Classical Integrability of the Zigzag Model

TL;DR

This paper proves the classical Liouville integrability and maximal superintegrability of the zigzag model, a relativistic N-body system from high energy limits of 2D QCD, by explicitly constructing conserved charges.

Contribution

It provides the first explicit construction of conserved charges demonstrating integrability and superintegrability of the zigzag model, linking it to a known S-matrix structure.

Findings

The zigzag model is classically integrable with explicit conserved charges.

The model is maximally superintegrable with additional independent charges.

Classical time delays are algebraically derived from the integrable structure.

Abstract

The zigzag model is a relativistic $N$-body system arising in the high energy limit of the worldsheet scattering in adjoint two-dimensional QCD. We prove classical Liouville integrability of this model by providing an explicit construction of $N$ charges in involution. Furthermore, we also prove that the system is maximally superintegrable by constructing $N-1$ additional independent charges. All of these charges are piecewise linear functions of coordinates and momenta. The classical time delays are determined algebraically from this integrable structure. The resulting $S$-matrix is the same as in the $N$-particle subsector of a massless $T\bar{T}$ deformed fermion.