Continuum limit of a qubit-regularized SU(3) lattice gauge theory with glueballs

TL;DR

This paper introduces a qubit-regularized SU(3) lattice gauge theory that exhibits a continuum limit with glueball-like excitations, connecting lattice models to conformal field theories and providing insights into strong interactions without quarks.

Contribution

The authors demonstrate a continuum limit of a qubit-regularized SU(3) lattice gauge theory mapped to a quantum clock model, revealing a UV fixed point described by Z3 parafermion CFT and resulting in a massive glueball spectrum.

Findings

Continuum limit with massive glueball excitations identified.

Ratio of lowest glueball masses with opposite charge conjugation computed as 1.459(2).

String tension to glueball mass ratio found to be 0.2648(2).

Abstract

We show that a simple qubit-regularized $\mathrm{SU}(3)$ lattice gauge theory (LGT) on a plaquette chain admits a continuum limit with massive glueball excitations, providing a minimal toy model of strong interactions without quarks. By mapping the plaquette-chain Hamiltonian to the three-state quantum clock model in a magnetic field, we demonstrate that the theory can be tuned to a continuum limit governed at short distances by the $\mathbb{Z}_3$ parafermion conformal field theory (CFT), which serves as the ultraviolet (UV) fixed point. A small relevant magnetic perturbation then drives the system to a massive continuum quantum field theory in the infrared (IR). The resulting relativistic massive particles can be interpreted as quasi one-dimensional analogues of glueballs. In the continuum theory we compute the ratio of the lowest glueball masses with opposite charge conjugation to be $m^{-}/m^{+} = \,1.459(2)$ and find $\sqrt{\sigma}/m^{+}\,= 0.2648(2)$, where $\sigma$ is the string tension between a static quark and antiquark.