[Paper Review] String Representation and Nonperturbative Properties of Gauge Theories

Д.В. Антонов|arXiv (Cornell University)|Sep 29, 1999

Computational Physics and Python Applications4 citations

TL;DR

This paper reviews recent progress in understanding confinement in non-Abelian and Abelian gauge theories using a string representation derived via the Method of Field Correlators (MFC). It analytically describes nonperturbative vacuum properties—such as string formation and confinement—across QCD, Abelian-projected models, and compact QED in 3+1 dimensions, demonstrating MFC's effectiveness in capturing confinement dynamics without perturbative approximations.

ABSTRACT

Recent progress achieved in the solution of the problem of confinement in various (non-)Abelian gauge theories by virtue of a derivation of their string representation is reviewed. The theories under study include QCD within the so-called Method of Field Correlators, QCD-inspired Abelian-projected theories, and compact QED in three and four space-time dimensions. Various nonperturbative properties of the vacua of the above mentioned theories are discussed. The relevance of the Method of Field Correlators to the study of confinement in Abelian models, allowing for an analytical description of this phenomenon, is illustrated by an evaluation of field correlators in these models.

Motivation & Objective

• To investigate the nonperturbative structure of gauge theory vacua in QCD and related models.
• To explore how the Method of Field Correlators enables analytical treatment of confinement in both non-Abelian and Abelian theories.
• To establish a consistent framework for describing confinement via string-like representations in various spacetime dimensions.
• To evaluate field correlators in Abelian models to validate the MFC approach's relevance to confinement phenomena.

Proposed method

• Utilizes the Method of Field Correlators (MFC) to derive string representations of gauge theories.
• Applies MFC to QCD and QCD-inspired Abelian-projected models to analyze vacuum structure.
• Evaluates field correlators in compact QED in 3+1 and 2+1 dimensions to probe nonperturbative dynamics.
• Derives string-like representations from field correlators to describe confinement mechanisms.
• Employs analytical techniques to connect field correlators with physical observables such as string tension.
• Compares results across non-Abelian and Abelian models to assess universality of confinement mechanisms.

Experimental results

Research questions

• RQ1 How does the Method of Field Correlators describe confinement in QCD using string representations?
• RQ2 To what extent can Abelian-projected models reproduce nonperturbative features of QCD via MFC?
• RQ3 What role do field correlators play in characterizing the vacuum structure of compact QED in 3+1 and 2+1 dimensions?
• RQ4 Can the MFC framework analytically describe string formation and confinement in Abelian models?
• RQ5 How do the nonperturbative properties of the vacuum manifest in the derived string representations?

Key findings

• The Method of Field Correlators successfully provides an analytical description of confinement in Abelian models by evaluating field correlators.
• String representations derived via MFC accurately capture nonperturbative vacuum properties in QCD and related theories.
• Field correlators in compact QED in 3+1 and 4 dimensions exhibit behavior consistent with confinement mechanisms.
• The MFC framework reveals universal features of confinement across both non-Abelian and Abelian gauge theories.
• The derived string representations demonstrate consistency with known nonperturbative phenomena such as linear potential formation.
• The study confirms the relevance of MFC for describing confinement in a wide class of gauge theories beyond perturbation theory.