Quantum Phases of a Vortex String

TL;DR

This paper explores the phase structure of magnetic k-strings in a mass-deformed N=4 theory, revealing a rich interplay of sigma model phases, topological effects, and monopole confinement phenomena.

Contribution

It demonstrates that the world-sheet dynamics of these strings are governed by an anisotropic O(3) sigma model with a theta term, connecting string kinks to confined monopoles.

Findings

Identification of different phases separated by a Kosterlitz-Thouless transition.

At  = , the sigma model flows to an interacting fixed point.

Kinks in the sigma model correspond to confined monopoles.

Abstract

We argue that the world-sheet dynamics of magnetic k-strings in the Higgs phase of the mass-deformed N=4 theory, is controlled by a bosonic O(3) sigma model with anisotropy and a topological theta term. The theory interpolates between a massless O(2) symmetric regime, a massive O(3) symmetric phase and another massive phase with a spontaneously broken Z_2 symmetry. The first two phases are separated by a Kosterlitz-Thouless transition. When \theta = \pi the O(3) symmetric phase flows to an interacting fixed point; sigma model kinks and their dyonic partners become degenerate, mirroring the behaviour of monopoles in the parent gauge theory. This leads to the identification of the kinks with monopoles confined on the string.