Bound states and glueballs in three-dimensional Ising systems

TL;DR

This paper investigates the spectrum of excitations in 3D Ising systems, revealing bound states and duality relations with Z(2) gauge theory, and explaining glueball spectra through bound state interpretation.

Contribution

It provides a non-perturbative analysis of bound states in 3D Ising models and establishes an exact duality with Z(2) gauge theory spectra.

Findings

Identification of non-perturbative bound states as fundamental excitations.

Demonstration of duality predicting spectral correspondence.

Explanation of glueball spectrum features via dual bound states.

Abstract

We study the spectrum of massive excitations in three-dimensional models belonging to the Ising universality class. By solving the Bethe-Salpeter equation for 3D $\phi^4$ theory in the broken symmetry phase we show that recently found non-perturbative states can be interpreted as bound states of the fundamental excitation. We show that duality predicts an exact correspondence between the spectra of the Ising model in the broken symmetry phase and of the Z(2) gauge theory in the confining phase. The interpretation of the glueball states of the gauge theory as bound states of the dual spin system allows us to explain the qualitative features of the glueball spectrum, in particular, its peculiar angular momentum dependence.