Georgi-Glashow Research Articles

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.

Topics of monopole dynamics in gluodynamics

Three topics of monopole dynamics in gluodynamics are presented. 1)Gauge (in)dependence of the monopole effective action (S.Ito, T.W.Park, T.Suzuki): MA and Laplacian abelian gauges show almost the same renormalization flow and renormalized trajectory. 2)The quantized dual abelian Higgs model (DAH) derived from SU(2) gluodynamics and its vacuum structure (Y.Koma, E.-M.Ilgenfritz, T.Suzuki,M.I.Polikarpov): Monte-Carlo analysis of DAH is done. The quantum average of the dual field strength shows a flux tube profile similar to the color-electric field profile measured in SU(2) gluodynamics. 3)Lattice instanton action from 3D SU(2) Georgi-Glashow model (GG) 3 (T.Yazawa, T.Suzuki): We determine an effective instanton action both in unitary and MA gauges. For some range of parameters, we obtain almost perfect actions which look the same in both gauges (gauge independence) and which reproduce well the string tension.

Finite temperature behavior of the 3D Polyakov model with massless quarks

The (2+1)D Georgi-Glashow (or Polyakov) model with the additional fundamental massless quarks is explored at finite temperature. In the case of vanishing Yukawa coupling, it is demonstrated that the interaction of a monopole and an antimonopole in the molecule via quark zero modes leads to the decrease of the Berezinsky-Kosterlitz-Thouless critical temperature when the number of quark flavors is equal to one. If the number of flavors becomes larger, monopoles are shown to exist only in the molecular phase at any temperatures exceeding a certain exponentially small one. This means that for such a number of flavors and at such temperatures, no fundamental matter can be confined by means of the monopole mechanism.

ACCOUNTING FOR THE FINITENESS OF THE HIGGS–BOSON MASS IN THE 3D GEORGI–GLASHOW MODEL

(2 + 1)-dimensional Georgi–Glashow model is explored in the regime when the Higgs boson is not infinitely heavy, but its mass is of the same order of magnitude as the mass of the W-boson. In the weak-coupling limit, the Debye mass of the dual photon and the expression for the monopole potential are found. The cumulant expansion applied to the average over the Higgs field is checked to be convergent for the known data on the monopole fugacity. These results are further generalized to the SU (N)-case. In particular, it is found that the requirement of convergence of the cumulant expansion establishes a certain upper bound on the number of colors. This bound, expressed in terms of the parameter of the weak-coupling approximation, allows the number of colors to be large enough. Finally, the string tension and the coupling constant of the so-called rigidity term of the confining string are found at arbitrary number of colors.

Effective Monopole Action at Finite Temperature in SU(2) Gluodynamics

Effective monopole action at finite temperature in SU(2) gluodynamics is studied on anisotropic lattices. Using an inverse Monte-Carlo method and the blockspin transformation for space directions, we determine 4-dimensional effective monopole action at finite temperature. We get an almost perfect action in the continuum limit under the assumption that the action is composed of two-point interactions alone. It depends on a physical scale $b_s$ and the temperature $T$. The temperature-dependence appears with respect to the spacelike monopole couplings in the deconfinement phase, whereas the timelike monopole couplings do not show any appreciable temperature-dependence. The dimensional reduction of the 4-dimensional SU(2) gluodynamics ((SU(2))$_{4D}$) at high temperature is the 3-dimensional Georgi-Glashow model ($(GG)_{3D}$). The latter is studied at the parameter region obtained from the dimensional red uction. We compare the effective instanton action of $(GG)_{3D}$ with the timelike monopole action obtained from (SU(2))$_{4D}$. We find that both agree very well for $T \ge 2.4T_c$ at large $b$ region. The dimensional reduction works well also for the effective action.

Confinement, chiral symmetry breaking, and the axial anomaly from domain formation at intermediate resolution

Based on general renormalization group arguments, Polyakov's loop-space formalism, and recent analytical lattice arguments, suggesting, after Abelian gauge fixing, a description of pure gluodynamics by means of a Georgi-Glashow like model, the corresponding vacuum fields are defined in a nonlocal way. Using lattice information on the gauge invariant field strength correlator in full QCD, the resolution scale ${\ensuremath{\Lambda}}_{b},$ at which these fields become relevant in the vacuum, is determined. For SU(3) gauge theory it is found that ${\ensuremath{\Lambda}}_{b}\ensuremath{\sim}2.4$ GeV, 3.1 GeV, and 4.2 GeV for ${(N}_{F}=4,$ ${m}_{q}=18$ MeV), ${(N}_{F}=4,$ ${m}_{q}=36$ MeV), and pure gluodynamics, repectively. Implications for the operator product expansion of physical correlators are discussed. It is argued that the emergence of magnetic (anti)monopoles in the vacuum at resolution ${\ensuremath{\Lambda}}_{b}$ is a direct consequence of the randomness in the formation of a low entropy Higgs condensate. This implies a breaking of chiral symmetry and a proliferation of the axial U(1) anomaly at this scale already. Justifying Abelian projection, a decoupling of non-Abelian gauge field fluctuations from the dynamics occurs. The condensation of (anti)monopoles at ${\ensuremath{\Lambda}}_{c}<{\ensuremath{\Lambda}}_{b}$ follows from the demand that vacuum fields ought to have vanishing action at any resolution. As monopoles condense they are reduced to their cores, and hence they become massless. Apparently broken gauge symmetries at resolutions ${\ensuremath{\Lambda}}_{c}<\ensuremath{\Lambda}<~{\ensuremath{\Lambda}}_{b}$ are restored in this process.

Hagedorn transition, vortices and D0 branes: lessons from 2+1 confining strings

We study the behaviour of Polyakov confining string in the Georgi-Glashow model in three dimensions near confining-deconfining phase transition described in hep-th/0010201. In the string language, the transition mechanism is the decay of the confining string into D0 branes (charged W bosons of the Georgi-Glashow model). In the world-sheet picture the world-lines of heavy D0 branes at finite temperature are represented as world-sheet vortices of a certain type, and the transition corresponds to the condensation of these vortices. We also show that the ``would be'' Hagedorn transition in the confining string (which is not realized in our model) corresponds to the monopole binding transition in the field theoretical language. The fact that the decay into D0 branes occurs at lower than the Hagedorn temperature is understood as the consequence of the large thickness of the confining string and finite mass of the $D0$ branes.

Confining strings and RG flow in the (2+1)-dimensional Georgi-Glashow model and its SU(3)-generalization

Confining strings and RG flow at finite temperature are investigated in the (2+1)-dimensional Georgi-Glashow model. This is done in the limit when the electric coupling constant is much larger than the square root of mass of the Higgs field, but much smaller than the vacuum expectation value of this field. The modification of the Debye mass of the dual photon with respect to the case when it is considered to be negligibly small compared to the Higgs mass, is found. Analogous modifications of the potential of monopole densities and string coupling constants are found. At finite temperature, the mass of the Higgs field scales according to a novel RG equation. It is checked that in the limit when the original theory is reduced by the RG flow to the 2D XY model, the so-evolved Higgs mass is still much smaller than the squared electric coupling constant. The SU(3)-theory of confining strings is also discussed within the same approximations.

Deconfinement at N > 2: SU(N) Georgi-Glashow model in 2+1 dimensions

We analyse the deconfining phase transition in the SU(N) Georgi-Glashow model in 2+1 dimensions. We show that the phase transition is second order for any N, and the universality class is different from the Z(N) invariant Villain model. At large N the conformal theory describing the fixed point is a deformed SU(N)_1 WZNW model which has N-1 massless fields. It is therefore likely that its self-dual infrared fixed point is described by the Fateev-Zamolodchikov theory of Z(N) parafermions.

Chicken or the egg; or who ordered the chiral phase transition?

We draw an analogy between the deconfining transition in the (2+1)-dimensional Georgi-Glashow model and the chiral phase transition in (3+1)-dimensional QCD. Based on the detailed analysis of the former we suggest that the chiral symmetry restoration in QCD at high temperature is driven by the thermal ensemble of baryons and antibaryons. The chiral symmetry is restored when roughly half of the volume is occupied by the baryons. Surprisingly enough, even though baryons are rather heavy, a crude estimate for the critical temperature gives ${T}_{c}=180 \mathrm{MeV}.$ In this scenario the binding of the instantons is not the cause but rather a consequence of the chiral symmetry restoration.

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.

Instanton molecules at high temperature - the Georgi-Glashow model and beyond

We show that correlators of some local operators in gauge theories are sensitive to the presence of the instantons even at high temperature where the latter are bound into instanton-anti-instanton "molecules". We calculate correlation functions of such operators in the deconfined phase of the 2+1 dimensional Georgi-Glashow model and discuss analogous quantities in the chirally symmetric phase of QCD. We clarify the mechanism by which the instanton-anti-instanton molecules contribute to the anomaly of axial U(1) at high temperature.

Deconfining phase transition in 2+1 D: the Georgi-Glashow model

We analyze the finite temperature deconfining phase transition in 2+1 dimensional Georgi-Glashow model. We show explicitly that the transition is due to the restoration of the magnetic $Z_2$ symmetry and that it is in the Ising universality class. We find that neglecting effects of the charged $W$ bosons leads to incorrect predictions for the value of the critical temperature and the universality class of the transition, as well as for various correlation functions in the high temperature phase. We derive the effective action for the Polyakov loop in the high temperature phase and calculate the correlation functions of magnetic vortex operators.

Phases and Residual Gauge Symmetries of Higgs Models

After elimination of the redundant variables, gauge theories may still exhibit symmetries associated with the gauge fields. The role of these residual gauge symmetries is discussed within the Abelian Higgs model and the Georgi–Glashow model. In the different phases of these models, these symmetries are realized differently. The characteristics of emergence and disappearance of the symmetries are studied in detail and the implications for the dynamics in Coulomb, Higgs, and confining phases are discussed.

Gravitating dyons and the Lue-Weinberg bifurcation

Gravitating t'Hooft-Polyakov magnetic monopoles can be constructed when coupling the Georgi-Glashow model to gravitation. For a given value of the Higgs boson mass, these gravitating solitons exist up to a critical value of the ratio of the vector meson mass to the Planck mass. The critical solution is characterized by a degenerate horizon of the metric. As pointed out recently by Lue and Weinberg, two types of critical solutions can occur, depending on the value of the Higgs boson mass. Here we investigate this transition for dyons and show that the Lue and Weinberg phenomenon is favorized by the presence of the electric-charge degree of freedom.

’t Hooft tensors as Kalb-Ramond fields of generalized monopoles in all odd dimensions:d=3andd=5

Rank $d\ensuremath{-}1$ antisymmetric tensor fields in d Euclidean dimensions, known as Kalb-Ramond fields, can describe monopole-like solutions. In $d=3$ dimensions this Kalb-Ramond monopole is the (singular) Dirac monopole, which in turn can be described by the (regular) 't Hooft-Polyakov monopole, via the 't Hooft tensor construction. This construction is extended to arbitrary odd dimensions by performing the $d=5$ case explicitly, exploiting the (regular) ``monopoles'' of generalized Georgi-Glashow models and identifying their 't Hooft tensors as the Kalb-Ramond fields. The relevant ``magnetic charges'' are expressed as topological invariants.

DdimensionalSO(d)-Higgs models with an instanton and sphaleron:d=2,3

The Abelian Higgs model and the Georgi-Glashow model in 2 and 3 Euclidean dimensions respectively, support both finite size instantons and sphalerons. The instantons are the familiar Nielsen-Oleson vortices and the 't Hooft-Polyakov monopole solutions respectively. We have constructed the sphaleron solutions and calculated the Chern-Simons charges N_cs for sphalerons of both models and have constructed two types of noncontractible loops between topologically distinct vacuua. In the 3 dimensional model, the sphaleron and the vacuua have zero magnetic and electric flux while the configurations on the loops have non vanishing magnetic flux.

Monopole Skyrmions

A systematic numerical study of the classical solutions to the combined system consisting of the Georgi–Glashow model and the SO(3) gauged Skyrme model is presented. The gauging of the Skyrme system permits a lower bound on the energy, so that the solutions of the composite system can be topologically stable. The solutions feature some very interesting bifurcation patterns, and it is found that some branches of these solutions are unstable.

Center vortices, nexuses, and the Georgi-Glashow model

In a gauge theory with no Higgs fields the mechanism for confinement is by center vortices, but in theories with adjoint Higgs fields and generic symmetry breaking, such as the Georgi-Glashow model, Polyakov showed that in $d=3$ confinement arises via a condensate of 't Hooft--Polyakov monopoles. We study the connection in $d=3$ between pure-gauge-theory and the theory with adjoint Higgs fields by varying the Higgs VEV $v.$ As one lowers $v$ from the Polyakov semiclassical regime $v\ensuremath{\gg}g (g$ is the gauge coupling) toward zero, where the unbroken theory lies, one encounters effects associated with the unbroken theory at a finite value $v\ensuremath{\simeq}g,$ where dynamical mass generation of a gauge-symmetric gauge-boson mass $m\ensuremath{\simeq}{g}^{2}$ takes place, in addition to the Higgs-generated non-symmetric mass $M\ensuremath{\simeq}\mathrm{vg}.$ This dynamical mass generation is forced by the infrared instability (in both 3 and 4 dimensions) of the pure-gauge theory. We construct solitonic configurations of the theory with both $m,M\ensuremath{\ne}0$ which are generically closed loops consisting of nexuses (a class of soliton recently studied for the pure-gauge theory), each paired with an antinexus, sitting like beads on a string of center vortices with vortex fields always pointing into (out of) a nexus (antinexus); the vortex magnetic fields extend a transverse distance $1/m.$ An isolated nexus with vortices is continuously deformable from the 't Hooft--Polyakov $(m=0)$ monopole to the pure-gauge--nexus-vortex complex $(M=0).$ In the pure-gauge $M=0$ limit the homotopy ${\ensuremath{\Pi}}_{2}(\mathrm{SU}(2)/U(1))=Z$ [or its analog for $\mathrm{SU}(N)]$ of the 't Hooft--Polyakov monopoles is no longer applicable, and is replaced by the center-vortex homotopy ${\ensuremath{\Pi}}_{1}({\mathrm{SU}(N)/Z}_{N}){=Z}_{N}$ of the center vortices.

Dyon-Skyrmion lumps

We make a numerical study of the classical solutions of the combined system consisting of the Georgi–Glashow model and the SO(3) gauged Skyrme model. Both monopole-Skyrmion and dyon-Skyrmion solutions are found. A new bifurcation is shown to occur in the gauged Skyrmion solution sector.