Localized Modes in the IR Phase of QCD

Abstract

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.

Comments: 5 pages, 7 figures; v2: minor improvements, published version