Photon Propagator, Monopoles, and the Thermal Phase Transition in Three Dimensional Compact QED

Abstract

We investigate the gauge boson propagator in three dimensional compact Abelian gauge model in the Landau gauge at finite temperature. The presence of the monopole plasma in the confinement phase leads to appearance of an anomalous dimension in the momentum dependence of the propagator. The anomalous dimension as well as an appropriate ratio of photon wave function renormalization constants with and without monopoles are observed to be order parameters for the deconfinement phase transition. We discuss the relation between our results and the confining properties of the gluon propagator in non-Abelian gauge theories. Here, we want to elaborate on cQED 3 as a toy model of confinement. Indeed, this has been the first non-trivial case in which confinement of electrically charged particles was understood analytically [1]. Confinement is caused here by a plasma of monopoles which emerge due to the compactness of the gauge field. Other common features of the two theories are the existence of a mass gap and of a confinement-deconfinement phase transition at some non-zero temperature. According to universality arguments [5] the phase transition of cQED 3 is expected to be of Kosterlitz-Thouless type [6].In QCD 4 , the deconfinement phase transition is widely believed to be caused by loss of monopole condensation (for a review see Ref. [7]) within the effective dual superconductor approach [8]. Studying the dynamics of the monopole current inside gluodynamics, monopole decondensation at the critical temperature is appearing as de-percolation, i.e. the decay of the infrared, percolating monopole cluster into short monopole loops [9]. This change of vacuum structure has a dimensionally reduced analog in the 3D monopole-antimonopole pair binding which has been observed in cQED 3 [10,11].At present, the gluon propagator in QCD 4 is under intensive study. The analogies mentioned before encouraged us to study the similarities between the gauge boson propagators in both theories. In order to fix the role of the monopole plasma in cQED 3 , not just for confinement of external charges but also for the non-perturbative modification of the gauge boson propagator, we consider it in the confinement and the deconfined phases. On the other hand, on the lattice at any temperature we are able to separate the monopole contribution to the propagator by means of eq. (2) below.We have chosen the Landau gauge since it has been adopted in most of the investigations of the gauge boson propagators in QCD [12,13] and QED [14,15]. In order to avoid the problem of Gribov copies [16], the alternative Laplacian gauge has been used recently [17]. The Coulomb gauge, augmented by a suitable global gauge in each time slice (minimal Coulomb gauge) has been advocated both analytically [18] and numerically [19].The numerical lattice results for gluodynamics show that the propagator for all these gauges in momentum space is less singular than p −2 in the immediate vicinity of p 2 = 0. Moreover, the results for the propagator at zero momentum are ranging from ...

Confinement and the photon propagator in 3D compact QED: A lattice study in the Landau gauge at zero and finite temperature

“…One of them, the deconfinement-sensitive D L , was studied already in Ref. [7], while the other, D T , was found to be extremely sensitive to the Gribov problem. Only exerting extreme care can one expose the change going on at the deconfinement transition.…”

“…In a recent letter [7] we answered the question what effect the confinement property has on the gauge boson propagator in this theory and what of the propagator is changing at the deconfinement temperature. The effects are twofold: first, an anomalous dimension appears which modifies the momentum dependence, and second, a mass is generated which can be well understood in terms of Polyakov's theory [1].…”

“…[7] in various respects. Since the propagator is studied in the Landau gauge, first of all we have investigated more carefully the quality of the gauge fixing and the importance of the Gribov copy problem, first on the propagator itself and then on the parameters that finally describe the functional form of the propagator.…”

“…In Ref. [7] we also have used the unique possibility in lattice simulations to remove the monopole degrees of freedom from the quantum gauge field in order to show that all nontrivial effects reside exclusively in the singular fields of the monopoles.…”

Phase structure of a U(1) lattice gauge theory with dual gauge fields

“…These studies are partly motivated by the work of Halperin, Lubensky, and Ma [1] which predicts a first-order phase transition. At present, it is established that the phase structure of three dimensional (3D) AHM on the lattice strongly depends on a parameter controlling fluctuations of the amplitudes |ϕ(x)| of the Higgs (Cooper-pair) field [2]. At the London limit in which |ϕ(x)| is fixed, there is only the confinement phase in the lattice model.…”