Solving two-dimensional adjoint QCD with a basis-function approach

TL;DR

This paper introduces a basis-function method to analyze the asymptotic spectrum of two-dimensional adjoint QCD, reproducing known results and providing insights into the properties of low-lying states.

Contribution

It develops a continuous, basis-function approach to solve two-dimensional adjoint QCD, complementing existing discretized methods and enabling independent validation of results.

Findings

Reproduced degeneracy of fermionic and bosonic masses at the supersymmetric point

Constructed complete asymptotic eigenfunctions across all parton sectors

Provided insights into the properties of the lowest states in the massless theory

Abstract

We apply a method ("eLCQ") to find the asymptotic spectrum of a Hamiltonian from its symmetries to two-dimensional adjoint QCD. Streamlining the approach, we construct a complete set of asymptotic eigenfunctions in all parton sectors and use it in a basis-function approach to find the spectrum of the full theory. We are able to reproduce previous results including the degeneracy of fermionic and bosonic masses at the supersymmetric point, and to understand the properties of the lowest states in the massless theory. The approach taken here is continuous at fixed parton number, and therefore complementary to standard (DLCQ-like) formulations. Despite its limitation to rather small parton numbers, it can be used to test and validate conclusions of other frameworks in an independent way.