bi-scalar fishnet theory and adapted to superspace to calculate the zero-mode-fixed thermodynamic free energy, the corresponding critical coupling, and the exact all-loop scaling dimensions of various operators. Furthermore, we confirm the results of the supersymmetric dynamical fishnet theory by applying our methods to four-dimensional $\mathcal{N} = 1$ superspace.