Fuzzy Spectroscopy of Bound States in Massive Quantum Field Theories

Abstract

Mesons and glueballs are paradigmatic bound states of confining quantum field theories (QFTs), but their nonperturbative spectroscopy in the continuum remains challenging beyond one spatial dimension. Here we perform such spectroscopy for the Ising QFT using a recently developed regularization based on noncommutative ``fuzzy'' geometry. On a thin fuzzy torus, we reproduce the universal low-lying ${\mathbb{E}}_8$ meson masses of the magnetically perturbed $(1+1)\mathrm{D}$ Ising QFT. By increasing the torus aspect ratio, we continuously track the second-lightest ${\mathbb{E}}_8$ meson as the system effectively crosses over from 1D to 2D. On the 2D fuzzy torus and sphere, we find a subthreshold scalar level and above-threshold response features consistent with previous estimates of glueball masses. The same excitations are revealed away from equilibrium using quench dynamics. Our results establish fuzzy geometries as nonperturbative spectroscopic probes of massive QFTs, including their bound-state evolution through dimensional crossover.

Comments: 18 pages, 12 figures