  We consider the $T\bar T$ deformation of 2d large $N$ YM theory on a
cylinder, sphere and disk. The collective field theory Hamiltonian for the
deformed theory is derived and the particular solutions to the equations of
motion of the collective theory are found for the sphere. The account of the
non-perturbative branch of the solution amounts to the first-order phase
transition at the $(A,\tau)$ plane. We analyze the third-order phase transition
in the deformed theory on the disk and derive the critical area as a function
of the boundary holonomy. A kind of Hagedorn behavior in the spectral density
is discussed.
