Infrared (IR) dimension function $d_{\mathrm{IR}}(\lambda )$ characterizes the space effectively utilized by QCD quarks at Dirac scale $\lambda$, and indirectly the space occupied by glue fields. It was proposed that its nonanalytic behavior in thermal infrared phase reflects the separation of QCD system into an IR component and an independent bulk. Here we study the “plateau modes” in the IR component, whose dimensional properties were puzzling. Indeed, in the recent metal-to-critical scenario of transition to IR phase, this low-dimensional plateau connects the Anderson-like mobility edge ${\lambda }_{\mathrm{IR}}=0$ in Dirac spectrum with mobility edges $\pm {\lambda }_{\mathrm{A}}$. For this structure to be truly Anderson-like, plateau modes have to be exponentially localized, implying that both the effective distances $L_{\mathrm{eff}}\propto L^{\gamma }$ and the effective volumes $V_{\mathrm{eff}}\propto L^{d_{\mathrm{IR}}}$ in these modes grow slower than any positive power of IR cutoff $L$. Although $\gamma =0$ was confirmed in the plateau, it was found that $d_{\mathrm{IR}}\approx 1$. Here we apply the recently proposed multidimension technique to the problem. We conclude that a plateau mode of pure-glue QCD at UV cutoff $a=0.085\mathrm{fm}$ occupies a subvolume of IR dimension zero with probability at least 0.9999, substantiating this aspect of metal-to-critical scenario to a respective degree.

• Received 30 October 2023
• Accepted 12 December 2023
• Corrected 18 January 2024

DOI:https://doi.org/10.1103/PhysRevD.109.014501

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Published by the American Physical Society