3D Georgi-Glashow Model Research Articles

Monopole-Based Scenarios of Confinement and Deconfinement in 3D and 4D

This review discusses confinement, as well as the topological and critical phenomena, in the gauge theories which provide the condensation of magnetic monopoles. These theories include the 3D SU(N) Georgi-Glashow model, the 4D [U(1)] N - 1 -invariant compact QED , and the [U(1)] N - 1 -invariant dual Abelian Higgs model. After a general introduction to the string models of confinement, an analytic description of this penomenon is provided at the example of the 3D SU(N) Georgi-Glashow model, with a special emphasis placed on the so-called Casimir scaling of k-string tensions in that model. We further discuss the string representation of the 3D [U(1)] N - 1 -invariant compact QED, as well as of its 4D generalization with the inclusion of the Θ -term. We compare topological effects, which appear in the latter case, with those that take place in the 3D QED extended by the Chern-Simons term. We further discuss the string representation of the ’t Hooft-loop average in the [U(1)] N - 1 -invariant dual Abelian Higgs model extended by the Θ -term, along with the topological effects caused by this term. These topological effects are compared with those occurring in the 3D dual Abelian Higgs model (i.e., the dual Landau-Ginzburg theory) extended by the Chern-Simons term. In the second part of the review, we discuss critical properties of the weakly-coupled 3D confining theories. These theories include the 3D compact QED, along with its fermionic extension, and the 3D Georgi-Glashow model.

(2 + 1)-dimensional Georgi–Glashow instantons in the Weyl gauge

Semiclassical instanton solutions in the 3D SU(2) Georgi-Glashow model are transformed into the Weyl gauge. This illustrates the tunneling interpretation of these instantons and provides a smooth regularization of the singular unitary gauge. The 3D Georgi-Glashow model has both instanton and sphaleron solutions, in contrast to 3D Yang-Mills theory which has neither, and 4D Yang-Mills theory which has instantons but no sphaleron, and 4D electroweak theory which has a sphaleron but no instantons. We also discuss the spectral flow picture of fundamental fermions in a Georgi-Glashow instanton background.

String Breaking and Z(2) Local Symmetry in the 3D Georgi-Glashow Model

In this work, we consider the London limit of the (2+1)D Georgi-Glashow model with dynamical quarks. Following Polyakov's monopole plasma approach and using dual methods to treat the relevant matter sector, we derive in a clear and straightforward manner the recently proposed gauging of the discrete Z(N) symmetry of the associated effective vortex theory. Our procedure applies to bosonic as well as to fermionic matter, enabling to derive a useful representation for the Wilson loop and discuss string breaking, due to the creation of dynamical quark-antiquark pairs. This phenomenon corresponds to a perimeter law, a behavior that has been already observed in the lattice.

Deconfining phase transition in the 3D Georgi–Glashow model with finite Higgs-boson mass

The (2+1)D Georgi–Glashow model is explored at finite temperature in the regime when the Higgs boson is not infinitely heavy. The resulting Higgs-mediated interaction of monopoles leads to the appearance of a certain upper bound for the parameter of the weak-coupling approximation. Namely, when this bound is exceeded, the cumulant expansion used for the average over the Higgs field breaks down. The finite-temperature deconfining phase transition with the account for the same Higgs-mediated interaction of monopoles is further analysed. It is demonstrated that in the general case, accounting for this interaction leads to the existence of two distinct phase transitions separated by the temperature region where W-bosons exist in both, molecular and plasma, phases. The dependence of possible ranges of the critical temperatures corresponding to these phase transitions on the parameters of the Georgi–Glashow model is discussed. The difference in the RG behaviour of the fugacity of W-bosons from the respective behaviour of this quantity in the compact-QED limit of the model is finally pointed out.

Lattice instanton action from 3D SU(2) Georgi-Glashow model

3D Georgi-Glashow model is studied on the lattice in the London limit in an infrared but an intermediate region before the screening appears. Abelian and instanton dominances are observed after abelian projections in a unitary gauge and roughly in the maximally abelian gauge. Using an inverse Monte-Carlo method, we determine an effective instanton action in both gauges. When we restrict ourselves to some regions of parameters $\beta$ and $\kappa$, we obtain an almost perfect instanton action, performing a block-spin transformation on the dual lattice. It takes a form of a Coulomb gas and reproduces fairly well the string tension obtained analytically by Polyakov. The almost perfect actions in both gauges look the same in the infrared region, which suggests gauge independence.

Center disorder in the 3D Georgi-Glashow model

We present a number of arguments relating magnetic disorder to center disorder, in pure Yang-Mills theory in D=3 and D=4 dimensions. In the case of the D=3 Georgi-Glashow model, we point out that the abelian field distribution is not adequatedly represented, at very large scales, by that of a monopole Coulomb gas. The onset of center disorder is associated with the breakdown of the Coulomb gas approximation; this scale is pushed off to infinity in the QED_3 limit of the 3D Georgi-Glashow model, but should approach the color-screening length in the pure Yang-Mills limit.

't Hooft-Polyakov monopoles and Dirac strings in the 3D Georgi-Glashow model:: A lattice investigation

After having roughly scanned the phase structure of the 3D Georgi-Glashow model on an 8 3 lattice, we investigate whether the vacuum supports an underlying (semiclassical) (anti)monopole structure. Starting from Monte Carlo generated equillibrium configurations, a Langevin-type relaxation procedure is applied in order to freeze out the quantum fluctuations. As expected, from continuum considerations, we find quasi stable plateaus in the action corresponding to pairs of monopoles-antimonopoles (m m ). These excitations are localized in space (although in general not spherical symmetric) and carry a magnetic charge of ±1. Our data show that the density of these pairs drops very sharply at the Higgs phase transition. In addition we observe stable abelian Dirac strings, which arise from (m m ) pairs annihilating through the boundaries.