Abstract
In this work we report on the Landau gauge photon propagator computed for pure gauge 4D compact QED in the confined and deconfined phases and for large lattices volumes: $32^4$, $48^4$ and $96^4$. In the confined phase, compact QED develops mass scales that render the propagator finite at all momentum scales and no volume dependence is observed for the simulations performed. Furthermore, for the confined phase the propagator is compatible with a Yukawa massive type functional form. For the deconfined phase the photon propagator seems to approach a free field propagator as the lattice volume is increased. In both cases, we also investigate the static potential and the average value of the number of Dirac strings in the gauge configurations $m$. In the confined phase the mass gap translates into a linearly growing static potential, while in the deconfined phase the static potential approaches a constant at large separations. Results shows that $m$ is, at least, one order of magnitude larger in the confined phase and confirm that the appearance of a confined phase is connected with the topology of the gauge group.
Highlights
AND MOTIVATIONThe quest to understand quark confinement has, long ago, lead to the formulation of QED on a hypercubic lattice [1] by Wilson
In the strong coupling limit, i.e., at low β 1⁄4 1=e2 where e is the bare coupling constant, the theory is confining in the sense that the static potential between fermions grows linearly with the distance
This suggests that the confinement mechanisms for the gluon and the photon have some similarities and, in particular, that the confining theory is associated with dynamically generated mass scales that make the propagator finite in the full momentum range for compact QED and for QCD
Summary
The quest to understand quark confinement has, long ago, lead to the formulation of QED on a hypercubic lattice [1] by Wilson. The Landau gauge photon propagator for the confined phase qualitatively follows the same type of behavior as the Landau gauge gluon propagator in QCD for pure YangMills theories; see, for example, [25,26,27,28,29,30,31] for lattice simulations of the Landau gauge gluon propagator and [32,33,34,35,36,37,38,39] for continuum estimations of the same correlation function (see the references therein) This suggests that the confinement mechanisms for the gluon and the photon have some similarities and, in particular, that the confining theory is associated with dynamically generated mass scales that make the propagator finite in the full momentum range for compact QED and for QCD. V we summarize our results and discuss the differences between the two phases
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