Confinement and screening of the Schwinger model on the Poincare half plane

TL;DR

This paper investigates the confinement and screening phenomena of the Schwinger model on the Poincare half plane, revealing how geometry influences phase behavior and Wilson loop characteristics.

Contribution

It demonstrates that the Poincare half plane's singularity affects confinement, and clarifies the roles of dynamical fermions and mass in the model's phase structure.

Findings

Massless Schwinger model shows perimeter Wilson loop behavior but can still be confining due to geometry.

Quenched Schwinger model exhibits finite energy for large charges, indicating screening.

Massive Schwinger model remains in screening phase regardless of geometry.

Abstract

We discuss the confining features of the Schwinger model on the Poincare half plane. We show that despite the fact that the expectation value of the large Wilson loop of massless Schwinger model displays the perimeter behavior, the system can be in confining phase due to the singularity of the metric at horizontal axis. It is also shown that in the quenched Schwinger model, the area dependence of the Wilson loop, in contrast to the flat case, is a not a sign of confinement and the model has a finite energy even for large external charges separation. The presence of dynamical fermions can not modify the screening or the confining behavior of the system. Finally we show that in the massive Schwinger model, the system is again in screening phase. The zero curvature limit of the solutions is also discussed.