Quantization of the Zigzag Model

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.