Renormalized finite temperature effective potential ofSU(2) Yang-Mills theory

It is shown that the renormalized finite temperature effective potential for continuumSU(2) Yang-Mills theory develops a non-perturbative minimum for sufficiently strong coupling, i.e. below a critical temperature. The corresponding phase can be the candidate for the confining phase of the continuum theory and becomes energetically favoured basicly due to the decay of theA ⁰ condensate into three gluons.     

Variational discussion of the hamiltonian Z(N) spin model in 1 + 1 and 2 + 1 dimensions

We study the Z(N) spin model, as well as its limiting forms for N → ∞ by means of a variational approach. We find, for 1 + 1 dimensions, the two transitions of the model separating the disordered, massless and ordered phases. In the case of 2 + 1 dimensions, we obtain only the disorder-order phase transition which implies for N → ∞ a single confining phase for the dual U(1) gauge theory.     

The two confining phases of lattice gauge theories

I suggest that the roughening transition of lattice gauge theories is the boundary between two different confining phases: In the hot phase the short-distance interquark potential is exponentially decreasing, while in the cool confining phase it is proportional to $\text{1}\text{R}$, independently of space dimensionality d. As d increases, the cool confining phase shrinks to zero and the system undergoes a first-order deconfining transition.     

Symmetry energy from QCD sum rules

We review the symmetry energy in the context of AdS/CFT correspondence. After constructing D -brane configurations corresponding to dense system in boundary theory, we calculate the symmetry energy by solving DBI action of D branes in confining and deconfining phase. We conclude that the density dependence of the symmetry energy has scaling law, whose power depends only on the dimensionality of the branes and space-time.     

Gauge theories with imaginary chemical potential and the phases of QCD

The phase structure of gauge theories with fermions as a function of imaginary chemical potential is related to the confining properties of the theory. It is controlled by a remnant of the Z_N which is present in the absence of fermions. At high temperature the theory has a first-order phase transition as a function of imaginary chemical potential . This transition is expected to be absent in the low-temperature phase. Monte Carlo simulations are proposed which would check these ideas. It is shown that properties of the theory at nonzero fermion density can be deduced from its behavior at finite imaginary chemical potential.     

Variational Study of 3-Dimensional SU(2) Lattice Gauge Theory with Independent Plaquette Trial Action

The phase structure of 3-dimensional SU(2) lattice gauge theory is studied using variational method with an independent plaquette trial action.The mean-plaquette internal energy E_P～β curve is smooth,which shows only one confining phase,and is better than that given by independent link trial action.     

A self-dual gauge model in four dimensions

We derive the gauge-theory analogue of the “generalized” X-Y model of Jose, Kadanoff, Kirkpartick and Nelson. This model is a “generalized” scalar electrodynamics which exhibits, in general, three phases: a Higgs phase, ordinary scalar electrodynamics and a confining phase. There is an exact duality map between the Higgs scalar QED and the confinement/freedom phase transitions. We also discuss whether the various transitions are first, order second order with cross-over phenomena, or whether there exists a tricritical point.     

Variational Study of 3-Dimensional SU(3) Lattice Gauge Theory with Independent Plaquette Trial Action

The phase structure of 3-dimensional SU(3) lattice gauge theory is studied by using the variational method wit11 an independent plaquette trial action. The mean plaquette internal cncrgy E_p～β curve is smooth, which shows only one confining phase, and is better than that given by the independent link trial action.     

The trace anomaly in coloured black holes

The influence of the trace anomaly of the energy-momentum tensor of gauge theories is discussed in a spherically symmetric space-time. It is found that for pure electric and magnetic fields, the point β(g) = ?g represents a phase transition from any asymptotically flat metric to an asymptotically non-flat metric which turns out to be confining in the electric case.     

Superconductivity in Supersymmetric Theories

The study of superconductivity has been undertaken through the breaking of supersymmetric gauge theories which automatically incorporate the condensation of monopoles and dyons leading to confining and superconducting phases. Constructing the effective Lagrangian near a singularity in moduli space for N=2 supersymmetric theory with SU(2) gauge group, it has been shown that when a mass term is added to this Lagrangian, the N=2 Supersymmetry is reduced to N=1 supersymmetry yielding the dyonic condensation which leads to confinement and superconductivity as the consequence of generalized Meissner effect. In the Coulomb phase of N=2 SU(3) Yang–Mills theory the gauge symmetry has been broken down to SU(2)×U(l) and it has been shown that on perturbing it by suitable tree-level superpotential this supersymmetry theory breaks to N=1 SU(2) Yang-Mills theory described by Higgs field in confining phase incorporating superconductivity.     

't Hooft's consistency condition as a consequence of analyticity and unitarity

We derive 't Hooft's consistency condition on the bound-state spectrum of a confining field theory from the principles of analytic S-matrix theory.     

Repetition of the quark-lepton states in a supersymmetric composite model with complementarity

In a supersymmetric composite model based on an SU(4)^loc_sc confining theory, complementarity is used to support the symmetry-breaking pattern and spectrum of massless particles in a confining phase. The model is found to accomodate two generations of quarks and leptons as quasi Nambu-Goldstone fermions and another two generations as chiral fermions. Masses of composite particles are examined and the quark-lepton generations are classified according the possible mass splittings. The suppression of dangerous flavor-changing interactions is considered also.     

Confining string formed by P vortices in the indirect Z(2) projection of SU(2) lattice gauge theory

We study the distribution of P vortices near the confining string in the indirect _Z(2) projection of SU(2) lattice gauge theory. We find that the density of vortices approaches the vacuum value at large distances and is strongly suppressed near the line connecting the test quark-antiquark pair. This implies that the condensate of P vortices is broken inside the confining string. The width of the _P-vortex density distribution increases with increasing distance between the quark and antiquark. Our best fit indicates the logarithmic dependence of this width on q q? separation.     

Infrared saturation and phases of gauge theories with BRST symmetry

We investigate the infrared limit of the quantum equation of motion of the gauge boson propagator in various gauges and models with a BRST symmetry. We find that the saturation of this equation at low momenta distinguishes between the Coulomb, Higgs and confining phase of the gauge theory. The Coulomb phase is characterized by a massless gauge boson. Physical states contribute to the saturation of the transverse equation of motion of the gauge boson at low momenta in the Higgs phase, while the saturation is entirely due to unphysical degrees of freedom in the confining phase. This corollary to the Kugo–Ojima confinement criterion in linear covariant gauges also is sufficient for confinement in general covariant gauges with BRST and anti-BRST symmetry, maximal Abelian gauges with an equivariant BRST symmetry, non-covariant Coulomb gauge and in the Gribov–Zwanziger theory.     

Seiberg-Witten geometry with various matter contents

We obtain the Seiberg-Witten geometry for four-dimensional N = 2 gauge theory with gauge group SO(2N_c) (N_c ⩽ 5) with massive spinor and vector hypermultiplets by considering the gauge symmetry breaking in the N = 2 E₆ theory with massive fundamental hypermultiplets. In a similar way the Seiberg-Witten geometry is determined for N = 2 SU(N_c) (N_c ⩽ 6) gauge theory with massive antisymmetric and fundamental hypermultiplets. Whenever possible we compare our results expressed in the form of ALE fibrations with those obtained by geometric engineering and brane dynamics, and find a remarkable agreement. We also show that these results are reproduced by using N = 1 confining phase superpotentials.     

Constructing local composite operators for glueball states from a confining Gribov propagator

The construction of BRST invariant local operators with the quantum numbers of the lightest glueball states, J ^PC=0⁺⁺,2⁺⁺,0^?+, is worked out by making use of an Euclidean confining renormalizable gauge theory. The correlation functions of these operators are evaluated by employing a confining gluon propagator of the Gribov type and shown to display a spectral representation with positive spectral densities. An attempt to provide a first qualitative analysis of the ratios of the masses of the lightest glueballs is also discussed.     

Center-symmetric dimensional reduction of hot Yang-Mills theory

It is expected that incorporating the center symmetry in the conventional dimensionally reduced effective theory for high-temperature SU(N_c) Yang-Mills theory, EQCD, will considerably extend its applicability towards the deconfinement transition. The construction of such a center-symmetric effective theory for the case of two colors is reviewed and lattice simulation results are presented. The simulations demonstrate that unlike EQCD, the new center-symmetric theory undergoes a second order confining phase transition in complete analogy with the full theory.     

Dynamics of an interacting Bose-Einstein condensate in a three-well potential

We study the dynamics of an ultracold interacting Bose-Einstein gas confined in a one-dimensional potential composed of three symmetrical wells. We numerically solve the time-dependent Schrödinger equation of the N-particle Hamiltonian for N = 50, 150, 500, 1000. We demonstrate that the quantum phase transition from a superfluid (SF) to a Mott insulator (MI) phase in the three-well potential depends on the strength of the interactions among the particles, the total number of particles, and the confining potential in which the particles move. We discuss the appearance of population revivals as a function of time and find that, even in the case when the interaction strength among the particles is very small, its effect has the consequence that the system never returns to the initial condition. A stationary state for long times is observed in the SF phase, while the particle population in each well remains almost equal to the initial condition in the MI phase.     

A Model Study of the Chiral Phase Diagram of QCD

In this paper we study the chiral phase transition of QCD at finite temperature and density by using the rank-2 confining separable gluon propagator model in the framework of Dyson–Schwinger Equations. The critical end point is located at (T _CEP , μ _CEP ) = (69, 270.3 MeV). It is also found that the first order phase transition might not end at one point, but experiences a two-phase coexisting meta-stable state. A comparison with the results in the previous literature is given.