Unusual Features of QCD Low-Energy Modes in IR Phase

Abstract

It was recently proposed that there is a phase in thermal QCD (IR phase) at temperatures well above the chiral crossover, featuring elements of scale invariance in the infrared (IR). Here we study the effective spatial dimensions, $d_{IR}$, of Dirac low-energy modes in this phase, in the context of pure-glue QCD. Our $d_{IR}$ is based on the scaling of mode support toward thermodynamic limit, and hence is an IR probe. Ordinary extended modes, such as those at high energy, have $d_{IR}=3$. We find $d_{IR}<3$ in the spectral range whose lower edge coincides with ${\lambda }_{IR}=0$, the singularity of spectral density defining the IR phase, and the upper edge with ${\lambda }_A$, the previously identified Anderson-like non-analyticity. Details near ${\lambda }_{IR}$ are unexpected in that only exact zero modes are $d_{IR}=3$, while a thin spectral layer near zero is $d_{IR}=2$, followed by an extended layer of $d_{IR}=1$ modes. With only integer values appearing, $d_{IR}$ may have topological origin. We find similar structure at ${\lambda }_A$, and associate its adjacent thin layer ($d_{IR}>\approx 2$) with Anderson-like criticality. Our analysis reveals the manner in which non-analyticities at ${\lambda }_{IR}$ and ${\lambda }_A$, originally identified in other quantities, appear in $d_{IR}(\lambda )$. This dimension structure may be important for understanding the near-perfect fluidity of the quark-gluon medium seen in accelerator experiments. The role of ${\lambda }_A$ in previously conjectured decoupling of IR component is explained.

5 pages, 5 figures; v2: minor changes, published version

References in corpus (4)

• Anderson Transitions
• Chiral phase transition in lattice QCD as a metal-insulator transition
• Anderson Localization in Quark-Gluon Plasma
• Chiral Symmetry Breaking and Chiral Polarization: Tests for Finite Temperature and Many Flavors

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