Confining Phase of Three Dimensional Supersymmetric Quantum Electrodynamics

TL;DR

This paper explores the confining phase in three-dimensional N=2 supersymmetric abelian gauge theories, identifying the conditions for stability and the role of monopoles and solitons, with implications for string theory.

Contribution

It generalizes the confining phase known from non-supersymmetric theories to N=2 supersymmetric abelian theories using a dual description and analyzes the role of monopoles and solitons.

Findings

Confining phase exists in N=2 supersymmetric abelian theories with monopole plasma.

Stable vacuum requires a plasma of chiral monopoles with opposite charges.

N=2 SU(2) Yang-Mills lacks this phase due to monopole charge uniformity.

Abstract

Abelian theories in three dimensions can have linearly confining phases as a result of monopole-instantons, as shown, for SU(2) Yang-Mills theory broken to its abelian subgroup, by Polyakov. In this article the generalization of this phase for N=2 supersymmetric abelian theories is identified, using a dual description. Topologically stable BPS-saturated and unsaturated particle and string solitons play essential roles. A plasma of chiral monopoles of charge 1 and -1 (along with their antichiral conjugates) are required for a stable confining vacuum. N=2 SU(2) Yang-Mills theory broken to U(1) lacks this phase because its chiral monopoles all have the same charge, leading to a runaway instability. The possibility of analogous confining phases of string theory, and a dual field theoretic model thereof, are briefly discussed.