Unusual Features of QCD Low-Energy Modes in the Infrared Phase

Area of Science:

• * High-energy physics and quantum chromodynamics (QCD).
• * Condensed matter physics, focusing on critical phenomena and Anderson localization.
• * Statistical mechanics and thermodynamics of strongly interacting matter.

Background:

• * A proposed infrared (IR) phase in thermal QCD exists at high temperatures, exhibiting scale invariance.
• * Understanding the properties of this IR phase is crucial for explaining experimental observations of the quark-gluon medium.
• * Previous studies identified spectral singularities (λ_IR and λ_A) within this phase.

Purpose of the Study:

• * To investigate the effective spatial dimensions (d_IR) of Dirac low-energy modes in the IR phase of pure-glue QCD.
• * To determine if the observed dimensions provide insights into the nature of the IR phase and its associated singularities.
• * To connect the dimensional properties to experimental findings, such as the near-perfect fluidity of the quark-gluon medium.

Main Methods:

• * Analysis of the scaling of Dirac low-energy mode support towards the thermodynamic limit.
• * Probing the spectral range defined by the IR phase singularity (λ_IR) and an Anderson-like nonanalyticity (λ_A).
• * Calculating effective spatial dimensions (d_IR) for different spectral layers.

Main Results:

• * Found effective spatial dimensions (d_IR) less than 3 for Dirac low-energy modes in the IR phase.
• * Observed distinct dimensional layers near spectral singularities: d_IR=3 for zero modes, d_IR=2 for a thin layer near zero, and d_IR=1 for an extended layer.
• * Identified a similar dimensional structure near λ_A, with a thin layer of d_IR ⪆2 associated with Anderson-like criticality.

Conclusions:

• * The integer values of d_IR suggest a potential topological origin for the observed dimensional structure.
• * The dimensional analysis clarifies how nonanalyticities at λ_IR and λ_A manifest in d_IR(λ).
• * This dimensional structure is a key factor in understanding the near-perfect fluidity of the quark-gluon medium and the decoupling of the IR component.