Two Phases for Compact U(1) Pure Gauge Theory in Three Dimensions

TL;DR

This paper demonstrates that by considering more general actions, three-dimensional compact U(1) gauge theory can exhibit two confining phases with distinct monopole behaviors, including a continuous phase transition useful for continuum limits.

Contribution

It introduces a two-phase structure in 3D compact U(1) gauge theory with generalized actions, revealing a continuous transition relevant for strongly correlated systems.

Findings

Two confining phases with different monopole properties

Existence of a continuous phase transition for certain parameters

Relevance to gauge theories in high-temperature superconductivity

Abstract

We show that if actions more general than the usual simple plaquette action ($\sim F_{\mu\nu}^2$) are considered, then compact $U(1)$ {\sl pure} gauge theory in three Euclidean dimensions can have two phases. Both phases are confining phases, however in one phase the monopole condensate spontaneously `magnetizes'. For a certain range of parameters the phase transition is continuous, allowing the definition of a strong coupling continuum limit. We note that these observations have relevance to the `fictitious' gauge field theories of strongly correlated electron systems, such as those describing high-$T_c$ superconductors.