Classical Integrability of the Zigzag Model

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.

arXiv comment9 pages; v2: clarifying comments and appendix added, published version

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• Infinite pseudo-conformal symmetries of classical $T\bar{T}$, $J\bar{T}$ and $J{T}_a$ - deformed CFTs
• 2d QCD and Integrability, Part I: 't Hooft model
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• Deterministic Chaos vs Integrable Models
• Is the horizon of an eternal black hole really smooth?
• Classical string correspondence in $2$ and $3$ spacetime dimensions