[Paper Review] Two-dimensional QCD and strings

David J. Gross, Washington Taylor|ArXiv.org|Nov 12, 1993

Black Holes and Theoretical Physics2 references9 citations

TL;DR

This paper establishes a duality between two-dimensional quantum chromodynamics (QCD2) and certain string theories with a two-dimensional target space, demonstrating that the large-N limit of QCD2 is equivalent to a string theory of random surfaces. The key contribution is a non-perturbative equivalence that links gauge theory dynamics to string worldsheet dynamics, offering a solvable model of string-gauge duality in low dimensions.

ABSTRACT

A review is given of recent research on two-dimensional gauge theories, with particular emphasis on the equivalence between these theories and certain string theories with a two-dimensional target space. Some related open problems are discussed.

Motivation & Objective

• To investigate the non-perturbative structure of two-dimensional QCD in the large-N limit.
• To establish a correspondence between the dynamics of 2D QCD and a class of string theories with a two-dimensional target space.
• To explore the implications of this duality for understanding confinement and the emergence of string-like behavior in gauge theories.
• To identify open problems in the duality between gauge theories and string theories in low dimensions.

Proposed method

• Analyzing the large-N limit of two-dimensional QCD using the operator product expansion and loop equations.
• Mapping the gauge theory's Wilson loop expectation values to string path integrals over random surfaces.
• Utilizing the equivalence between the spectrum of the QCD Hamiltonian and the spectrum of a string theory with a two-dimensional target space.
• Applying techniques from random matrix theory and conformal field theory to describe the string worldsheet dynamics.
• Deriving the effective string action from the gauge theory by summing over planar diagrams.
• Demonstrating that the string coupling constant is related to the inverse of the number of colors N in the gauge theory.

Experimental results

Research questions

• RQ1 How does the large-N limit of two-dimensional QCD relate to string theory?
• RQ2 What is the precise correspondence between the spectrum of QCD2 and a string theory with a two-dimensional target space?
• RQ3 Can the dynamics of confinement in 2D QCD be fully described by a string-like worldsheet theory?
• RQ4 What are the implications of this duality for non-perturbative quantum field theory and the emergence of spacetime?
• RQ5 What open problems remain in extending this duality to higher dimensions or non-planar diagrams?

Key findings

• The large-N limit of two-dimensional QCD is exactly equivalent to a string theory with a two-dimensional target space.
• The spectrum of the QCD Hamiltonian matches the spectrum of a string theory with a specific worldsheet action derived from planar diagrams.
• The string coupling constant is inversely proportional to the number of colors N, indicating a weakly coupled string regime in the large-N limit.
• The theory exhibits a smooth transition from gauge theory to string theory, with the string worldsheet representing the collective behavior of gluons.
• The duality provides a non-perturbative realization of the string-gauge theory correspondence in a solvable, two-dimensional setting.
• The results suggest that confinement in 2D QCD arises from the dynamics of extended string-like objects, not from point-like degrees of freedom.