Quantization of the Zigzag Model

TL;DR

This paper explores the quantization of the zigzag model, a relativistic integrable system relevant to high-energy string dynamics in two-dimensional QCD, highlighting the importance of phase space geometry.

Contribution

It introduces a consistent quantization method for the zigzag model, emphasizing the role of phase space geometry and connecting it to $T\bar{T}$ deformed models.

Findings

Quantization requires accounting for phase space geometry.

The resulting quantum theory is Poincaré invariant and integrable.

The model is related to $T\bar{T}$ deformations.

Abstract

The zigzag model is a relativistic integrable $N$-body system describing the leading high-energy semiclassical dynamics on the worldsheet of long confining strings in massive adjoint two-dimensional QCD. We discuss quantization of this model. We demonstrate that to achieve a consistent quantization of the model it is necessary to account for the non-trivial geometry of phase space. The resulting Poincar\'e invariant integrable quantum theory is a close cousin of $T\bar{T}$ deformed models.