In the present paper we discuss various aspects of the 't Hooft model for two-dimensional QCD in the limit of an infinite number of colors in the Coulomb gauge. The properties of mesonic excitations are addressed, with special attention paid to the pionic one. The twofold role of the pion is discussed: being a genuine q state it is also a Goldstone boson of two-dimensional QCD. In particular, it is demonstrated explicitly how the soft-pion theorems are satisfied. It is pointed out that the Coulomb-gauge choice seems to be indispensable in studies of hadronic observables with the pions involved.

Two-dimensional QCD in the Coulomb gauge

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" Poincare subalgebra. This model describes the $N$-particle subsector of a $T\bar T$-deformed massless fermion.

Confining strings, infinite statistics, and integrability

The canonical description is presented for the string with pointlike masses at the ends in 1+1 dimensions in two different gauges: in the proper time gauge and in the light cone one. The classical canonical transformation is written out explicitly, which relates physical variables in both gauges, and equivalence of two classical theories is demonstrated in such a way. Both theories are quantized, and it is shown that quantum theories are not unitary equivalent. It happens due to the fact that the canonical transformation depends on interaction. The quantum Poincare algebra proves to be closed in both cases, so that the requirement of Poincare covariance is not able to distinguish between two versions of the theory.

A.V.Nefediev

Papers

1+1 string with quarks at the ends revisited