Asymptotic-freedom and massive glueballs in a qubit-regularized SU(2) gauge theory

TL;DR

This paper introduces a qubit-regularized SU(2) lattice gauge theory model that captures key features of Yang-Mills theory, including asymptotic freedom and massive glueball states, using a simplified one-dimensional setup.

Contribution

It maps a qubit-regularized SU(2) gauge theory to the Transverse Field Ising Model and demonstrates its continuum limit reproduces known Yang-Mills phenomena.

Findings

The model exhibits asymptotic freedom in the continuum limit.

Massive glueball states are identified as E8 quantum field theory excitations.

The ratio of string tension to glueball mass is approximately 0.249.

Abstract

We argue that a simple qubit-regularized $\mathrm{SU}(2)$ lattice gauge theory (LGT) on a plaquette chain serves as a pseudo-one-dimensional toy model for Yang-Mills (YM) theory in three spatial dimensions. We map the chain Hamiltonian to the Transverse Field Ising Model (TFIM) in a uniform magnetic field and demonstrate that it can be tuned to a continuum limit in which the short-distance physics is governed by the asymptotically free Ising conformal field theory (CFT) describing free Majorana fermions, while the long-distance regime contains massive excitations of the $E_8$ quantum field theory (QFT) that can be interpreted as one-dimensional analogues of glueballs. Furthermore, we find $\sqrt{\sigma}/m_1 = 0.249(1)$ where $\sigma$ is the string tension between two static quarks and $m_1$ is the mass of the lightest glueball.