Localized Modes in the IR Phase of QCD

Infrared (IR) dimension function $d_\text{IR}(\lambda)$ 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 non-analytic 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 IR component, whose dimensional properties were puzzling. Indeeed, in the recent metal-to-critical scenario of transition to IR phase, this low-dimensional plateau connects the Anderson-like mobility edge $\lambda_\text{IR}=0$ in Dirac spectrum with mobility edges $\pm \lambda_\text{A}$. For this structure to be truly Anderson-like, plateau modes have to be exponentially localized, implying that both the effective distances $L_\text{eff} \propto L^\gamma$ and the effective volumes $V_\text{eff} \propto L^{d_\text{IR}}$ 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 $d_\text{IR}\approx 1$. Here we apply the recently proposed multidimension technique to the problem. We conclude that a plateau mode of pure-glue QCD at UV cutoff $a \!=\! 0.085\,$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.