Abstract

Two-dimensional QCD with adjoint fermions has many attractive features, yet its single-particle content remains largely unknown. To lay the foundation for a crucially improved approximation of the theory's spectrum, we developed a method to find the basis of eigenstates using the symmetry structure of the asymptotic theory where pair production is disallowed. This method produces complete sets of multi-dimensional harmonic functions for the massless and the massive theory. Previously only part of such a basis was known. The method presented here should be applicable to other theories and has the promise of factoring out the long-range Coulomb-type part of interactions. The role of pair production and implications for the bosonized theory in the case of adjoint QCD$_2$ are discussed.

Highlights

  • Two-dimensional adjoint quantum chromodynamics, QCD2A, is a non-Abelian Yang-Mills theory coupled to fermions in the adjoint representation, and based on the Lagrangian

  • Few single-particle states have been identified to date [3,4,8], which has led to speculations that there is no Regge trajectory in massless QCD2A [6]

  • Starting from the QCD2A Lagrangian, Eq (1), the dynamics of a system of adjoint fermions interacting via a nondynamical gluon field in two dimensions can be described by a light-cone momentum operator Pþ and Hamiltonian operator P−

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Summary

INTRODUCTION

Two-dimensional adjoint quantum chromodynamics, QCD2A, is a non-Abelian Yang-Mills theory coupled to fermions in the adjoint representation, and based on the Lagrangian. QCD2A exhibits a phase transition from confinement to screening in the limit of vanishing mass m of the adjoint fermions. Few single-particle states have been identified to date [3,4,8], which has led to speculations that there is no Regge trajectory in massless QCD2A [6] This is understandable in a screening theory in which long strings should fall apart, but leaves one to explain what happens to the many singletrace states.

Introductory remarks
N δijδkl
Exhaustive symmetrization
Classification of states
Some group theory
Using “eLCQ”: Some suggestions
The role of pair production
Implications for the bosonized theory
CONCLUSION AND DISCUSSION
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