On the roughening transition in abelian lattice gauge theories

We study the width of the confining string between static quarks in abelian lattice gauge theories using strong coupling expansions. We consider gauge groups Z_n and U(1) in 3 and 4 dimensions. This extends previous work with Lüscher, where SU(2) and Z₂ were studied. In ν = 3 dimensions we find evidence for a roughening transition. It is characterized by a divergence of the string width for an infinitely far separated quark-antiquark pair, while the string tension remains non-zero. In ν = 4 dimensions for the abelian groups we do not have evidence for a roughening transition away from a phase transition.     

Generalized roughening transition and its effect on the string tension

The well-understood roughening transition of an interface in the d = 3 Ising model implies an essential singularity in the string tension of the dual Z₂ gauge model. The roughening transition corresponds to the delocalization of the string due to strong long-wavelength fluctuations, and this reformulation can be generalized to other gauge groups and to d = 4 also. It is not a deconfining transition - it is expected to occur deep in the confining region - but its presence would raise serious questions about the continuation of strong coupling expansions of the tension beyond this point. In this paper predictions on the roughening transition are confronted with the available information on the string tension for different gauge groups in three dimensions.     

Confinement of monopole field lines in a superconductor at T ≠ 0

We apply the Bogoliubov-de Gennes equations to the confinement of a monopole-antimonopole pair in a superconductor. This is related to the problem of a quark-antiquark pair bound by a confining string, consisting of a colour-electric flux tube, dual to the magnetic vortex of type-II superconductors. We study the confinement of the field lines due to the superconducting state and calculate the effective potential between the two monopoles. The monopoles can be simulated in a real experiment inserting two long and thin magnetic rods. At short distances the potential is Coulombic and at large distances the potential is linear, as previously determined solving the Ginzburg-Landau equations. The magnetic field lines and the string tension are also studied as a function of the temperature T. Because we take into account the explicit fermionic degrees of freedom, this work may open new perspectives to the breaking of chiral symmetry or to colour superconductivity.     

A nonlocal Poisson bracket of the sine-Gordon model

It is well known that the classical string on a two-sphere is more or less equivalent to the sine-Gordon model. We consider the non-abelian dual of the classical string on a two-sphere. We show that there is a projection map from the phase space of this model to the phase space of the sine-Gordon model. The corresponding Poisson structure of the sine-Gordon model is nonlocal with one integration.     

Chiral phase transition from string theory

The low energy dynamics of a certain D-brane configuration in string theory is described at weak t'Hooft coupling by a nonlocal version of the Nambu-Jona-Lasinio model. We study this system at finite temperature and strong t'Hooft coupling, using the string theory dual. We show that for sufficiently low temperatures chiral symmetry is broken, while for temperatures larger then the critical value, it gets restored. We compute the latent heat and observe that the phase transition is of the first order.     

Notes on Black Hole Phase Transitions

In these notes we present a summary of existing ideas about phase transitions of black hole spacetimes in semiclassical gravity and offer some thoughts on three possible scenarios or mechanisms by which these transitions could take place. We begin with a review of the thermodynamics of a black hole system and emphasize that the phase transition is driven by the large entropy of the black hole horizon. Our first theme is illustrated by a quantum atomic black hole system, generalizing to finite-temperature a model originally offered by Bekenstein. In this equilibrium atomic model, the black hole phase transition is realized as the abrupt excitation of a high energy state, suggesting analogies with the study of two-level atoms. Our second theme argues that the black hole system shares similarities with the defect-mediated Kosterlitz–Thouless transition in condensed matter. These similarities suggest that the black hole phase transition may be more fully understood by focusing upon the dynamics of black holes and white holes, the spacetime analogy of vortex and antivortex topological defects. Finally, we compare the black hole phase transition to another transition driven by an (exponentially) increasing density of states, the Hagedorn transition first found in hadron physics in the context of dual models or the old string theory. In modern string theory the Hagedorn transition is linked by the Maldacena conjecture to the Hawking–Page black hole phase transition in Anti-de Sitter (AdS) space, as observed by Witten. Thus, the dynamics of the Hagedorn transition may yield insight into the dynamics of the black hole phase transition. We argue that characteristics of the Hagedorn transition are already contained within the dynamics of classical string systems. Our third theme points to carrying out a full nonperturbative and nonequilibrium analysis of the large N behavior of classical SU(N) gauge theories to understand its Hagadorn transition. By invoking the Maldacena conjecture we can then gain valuable insight into black hole phase transitions in AdS space.     

Confinement-deconfinement interplay in quantum phases of doped Mott insulators

In the t-J model, the electron fractionalization is dictated by the phase string effect. We find that in the underdoped regime, the antiferromagnetic and superconducting phases are dual: in the former, holons are confined while spinons are deconfined, and vice?versa in the latter. These two phases are separated by a novel phase, the so-called Bose-insulating phase, where both holons and spinons are deconfined. A pair of Wilson loops was found to constitute a complete set of order parameters determining this zero-temperature phase diagram. The quantum phase transitions between these phases are suggested to be of non-Landau-Ginzburg-Wilson type.     

Hadron potentials within the gauge/string correspondence

It is known, since the 70s, that the large N 't Hooft limit of gauge theories is related to string theories. In 1998, J. M. Maldacena identified precisely such a relation: the so-called AdS/CFT correspondence which speculates a duality between a large N strongly-coupled supersymmetric and conformal Yang-Mills theory in four dimensions and a weakly-coupled string theory defined in a five-dimensional anti-de Sitter AdS₅ space-time. This review aims at introducing concepts and methods used to derive, in the framework of the gauge/string correspondence, the interaction potentials of mesons and baryons at zero and finite temperature. The dual string configurations associated with the different kinds of hadrons are described and their behaviours at short and large distances are understood. Although the application of Maldacena's AdS/CFT conjecture to QCD is not straightforward, QCD being neither supersymmetric nor conformal, the AdS/QCD correspondence approach attempts to identify the dual theory of QCD. Especially, the study of heavy quark-antiquark bound-states leads to establish general dual criteria for the confinement.     

Cavitation in holographic sQGP

We study the possibility of cavitation in the non-conformal N=^2?SU(N) theory which is a mass deformation of N=4SU(N) Yang-Mills theory. The second order transport coefficients are known from the numerical work using AdS/CFT by Buchel and collaborators. Using these and the approach of Rajagopal and Tripuraneni, we investigate the flow equations in a (1+1)-dimensional boost invariant set up. We find that the string theory model does not exhibit cavitation before phase transition is reached. We give a semi-analytic explanation of this finding.     

The Hagedorn transition and the number of degrees of freedom of string theory

Extending recent discussions of the Hagedorn transition in string theory, we argue that this transition is a first-order phase transition with a very large heat (corresponding to a genus-zero contribution to the free energy that appears above the critical temperature). Formally analyzing the k-loop contributions to the free energy at temperatures far above the Hagedorn temperature leads to a number of interesting speculations about the underlying degrees of freedom in string theory.     

Deconfinement in the two-dimensional XY model

The unbinding of vortex-antivortex pairs for the classical two-dimensional XY model in a magnetic field is studied. A single such pair is connected by a string of overturned spins, leading to linear confinement. We show that this system supports two phase transitions, one in which closed strings proliferate, and a second in which vortices unbind. The transitions are shown to be dual to one another, and are remarkably continuous. Possible consequences for a variety of systems are discussed.     

The quantum dual string wave functional in Yang-Mills theories

From any solution of the classical Yang-Mills equations, we define a string wave functional based on the Wilson loop integral. Its precise definition is given by replacing the string by a finite set of N points, and taking the limit N → ∞. We show that this functional satisfies the Schrödinger equation of the relativistic dual string to leading order in N. We speculate about the relevance of this object to the quantum problem.     

U(3) four-dimensional lattice gauge theory and Monte Carlo calculations

Monte Carlo results for the pure U(3) lattice gauge theory on a 6⁴ lattice are reported. Wilson loops and the string tension are presented. The first-order phase transition in U(3) is reflected quite clearly in a discontinuity in the string tension at β = β_c. The U(1) factor of U(3) is extracted using the determinant of the Wilson loops. As expected, the U(1) component appears to deconfine at the phase transition..     

Grand canonical simulations of string tension in elastic surface model

We report a numerical evidence that the string tension σ can be viewed as an order parameter of the phase transition, which separates the smooth phase from the crumpled one, in the fluid surface model of Helfrich and Polyakov-Kleinert. The model is defined on spherical surfaces with two fixed vertices of distance L. The string tension σ is calculated by regarding the surface as a string connecting the two points. We find that the phase transition strengthens as L is increased, and that σ vanishes in the crumpled phase and non-vanishes in the smooth phase.     

The Effects of the Pion String at Heavy ion Collisions

We study the possible signals of the pion string associated with the QCD chiral phase transition in LHC Pb–Pb collision at energy s=5.5 TeV.We follow the Kibble–Zurek mechanism to discuss the production and evolution of the pion string.We will show that if the QCD chiral phase transition really takes place in the LHC Pb-Pb collision process and the phase transition is in the second order,the pion string will be inevitably produced and subsequently decay.The main effect of this phenomenon is that there is a generation of a large number of pions in the final state produced by the decay of the pion string, and these pions are mostly distributed in a low momentum region with p～143MeV; also there are lots of neutral pions distributed in a low momentum region with the mean momentum at p～21MeV.     

How well do Monte Carlo simulations distinguish between U(1) and SU(2)?: A study of the string tension in U(1) lattice gauge theory

To investigate how a system with a known deconfining phase transition behaves when studied on finite lattices via Monte Carlo simulations, we have made such studies of compact U(1) lattice gauge theory for 8⁴, 10⁴, and 12⁴ lattices. We have concentrated on the mean plaquette energy and the string tension. The string tension does not vanish on a finite lattice, but using finite size scaling arguments the indications are that it does vanish on an infinite lattice, where we predict the critical coupling β_c = 1.008 and the correlation length exponent $\text{ν =}\text{1}\text{3}$. We compare our results to those for SU(2) and find that although there are differences, they are not yet definitive.     

BRST invariant mixed string vertex for the bosonic string

We construct a BRST invariant (N + M)-string vertex including both open and closed string states. When we saturate it with N open string and M closed string physical states it reproduces their corresponding scattering amplitude. As a particular case we obtain a BRST invariant vertex for the open-closed string transition.