Comments on 1+1d QCD with heavy adjoint quarks

Abstract

In this paper, we determine at weak coupling the non-relativistic $n$-body Schrödinger 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 Schrödinger 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.

v3. 36 pages; references added, comments added, typos corrected

References in corpus (1)

• Asymptotic properties of mass spectrum in 't Hooft's model of mesons