The Higgs and Coulomb/Confining Phases in "Twisted-Mass" Deformed CP(N-1) Model

We consider non-supersymmetric two-dimensional CP(N-1) model deformed by a term presenting the bosonic part of the twisted mass deformation of N=2 supersymmetric version of the model. Our deformation has a special form preserving a Z_N symmetry at the Lagrangian level. In the large mass limit the model is weakly coupled. Its dynamics is described by the Higgs phase, with Z_N spontaneously broken. At small masses it is in the strong coupling Coulomb/confining phase. The Z_N symmetry is restored. Two phases are separated by a phase transition. We find the phase transition point in the large-N limit. It lies at strong coupling. As was expected, the phase transition is related to broken versus unbroken Z_N symmetry in these two respective phases. The vacuum energies for these phases are determined too.