Large-N Solution of the Heterotic CP(N-1) Model with Twisted Masses

TL;DR

This paper provides a large-N analytical solution to the heterotic CP(N-1) model with twisted masses, revealing three phases, phase transitions, and the conditions for supersymmetry breaking.

Contribution

It extends the large-N solution of the heterotic CP(N-1) model to include twisted masses, analyzing phase structure and supersymmetry breaking.

Findings

Identified three distinct phases with different symmetry properties.

Discovered phase transitions on the twisted mass parameter plane.

Showed supersymmetry is broken except on a specific circle in parameter space.

Abstract

We address a number of unanswered questions in the N=(0,2)-deformed CP(N-1) model with twisted masses. In particular, we complete the program of solving CP(N-1) model with twisted masses in the large-N limit. In hep-th/0512153 nonsupersymmetric version of the model with the Z_N symmetric twisted masses was analyzed in the framework of Witten's method. In arXiv:0803.0698 this analysis was extended: the large-N solution of the heterotic N=(0,2) CP(N-1) model with no twisted masses was found. Here we solve this model with the twisted masses switched on. Dynamical scenarios at large and small m are studied (m is the twisted mass scale). We found three distinct phases and two phase transitions on the m plane. Two phases with the spontaneously broken Z_N-symmetry are separated by a phase with unbroken Z_N. This latter phase is characterized by a unique vacuum and confinement of all U(1) charged fields ("quarks"). In the broken phases (one of them is at strong coupling) there are N degenerate vacua and no confinement, similarly to the situation in the N=(2,2) model. Supersymmetry is spontaneously broken everywhere except a circle |m|=\Lambda in the Z_N-unbroken phase. Related issues are considered. In particular, we discuss the mirror representation for the heterotic model in a certain limiting case.