# Integrable Fishnet from $\gamma$-Deformed $\mathcal{N}=2$ Quivers

## TL;DR

This paper introduces bi-fermion fishnet theories as integrable sectors of non-maximally supersymmetric gauge theories, analyzing their structure, deformations, and operator dimensions.

## Contribution

It constructs bi-fermion fishnet models, explores their emergence from $ ext{Lunin-Maldacena}$ deformations, and computes operator dimensions at conformal fixed points.

## Key findings

- Bi-fermion theories form hexagonal fishnet lattice diagrams.
- Explicit conformal fixed points are identified for various deformations.
- Operator scaling dimensions are computed across deformation parameters.

## Abstract

We introduce bi-fermion fishnet theories, a class of models describing integrable sectors of four-dimensional gauge theories with non-maximal supersymmetry. Bi-fermion theories are characterized by a single complex scalar field and two Weyl fermions interacting only via chiral Yukawa couplings. The latter generate oriented Feynman diagrams forming hexagonal lattices, whose fishnet structure signals an underlying integrability that we exploit to compute anomalous dimensions of BMN-vacuum operators. Furthermore, we investigate Lunin-Maldacena deformations of $\mathcal{N}=2$ superconformal field theories with deformation parameter $\gamma$ and prove that bi-fermion models emerge in the limit of large imaginary $\gamma$ and vanishing 't Hooft coupling $g$, with $g e^{-i \gamma/2}$ fixed. Finally, we explicitly find non-trivial conformal fixed points and compute the scaling dimensions of operators for any $\gamma$ and in presence of double-trace deformations.