The Heavy Quark Potential in Two-Dimentional QCD with Adjoint Matter

TL;DR

This paper investigates the heavy quark potential in two-dimensional QCD with adjoint matter using a loop formulation, revealing how confinement and Casimir effects manifest in this simplified model.

Contribution

It introduces a loop formulation approach to analyze the heavy quark potential in 2D QCD with adjoint matter, including effects of massive adjoint fields.

Findings

Large adjoint loops contribute to confinement via Casimir effects.

Small loops primarily renormalize the string tension.

Results extend to massive adjoint fields.

Abstract

Using a loop formulation approach of QCD$_2$, we study the potential between two heavy quarks in the presence of adjoint scalar fields, and demonstrate how 't Hooft's planar rule is manifested in this formulation. Based on some physical assumptions, we argue that large adjoint loops ``confined'' inside an external fundamental one give a Casimir type contribution to the potential energy, while the small loops only renormalize the string tension. We also extend the results to the case of massive adjoint fields.