Unusual Features of QCD Low-Energy Modes in the Infrared 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 ${d}_{\mathrm{IR}}$ of Dirac low-energy modes in this phase, in the context of pure-glue QCD. Our ${d}_{\mathrm{IR}}$ 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 ${d}_{\mathrm{IR}}=3$. We find ${d}_{\mathrm{IR}}<3$ in the spectral range whose lower edge coincides with ${\ensuremath{\lambda}}_{\mathrm{IR}}=0$, the singularity of spectral density defining the IR phase, and the upper edge with ${\ensuremath{\lambda}}_{A}$, the previously identified Anderson-like nonanalyticity. Details near ${\ensuremath{\lambda}}_{\mathrm{IR}}$ are unexpected in that only exact zero modes are ${d}_{\mathrm{IR}}=3$, while a thin spectral layer near zero is ${d}_{\mathrm{IR}}=2$, followed by an extended layer of ${d}_{\mathrm{IR}}=1$ modes. With only integer values appearing, ${d}_{\mathrm{IR}}$ may have a topological origin. We find similar structure at ${\ensuremath{\lambda}}_{A}$, and associate its adjacent thin layer (${d}_{\mathrm{IR}}⪆2$) with Anderson-like criticality. Our analysis reveals the manner in which nonanalyticities at ${\ensuremath{\lambda}}_{\mathrm{IR}}$ and ${\ensuremath{\lambda}}_{A}$, originally identified in other quantities, appear in ${d}_{\mathrm{IR}}(\ensuremath{\lambda})$. This dimension structure may be important for understanding the near-perfect fluidity of the quark-gluon medium seen in accelerator experiments. The role of ${\ensuremath{\lambda}}_{A}$ in previously conjectured decoupling of IR component is explained.

Topics & Concepts