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.

arXiv commentv3. 36 pages; references added, comments added, typos corrected

References in corpus (21)

• Entropy and Area
• QCD forces and heavy quark bound states
• Comments on string theory backgrounds with non-relativistic conformal symmetry
• Symmetries and Strings of Adjoint QCD${}_2$
• String Spectrum of 1+1-Dimensional Large N QCD with Adjoint Matter
• $1+1$-Dimensional Large $N$ QCD coupled to Adjoint Fermions
• Two Dimensional QCD coupled to Adjoint Matter and String Theory
• The ground state of three quarks
• Gluon flux-tube distribution and linear confinement in baryons
• Universality in Two Dimensional Gauge Theory.
• Anomalies, a mod 2 index, and dynamics of 2d adjoint QCD
• The Spectrum of a Large N Gauge Theory Near Transition from Confinement to Screening
• Solving 2D QCD with an adjoint fermion analytically
• Some Aspects of Three-Quark Potentials
• String Field Theory of Two Dimensional QCD: A Realization of W-infinity Algebra
• A Simple Worldsheet Black Hole
• Adjoint Majorana QCD${}_2$ at Finite $N$
• Vacuum Structure and $\theta$ States of Adjoint QCD in Two Dimensions
• Confining Strings, Infinite Statistics and Integrability
• Classical Integrability of the Zigzag Model
• Asymptotic properties of mass spectrum in 't Hooft's model of mesons

Cited by in corpus (2)

• 2d QCD and Integrability, Part I: 't Hooft model
• $1/N$ Corrections in ${\text{QCD}}_2$: Small Mass Limit and Threshold States