Confining Strings, Infinite Statistics and Integrability

We study confining strings in massive adjoint two-dimensional chromodynamics. Off-shell, as a consequence of zigzag formation, the resulting worldsheet theory provides a non-trivial dynamical realization of infinite quon statistics. Taking the high energy limit we identify a remarkably simple and novel integrable relativistic $N$-body system. Its symmetry algebra contains an additional "shadow" Poincar\'e subalgebra. This model describes the $N$-particle subsector of a $T\bar T$-deformed massless fermion.