Unusual Features of QCD Low-Energy Modes in IR Phase

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. 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 $d_{IR} \approx 2$) 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.