Duality and scaling in 3-dimensional scalar electrodynamics

TL;DR

This paper investigates the duality in 3D scalar electrodynamics near phase transitions, using numerical simulations to test theoretical predictions about critical exponents and their implications for gauge and scalar theories.

Contribution

It provides empirical validation for duality predictions in 3D scalar electrodynamics through lattice Monte Carlo simulations, and discusses discrepancies and additional relationships in different regions.

Findings

Several critical exponents agree with duality predictions.

Some exponents, like photon correlation length, show discrepancies.

In the type I region, a relationship between magnetic flux tubes and solitons is identified.

Abstract

Three-dimensional scalar electrodynamics, with a local U(1) gauge symmetry, is believed to be dual to a scalar theory with a global U(1) symmetry, near the phase transition point. The conjectured duality leads to definite predictions for the scaling exponents of the gauge theory transition in the type II region, and allows thus to be scrutinized empirically. We review these predictions, and carry out numerical lattice Monte Carlo measurements to test them: a number of exponents, characterising the two phases as well as the transition point, are found to agree with expectations, supporting the conjecture. We explain why some others, like the exponent characterising the photon correlation length, appear to disagree with expectations, unless very large system sizes and the extreme vicinity of the transition point are considered. Finally, we remark that in the type I region the duality implies an interesting quantitative relationship between a magnetic flux tube and a 2-dimensional non-topological soliton.