Vortex mass in the three-dimensional $O(2)$ scalar theory

TL;DR

This paper investigates the vortex mass in the three-dimensional $O(2)$ scalar theory, combining Monte Carlo simulations and field theory to understand topological particle stability beyond classical constraints.

Contribution

It provides the first numerical determination of vortex mass in 3D $O(2)$ theories, challenging classical no-go theorems on topological particle stability.

Findings

Vortex mass is numerically determined in 3D $O(2)$ theory.

Obstruction from Derrick's theorem does not necessarily prevent stable topological particles.

Results suggest stability of vortices beyond classical approximation.

Abstract

We study the spontaneously broken phase of the $XY$ model in three dimensions, with boundary conditions enforcing the presence of a vortex line. Comparing Monte Carlo and field theoretic determinations of the magnetization and energy density profiles, we numerically determine the mass of the vortex particle in the underlying $O(2)$-invariant quantum field theory. The result shows, in particular, that the obstruction posed by Derrick's theorem to the existence of stable topological particles in scalar theories in more than two dimensions does not in general persist beyond the classical level.