# The fate of the Konishi multiplet in the \beta-deformed Quantum Spectral Curve

## TL;DR

This paper explores the impact of the eta-deformation on the Quantum Spectral Curve, focusing on the Konishi multiplet, and develops methods to solve and perturbatively analyze the associated Q-systems.

## Contribution

It introduces a systematic approach to set boundary conditions and solve the eta-deformed Quantum Spectral Curve for Konishi multiplet states, extending known results.

## Key findings

- Confirmed and extended loop order results in the literature.
- Developed methods for boundary condition setting and perturbative solutions.
- Analyzed the solution space for eta-deformed Konishi operators.

## Abstract

We investigate the solution space of the $\beta$-deformed Quantum Spectral Curve by studying a sample of solutions corresponding to single-trace operators that in the undeformed theory belong to the Konishi multiplet. We discuss how to set the precise boundary conditions for the leading Q-system for a given state, how to solve it, and how to build perturbative corrections to the $\mathbf{P}\mu$-system. We confirm and add several loop orders to known results in the literature.