Instanton and Superconductivity in Supersymmetric CP(N-1) Model

TL;DR

This paper explores instantons and superconductivity phenomena in the supersymmetric CP(N-1) model, revealing deep connections to four-dimensional N=2 gauge theories and proposing applications to spin and charge separation phenomena.

Contribution

It demonstrates the emergence of BPS mass formulas and CMS curves in the two-dimensional model, linking them to four-dimensional theories and analyzing their behavior at critical points.

Findings

BPS mass formula and CMS curves appear in the 2D model.

Mapping to N-vector spin model at large n limit.

Application to spin and charge separation phenomena.

Abstract

The two dimensional supersymmetric CP(N-1) model has a striking similarity to the N=2 supersymmetric gauge theory in four dimensions. The BPS mass formula and the curve of the marginal stability (CMS), which exist in the four dimensional gauge theory, appears in this two dimensional CP(N-1) model. These two quntities are derived by a one-dimensional n-vector spin model in the large n limit for the N=2 case. This mapping is further investigated at the critical point. An application of the study of the BPS mass formula is proposed to the phenomena of the spin and charge separations in the Higgs phase.