The BPS Spectra of Gauge Theories in Two and Four Dimensions

TL;DR

The paper uncovers a precise 2D–4D link between BPS spectra in ${\cal N}=(2,2)$ two-dimensional abelian gauge theories and massive hypermultiplets in four-dimensional ${\cal N}=2$ theories, showing that central charges and spectra align as holomorphic functions of masses and dynamical scales. Theory A's exact spectrum is obtained via twisted superpotential methods, while Theory B's spectrum follows from Seiberg–Witten data; the two are shown to coincide across weak and strong coupling regions, including a special baryonic-root case connecting to the ${\rm CP}^{N-\tilde N-1}$ sigma-model. Curves of marginal stability and monodromies match between the two theories, and M-theory brane constructions provide a geometric underpinning that reproduces the central charges and BPS states as M2-brane boundaries on M5-branes. The results yield a nontrivial strong-coupling prediction for the 4D theory and reveal deep structural parallels between 2D sigma-model dynamics and 4D ${\cal N}=2$ gauge dynamics, with a unifying brane picture.

Abstract

We study N=(2,2) supersymmetric abelian gauge theories in two dimensions. The exact BPS spectrum of these models is shown to coincide with the spectrum of massive hypermultiplets of certain N=2 supersymmetric gauge theories in four dimensions. A special case of these results involves a surprising connection between four-dimensional N=2 SQCD with N colours and N_{f}>N flavours at the root of the baryonic Higgs branch and the supersymmetric CP^{2N-N_{f}-1} sigma-model in two dimensions. This correspondence implies a new prediction for the strong-coupling spectrum of the four-dimensional theory.

Figures (2)

• Figure 1: The IIA configuration for theory A
• Figure 2: The IIA configuration for theory B