[Paper Review] Conformal non-Abelian Thirring models

Oleg Soloviev|ArXiv.org|Jul 27, 1993

Nonlinear Waves and Solitons4 references3 citations

TL;DR

This paper establishes the Hamiltonian quantization of non-Abelian Thirring models and demonstrates its consistency with the path integral approach. It identifies nonperturbative conformal fixed points in the theory that are in one-to-one correspondence with general solutions of the Virasoro master equation, clarifying the BRST structure underlying this equation.

ABSTRACT

The Lie-Poisson structure of non-Abelian Thirring models is discussed and the Hamiltonian quantization of these theories is carried out. The consistency of the Hamiltonian quantization with the path integral method is established. It is shown that the space of non-Abelian Thirring models contains the nonperturbative conformal points which are in one-to-one correspondence with general solutions of the Virasoro master equation. A BRST nature of the mastert equation is clarified.

Motivation & Objective

• To investigate the Hamiltonian quantization of non-Abelian Thirring models and verify its consistency with path integral quantization.
• To identify nonperturbative conformal fixed points within the space of non-Abelian Thirring models.
• To clarify the role of the Virasoro master equation in characterizing conformal points in these models.
• To establish the BRST nature of the Virasoro master equation in the context of conformal field theories.
• To provide a rigorous framework connecting Lie-Poisson structures, conformal invariance, and nonperturbative quantization in 1+1 dimensional quantum field theories.

Proposed method

• Utilizes the Lie-Poisson structure of the classical non-Abelian Thirring model to derive its Hamiltonian formulation.
• Applies canonical quantization techniques to the Hamiltonian formulation, ensuring consistency with the path integral method.
• Analyzes the space of solutions to the Virasoro master equation as a characterization of conformal fixed points in the model.
• Identifies the BRST symmetry underlying the Virasoro master equation, revealing its cohomological structure.
• Employs a systematic treatment of constraints and gauge symmetries to ensure consistency of the quantization procedure.
• Uses the framework of conformal field theory to interpret the resulting quantum theories as conformal field theories at critical points.

Experimental results

Research questions

• RQ1 How can the Hamiltonian quantization of non-Abelian Thirring models be consistently formulated and related to the path integral approach?
• RQ2 What is the precise correspondence between conformal fixed points in the non-Abelian Thirring model and solutions of the Virasoro master equation?
• RQ3 What is the role of BRST symmetry in the structure of the Virasoro master equation within this context?
• RQ4 How do the Lie-Poisson structures of the classical theory relate to the quantum conformal invariance of the model?
• RQ5 What are the implications of the nonperturbative conformal points for the renormalization group flow of the model?

Key findings

• The Hamiltonian quantization of non-Abelian Thirring models is fully consistent with the path integral quantization method.
• The space of non-Abelian Thirring models contains nonperturbative conformal fixed points that are in one-to-one correspondence with general solutions of the Virasoro master equation.
• The Virasoro master equation is shown to possess a BRST structure, with its solutions corresponding to physical states in the quantum theory.
• The conformal fixed points are characterized by the vanishing of the beta function and the preservation of conformal symmetry at the quantum level.
• The Lie-Poisson structure of the classical theory provides a natural framework for identifying the constraints and symmetries essential for consistent quantization.
• The results establish a deep connection between integrable field theories, conformal field theory, and the cohomological structure of the Virasoro algebra.