The Two Phases of Topologically Massive Compact $U(1)$ Theory

TL;DR

This paper investigates a topologically massive compact U(1) gauge theory in 3D, revealing a phase transition at a critical Chern-Simons coefficient, separating a phase with confined monopoles and broken magnetic flux symmetry from a deconfined phase.

Contribution

It applies a mean field gauge invariant variational method to identify a Berezinsky-Kosterlitz-Thouless type phase transition in the theory, highlighting the role of monopole binding and magnetic vortex behavior.

Findings

Identifies a phase transition at n=8 in the Chern-Simons coefficient.

Shows monopoles are bound for n>8 and unbound for n<8.

Demonstrates spontaneous magnetic flux symmetry breaking for n<8.

Abstract

The mean field like gauge invariant variational method formulated recently, is applied to a topologically massive QED in 3 dimensions. We find that the theory has a phase transition in the Chern Simons coefficient $n$. The phase transition is of the Berezinsky-Kosterlitz - Thouless type, and is triggered by the liberation of Polyakov monopoles, which for $n>8$ are tightly bound into pairs. In our Hamiltonian approach this is seen as a similar behaviour of the magnetic vortices, which are present in the ground state wave functional of the compact theory. For $n>8$, the low energy behavior of the theory is the same as in the noncompact case. For $n<8$ there are no propagating degrees of freedom on distance scales larger than the ultraviolet cutoff. The distinguishing property of the $n<8$ phase, is that the magnetic flux symmetry is spontaneoously broken.