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

TL;DR

The paper derives an exact description of the BPS spectrum for a two-dimensional ${\mathcal N}=(2,2)$ U(1) gauge theory with twisted masses and $N$ equal-charge chiral multiplets. It identifies two dual descriptions in the Higgs and Coulomb phases related by a massive analog of mirror symmetry, and shows that BPS masses are governed by a central charge $Z$ that combines both Noether and topological data via holomorphic functions $\vec{m}$ and $\vec{m}_D$, with $m_D$ determined by a degenerate elliptic curve. Quantum effects in the two phases reveal monodromies, curves of marginal stability, and an exact 2D–4D correspondence to ${\cal N}=2$ theories, including a Seiberg-Witten–style period interpretation. The exact spectrum is encoded in elliptic-curve periods, providing a nonperturbative bridge between 2D gauge dynamics and 4D Seiberg-Witten theory, and predicting detailed dyon spectra and CMS structures across parameter space.

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.