# Quantum Fishchain in $AdS_5$

## TL;DR

This paper quantizes the quantum fishchain model in $AdS_5$, establishing a full quantum duality with the planar fishnet CFT and reproducing known spectra in the ${rak u}(1)$ sector.

## Contribution

It provides the first canonical quantization of the fishchain model in $AdS_5$ and confirms the quantum duality with the fishnet CFT.

## Key findings

- Proves the quantum duality in the ${rak u}(1)$ sector.
- Reproduces the exact spectrum for analytically known cases.
- Establishes the quantum integrability of the fishchain model.

## Abstract

In our previous paper we derived the holographic dual of the planar fishnet CFT in four dimensions. The dual model becomes classical in the strongly coupled regime of the CFT and takes the form of an integrable chain of particles in five dimensions. Here we study the theory at the quantum level. By applying the canonical quantization procedure with constraints, we show that the model describes a quantum chain of particles propagating in $AdS_5$. We prove the duality at the full quantum level in the ${\mathfrak u}(1)$ sector and reproduce exactly the spectrum for the cases when it is known analytically.