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

TL;DR

This paper analyzes the phase structure of a deformed CP(N-1) model, revealing a phase transition between Higgs and Coulomb/confining phases associated with Z_N symmetry breaking and restoration.

Contribution

It identifies the phase transition point in the large-N limit of a twisted-mass deformed CP(N-1) model, connecting symmetry breaking to different coupling regimes.

Findings

Higgs phase with Z_N broken at large mass

Coulomb/confining phase with Z_N restored at small mass

Phase transition occurs at strong coupling in the large-N limit

Abstract

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.