Comments on 1+1d QCD with heavy adjoint quarks

TL;DR

This paper derives the non-relativistic Schrödinger equations for low-lying bound states in 2D adjoint QCD with heavy quarks, revealing potential solvability and connections to known quantum systems.

Contribution

It formulates the n-body Schrödinger equations for adjoint QCD in 2D at weak coupling and links the three-body problem to a solvable electric dipole model.

Findings

Three-body problem reduces to a Schrödinger equation for a dipole in an electric field.

Eigenstates involve triconfluent Heun functions.

Bound states resemble particles in a 2D Cornell potential.

Abstract

In this paper, we determine at weak coupling the non-relativistic $n$-body Schr\"{o}dinger equation that describes the low-lying color singlet bound states of two dimensional adjoint $QCD$ with heavy quarks. In the case of three adjoint quarks, we show that the three-body equation reduces equivalently to the Schr\"{o}dinger equation that describes a point electric dipole in an electric field in a plane angular sector. We conjecture that the three-body problem is solvable. The eigenstates are given in terms of the triconfluent Heun functions. Our conjecture implies that a bound state of three adjoint quarks is described by a particle confined in a two dimensional Cornell potential. We expect the $n$-parton problem also to be solvable in a similar fashion.