[Paper Review] Scales and Phases of Non-Perturbative QCD

Edward Shuryak|ArXiv.org|Nov 4, 1999

Physics of Superconductivity and Magnetism3 citations

TL;DR

This paper explores non-perturbative scales and phases in Quantum Chromodynamics (QCD), focusing on the transition from perturbative to non-perturbative regimes, the instanton liquid model as a description of the QCD vacuum, and the phase diagram of QCD at finite temperature and density—particularly highlighting recent advances in color superconductivity. The key contribution lies in unifying insights from instanton physics and finite-density QCD to clarify the emergence of distinct non-perturbative phenomena.

ABSTRACT

This is a short write-up of lectures at UK Theory Institute, Swansea UK, Sept.99; and XVII School ``QCD: Perturbative or Non-perturbative?'' Lisbon,Portugal, Oct.99. The covered topic include (i) discussion of the scales at which perturbative description should be changed by the non-perturbative one. A number of various examples are considered, leading to different scales, related to instantons or confinement effects; (ii) Instanton vacuum as an Instanton Liquid; (iii) The phase diagram of QCD at finite temperature and density, and especially description of a recent progress in Color Superconductivity.

Motivation & Objective

• To identify and compare multiple non-perturbative energy scales in QCD arising from instantons and confinement.
• To examine the instanton vacuum as a liquid of instantons, providing a phenomenological model for the QCD vacuum structure.
• To analyze the QCD phase diagram under finite temperature and density conditions, particularly focusing on the emergence of color superconducting phases.
• To summarize recent theoretical progress in understanding color superconductivity as a key non-perturbative phase of dense QCD.

Proposed method

• Analyzes perturbative-to-non-perturbative crossover scales using various physical examples, including instanton-induced interactions.
• Applies the instanton liquid model to describe the QCD vacuum as a dense medium of self-interacting instantons.
• Reviews lattice QCD and effective field theory approaches to finite-temperature and finite-density QCD.
• Integrates results from effective models and symmetry considerations to describe the phase structure of QCD at high baryon density.
• Uses dimensional analysis and effective Lagrangians to estimate critical scales and transition temperatures.
• Synthesizes theoretical developments in color superconductivity, including gap equations and pairing mechanisms in dense quark matter.

Experimental results

Research questions

• RQ1 What are the characteristic energy scales at which perturbative QCD breaks down and non-perturbative effects dominate?
• RQ2 How does the instanton liquid model provide a consistent description of the QCD vacuum and its non-perturbative properties?
• RQ3 What is the structure of the QCD phase diagram at finite temperature and baryon density, particularly in the region of high density?
• RQ4 What are the key theoretical developments in understanding color superconductivity in dense quark matter?
• RQ5 How do instanton effects and confinement mechanisms contribute to the emergence of distinct non-perturbative phases in QCD?

Key findings

• Multiple non-perturbative scales emerge in QCD, including those related to instanton size and confinement, with distinct physical origins.
• The instanton liquid model provides a viable framework for understanding the QCD vacuum as a medium of interacting instantons, supporting chiral symmetry breaking.
• At high baryon density, QCD exhibits a phase transition to a color superconducting state, characterized by diquark pairing and a gap in the quark spectrum.
• Recent theoretical progress indicates that color superconductivity is a robust non-perturbative phase of dense QCD, with pairing gaps on the order of tens of MeV.
• The phase diagram of QCD at finite temperature and density features a rich structure, with color superconductivity dominating at high density and low temperature.
• The transition from perturbative to non-perturbative dynamics is not sharp but occurs over a range of scales, with instantons playing a central role in the crossover region.