Excitations of Ising Strings on a Lattice

TL;DR

This paper investigates the excitation spectrum of Ising strings in a lattice gauge theory, revealing strong mixing with glueball states and the absence of light resonances, thus enhancing understanding of confining string dynamics.

Contribution

It provides the first detailed lattice simulation analysis of Ising string excitations and their interaction with glueball states in the ${ m Z}_2$ gauge theory.

Findings

Strong mixing between string excitations and glueball states

No evidence of light massive resonances on the string worldsheet

Insights into the spectrum of confining strings in lattice gauge theories

Abstract

The 3d Ising model in the low temperature (ferromagnetic) phase describes dynamics of two-dimensional surfaces -- domain walls between clusters of parallel spins. The Kramers--Wannier duality maps these surfaces into worldsheets of confining strings in the Wegner's ${\mathbb Z}_2$ gauge theory. We study the excitation spectrum of long Ising strings by simulating the ${\mathbb Z}_2$ gauge theory on a lattice. We observe a strong mixing between string excitations and the lightest glueball state and do not find indications for light massive resonances on the string worldsheet.