BPS Spectrum of Supersymmetric CP(N-1) Theory with Z_N Twisted Masses

TL;DR

This paper thoroughly analyzes the BPS spectrum of the supersymmetric CP(N-1) model with Z_N twisted masses, correcting previous incomplete results, and reveals the structure of BPS towers and their stability regions.

Contribution

It amends the Dorey formula and provides a complete analysis of the BPS spectrum and curves of marginal stability using the exact superpotential and mirror symmetry.

Findings

Identifies N-1 BPS towers at weak coupling

Finds CMS as circles in the large-N limit

Shows N-1 towers collapse into N stable states inside CMS

Abstract

We revisit the BPS spectrum of the supersymmetric CP(N-1) two-dimensional model with Z_N-symmetric twisted masses m_l (l=0,1, ..., N-1). A related issue we address is that of the curves of marginal stability (CMS) in this theory. Previous analyses were incomplete. We close the gap by exploiting a number of consistency conditions. In particular, we amend the Dorey formula for the BPS spectrum. Our analysis is based on the exact Veneziano--Yankielowicz-type superpotential and on the strong-coupling spectrum of the theory found from the mirror representation at small masses, |m_l| << \Lambda . We show that at weak coupling the spectrum, with necessity, must include N-1 BPS towers of states, instead of just one, as was thought before. Only one of the towers is seen in the quasiclassical limit. We find the corresponding CMS for these towers, and argue that in the large-N limit they become circles, filling out a band on the plane of a single mass parameter of the model at hand. Inside the CMS, N-1 towers collapse into N stable states.