Duality, Phases, Spinors and Monopoles in SO(N) and Spin(N) Gauge Theories

TL;DR

This paper explores dualities in four-dimensional N=1 supersymmetric Spin(N) gauge theories, revealing how monopoles and spinors relate under duality and analyzing phases with matter in the vector representation.

Contribution

It demonstrates the correspondence between Z_2 monopoles and massive spinors in dual theories, providing new insights into the phases of SO(N) gauge theories with matter.

Findings

Monopoles correspond to massive spinors under duality.

Electric spinor sources can be viewed as Z_2 magnetic sources in the dual.

Analysis of phases with matter in the vector representation.

Abstract

Four-dimensional N=1 supersymmetric Spin(N) gauge theories with matter in the vector and spinor representations are considered. Dual descriptions are known for some of these theories. It is noted that when masses are given to all fields in the spinor representation, the dual gauge group G breaks to a group H such that \pi_2(G/H)=Z_2. The quantum numbers of the associated Z_2 monopole and those of the massive spinors are shown to agree, suggesting that the monopole is the image of the massive spinors under duality. It follows that electric sources in the spinor representation, needed as test charges to determine the phase of an SO(N) gauge theory, can be introduced as Z_2-valued magnetic sources in the dual nonabelian gauge theory. This fact is used to study the phases of SO(N) gauge theories with matter in the vector representation.