Confining Phase of Three Dimensional Supersymmetric Quantum Electrodynamics

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.