Transition In Gauge Theory Research Articles

Partial deconfinement: a brief overview

The confinement/deconfinement transition in gauge theory plays important roles in physics, including the description of thermal phase transitions in the dual gravitational theory. Partial deconfinement implies an intermediate phase in which color degrees of freedom split into the confined and deconfined sectors. The partially-deconfined phase is dual to the small black hole that lies between the large black hole and graviton gas. Better understandings of partial deconfinement may provide us with a clue how gravity emerges from the field theory degrees of freedom. In this article, we briefly review the basic properties of partial deconfinement and discuss applications.

Jumping out of the light-Higgs conformal window

We investigate generic properties of the conformal phase transition in gauge theories featuring Higgs-like fundamental particles. These theories provide an excellent arena to properly investigate conformal dynamics and discover novel features. We show that the phase transition at the boundary of the Higgs conformal window is not smooth but a jumping one for the known perturbative examples. In addition the general conditions under which the transition is either jumping or smooth are provided. Jumping implies that the massive spectrum of the theory will jump at the phase transition. It, however, still allows for one of the states, the would be dilaton of the theory, to be lighter than the heaviest states in the broken phase. Finally we exhibit a calculable Higgs model in which we can, in perturbation theory, determine the Higgs conformal window, the spectrum in the conformally broken phase and demonstrate it to possess a jumping type conformal phase transition.

Magnetic susceptibility of quark matter within Fermi-liquid theory

Possibility of spontaneous magnetization in QCD and magnetic properties of quark matter are discussed by evaluating the magnetic susceptibility within Fermi-liquid theory. The screening effects for gluons are taken into account to figure out the specific properties of the magnetic transition in gauge theories. It is shown that the static screening effect in terms of the Debye mass does not necessarily work against the magnetic instability; it promotes the instability, depending on the coupling constant and the number of flavors.

FINITE-SIZE SCALING AND DECONFINEMENT TRANSITION: THE CASE OF 4D SU(2) PURE GAUGE THEORY

A recently introduced method for determining the critical indices of the deconfinement transition in gauge theories, already tested for the case of 3D SU (3) pure gauge theory, is applied here to 4D SU (2) pure gauge theory. The method is inspired by universality and based on the finite size scaling behavior of the expectation value of simple lattice operators, such as the plaquette. We obtain an accurate determination of the critical index ν, in agreement with the prediction of the Svetitsky–Yaffe conjecture.

Confinement-deconfinement order parameter and Dirac's quantization condition

We describe a monopole-like order parameter for the confinement-deconfinement transition in gauge theories where dynamical charges and monopoles coexist. It has been recently proposed in a collaboration with J. Fröhlich. It avoids an inconsistency in the treatment of small scales present in earlier definitions of monopole fields by respecting Dirac's quantization condition for electromagnetic fluxes. An application to SU(2) lattice Yang-Mills theory is outlined, naturally fitting in the 't Hooft scenario for confinement.

Finite-size scaling and deconfinement transition in gauge theories

A new method is proposed for determining the critical indices of the deconfinement transition in gauge theories, based on the finite-size scaling analysis of simple lattice operators, such as the plaquette. A precise determination of the critical index ν, in agreement with the prediction of the Svetitsky-Yaffe conjecture, is obtained for SU(3) gauge theory in (2+1)-dimension. Preliminary results for SU(2) in (3+1)-dimension are also given.

Phase transition in gauge theories and multiple-point model

The phase transition in the regularized U(1) gauge theory is investigated by using the dual Abelian Higgs model of scalar monopoles. The corresponding-renormalization-group-improved effective potential, analogous to the Coleman-Weinberg one, is considered in the two-loop approximation for β functions, and the phase-transition (critical) dual and nondual couplings are calculated in the U(1) gauge theory. It is shown that the critical value of the renormalized electric fine-structure constant,α crit≈0.208, obtained in this study agrees with the lattice result for compact QED: α latcrit ≈0.20±0.015. This result and the behavior of α in the vicinity of the phase-transition point are compared with the multiple-point-model prediction for the values of α near the Planck scale. Such a comparison is very encouraging for the multiple point model assuming the existence of the multiple critical point at the Planck scale.

Finite-size scaling and the deconfinement transition in gauge theories

We introduce a new method for determining the critical indices of the deconfinement transition in gauge theories. The method is based on the finite size scaling behavior of the expectation value of simple lattice operators, such as the plaquette. We test the method for the case of SU(3) pure gauge theory in (2+1) dimensions and obtain a precise determination of the critical index $\nu$, in agreement with the prediction of the Svetitsky-Yaffe conjecture.

MagneticZNsymmetry in hot QCD and the spatial Wilson loop

We discuss the relation between the deconfining phase transition in gauge theories and the realization of the magnetic ${Z}_{N}$ symmetry. At low temperature the ${Z}_{N}$ symmetry is spontaneously broken while above the phase transition it is restored. This is intimately related to the change of behavior of the spatial 't Hooft loop. We also point out that the realization of magnetic symmetry has a bearing on the behavior of the spatial Wilson loop. We give a physical argument to the effect that at zero temperature the spatial Wilson loop must have perimeter law behavior in the symmetric phase but area law behavior in the spontaneously broken phase. At high temperature the argument does not hold and the restoration of magnetic ${Z}_{N}$ is consistent with the area law for the Wilson loop.

Conformal phase transition in gauge theories

The conception of the conformal phase transiton (CPT), which is relevant for the description of nonperturbative dynamics in gauge theories, is introduced and elaborated. The main features of such a phase transition are established. In particular, it is shown that in the CPT there is an abrupt change of the spectrum of light excitations at the critical point, though the phase transition is continuous. The structure of the effective action describing the CPT is elaborated and its connection with the dynamics of the partially conserved dilatation current is pointed out. The applications of these results to QCD, models of dynamical electroweak symmetry breaking, and to the description of the phase diagram in (3+1)-dimensional SU${(N}_{c})$ gauge theories are considered.

Phase transition in gauge theories

In this short review we present the consequences of the spontaneously broken gauge theories will lead to when describing matter at high temperature and density. It appears various phase transitions should occur leading to the restoration of symmetry at high temperature of the originally broken one. Symmetry behaviour in external magnetic fields and in the early universe has been briefly mentioned.

Symmetry-breaking aspects of the roughening transition in gauge theories

An infinitely long chromoelectric flux tube breaks translation invariance in transverse directions spontaneously. We argue that the associated Goldstone bosons live effectively in 1 + 1 dimensions and therefore, by the Mermin-Wagner-Coleman theorem, destabilize the flux tube. A large class of effective lagrangians describing the long-wavelength fluctuations of (finite) flux tubes is furthermore shown to give rise to a quark potential V( L) = αL + β + γL −1 + O( L −2), where γ is a universal constant.