Dual approaches for defects condensation

TL;DR

This paper reviews and compares two dual methods for modeling defect condensation, demonstrating their equivalence in describing the phase where defects like monopoles or vortices are fully condensed.

Contribution

It provides a detailed analysis showing the duality and equivalence of two approaches to defect condensation in the limit of full defect proliferation.

Findings

The two methods are dual equivalent in the defect condensation limit.

Both approaches lead to the same effective theory for the condensed phase.

The analysis clarifies the relationship between the fundamental and condensed defect phases.

Abstract

We review two methods used to approach the condensation of defects phenomenon. Analyzing in details their structure, we show that in the limit where the defects proliferate until occupy the whole space these two methods are dual equivalent prescriptions to obtain an effective theory for the phase where the defects (like monopoles or vortices) are completely condensed, starting from the fundamental theory defined in the normal phase where the defects are diluted.