The BPS Spectra of Two-Dimensional Supersymmetric Gauge Theories with Twisted Mass Terms

TL;DR

This paper provides an exact analysis of the BPS spectrum in two-dimensional N=(2,2) supersymmetric U(1) gauge theories with twisted mass terms, revealing dual descriptions and phenomena akin to four-dimensional N=2 theories.

Contribution

It offers the first exact description of the BPS spectrum across all twisted mass values and uncovers a massive mirror symmetry relating Coulomb and Higgs phase descriptions.

Findings

Exact BPS spectrum for all twisted masses in U(1) gauge theories.

Dual descriptions in Higgs and Coulomb phases linked by massive mirror symmetry.

Observation of phenomena like BPS dyons, monodromies, and curves of marginal stability.

Abstract

The vacuum structure and spectra of two-dimensional gauge theories with N=(2,2) supersymmetry are investigated. These theories admit a twisted mass term for charged chiral matter multiplets. In the case of a U(1) gauge theory with N chiral multiplets of equal charge, an exact description of the BPS spectrum is obtained for all values of the twisted masses. The BPS spectrum has two dual descriptions which apply in the Higgs and Coulomb phases of the theory respectively. The two descriptions are related by a massive analog of mirror symmetry: the exact mass formula which is given by a one-loop calculation in the Coulomb phase gives predictions for an infinite series of instanton corrections in the Higgs phase. The theory is shown to exhibit many phenomena which are usually associated with N=2 theories in four dimensions. These include BPS-saturated dyons which carry both topological and Noether charges, non-trivial monodromies of the spectrum in the complex parameter space, curves of marginal stability on which BPS states can decay and strongly coupled vacua with massless solitons and dyons.