On a harmonic solution for two-dimensional adjoint QCD

TL;DR

This paper introduces a method to construct a complete basis of eigenstates for two-dimensional adjoint QCD, improving the approximation of its spectrum by leveraging symmetry and harmonic functions, applicable to other theories.

Contribution

It develops a novel approach to find eigenstate bases using symmetry in the asymptotic theory, extending previous partial knowledge and aiding spectrum analysis.

Findings

Constructed complete multi-dimensional harmonic basis for adjoint QCD

Enhanced understanding of the role of pair production in the theory

Method applicable to other gauge theories with similar symmetry structures

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.