Unusual Features of QCD Low-Energy Modes in the Infrared 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, 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 nonanalyticity. 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 a topological origin. We find similar structure at lambda(A), and associate its adjacent thin layer (d(IR)(sic)2) with Anderson-like criticality. Our analysis reveals the manner in which nonanalyticities 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.