[Paper Review] Non-perturbative aspects of (supersymmetric) gauge theories

Frank D. Ferrari|ArXiv.org|Feb 22, 1997

Black Holes and Theoretical Physics3 citations

TL;DR

This paper explores non-perturbative dynamics in four-dimensional non-Abelian gauge theories, focusing on supersymmetric models where rigorous results have been obtained. It highlights rich strong-coupling phenomena such as confinement and dynamical symmetry breaking, offering insights relevant to future phenomenological models, though quantitative computations in non-supersymmetric QCD remain out of reach.

ABSTRACT

At an elementary level, we present some non-perturbative aspects of non-abelian gauge theories in four dimensional space-time. Some rigorous results have been obtained in the framework of supersymmetric theories, and a very rich physics related to the strong-coupling dynamics of gauge fields has been discovered. Some of the new phenomena which appeared may play a significant role in future phenomenological models. However, quantitative computations in non-supersymmetric theories, like quantum chromodynamics, is out of reach for the moment.

Motivation & Objective

• To investigate non-perturbative phenomena in four-dimensional non-Abelian gauge theories, particularly within supersymmetric frameworks.
• To identify and analyze rigorous results in supersymmetric gauge theories that reveal strong-coupling dynamics.
• To explore the potential relevance of these non-perturbative effects for future phenomenological models.
• To assess the current limitations in performing quantitative computations in non-supersymmetric theories like QCD.

Proposed method

• Analytical study of supersymmetric gauge theories using non-perturbative techniques.
• Leveraging known exact results in supersymmetric theories to probe strong-coupling behavior.
• Drawing comparisons between supersymmetric and non-supersymmetric gauge theories to highlight differences in tractability.
• Focusing on phenomena such as confinement, dynamical mass generation, and vacuum structure in the non-perturbative regime.
• Using theoretical frameworks such as Seiberg duality and superconformal invariance to analyze dynamics.
• Presenting qualitative and structural insights into non-perturbative effects without relying on perturbative expansions.

Experimental results

Research questions

• RQ1 What non-perturbative phenomena emerge in four-dimensional supersymmetric gauge theories?
• RQ2 How do strong-coupling dynamics in supersymmetric theories differ from those in non-supersymmetric QCD?
• RQ3 What rigorous results can be derived in supersymmetric gauge theories that shed light on non-perturbative behavior?
• RQ4 Which non-perturbative effects in supersymmetric theories may inform future phenomenological models?
• RQ5 Why are quantitative computations in non-supersymmetric gauge theories like QCD currently infeasible?

Key findings

• Rigorous non-perturbative results have been obtained in supersymmetric gauge theories, revealing rich dynamics at strong coupling.
• Phenomena such as confinement and dynamical chiral symmetry breaking are realized in these models, consistent with non-perturbative field theory expectations.
• The structure of the vacuum and the spectrum of stable states in supersymmetric theories exhibit non-trivial behavior not accessible through perturbation theory.
• Supersymmetry provides a framework where exact results can be derived, offering insights into strong-coupling physics.
• Despite progress in supersymmetric models, quantitative analysis of non-supersymmetric theories like QCD remains out of reach with current methods.