The BPS Spectra of Gauge Theories in Two and Four Dimensions

TL;DR

This paper explores the exact BPS spectrum of 2D N=(2,2) abelian gauge theories and reveals a surprising connection to 4D N=2 supersymmetric gauge theories, providing new insights into their spectra at strong coupling.

Contribution

It establishes a novel correspondence between 2D and 4D supersymmetric gauge theories, linking their BPS spectra and predicting strong-coupling behavior.

Findings

BPS spectrum in 2D matches hypermultiplet spectrum in 4D

Connection between 4D SQCD and 2D sigma-models

New predictions for 4D strong-coupling spectrum

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.