AI 中文总结
本文利用基于非交换模糊几何的正则化方法，研究了伊辛QFT的束缚态光谱，重现了（1+1）维伊辛QFT的低能E8介子质量，追踪了维度交叉过程中E8介子的演化，确立了模糊几何作为大质量QFT非微扰光谱探针的作用。
AI 中文摘要
介子和胶子球是禁闭量子场论（QFT）的典型束缚态，但在连续统中，其非微扰光谱学在空间维度超过1维时仍具挑战性。本文利用新近开发的基于非交换“模糊”几何的正则化方法，对伊辛QFT开展此类光谱学研究。在薄模糊环面上，我们重现了磁扰动（1+1）维伊辛QFT的通用低能E8介子质量。通过增大环面的纵横比，我们连续追踪次轻的E8介子，发现系统有效从1维过渡到2维。在2维模糊环面和球面上，我们发现一个亚阈值标量能级和与先前胶子球质量估计一致的超阈值响应特征。利用淬火动力学，我们在非平衡态下也观测到相同的激发。我们的结果确立了模糊几何作为大质量QFT的非微扰光谱探针的有效性，包括其束缚态在维度交叉过程中的演化。
英文摘要
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.
Comments18 pages, 12 figures
