Magnetic Z(N) symmetry 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 behaviour of the spatial 't Hooft loop discussed in hep-ph/9909516. We also point out that the realization of the magnetic symmetry has bearing on the behaviour 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 behaviour in the symmetric phase but area law behaviour in the spontaneously broken phase. At high temperature the argument does not hold and the restoration of magnetic Z(N) is consistent with area law for the Wilson loop.Comment: 30 pages, discussion of the Wilson loop at high temperature completely revised, new references adde

The Higgs field and the ultraviolet behaviour of the vortex operator in 2+1 dimensions

We calculate the change in the ultraviolet behaviour of the vortex operator due to the presence of dynamical Higgs field in both 2+1 dimensional QED and the 2+1 dimensional Georgi-Glashow model. We find that in the QED case the presence of the Higgs field leads at the one loop level to power like correction to the propagator of the vortex operator. On the other hand, in the Georgi-Glashow model, the adjoint Higgs at one loop has no affect on the vortex propagator. Thus, as long as the mass of the Higgs field is much larger than the gauge coupling constant, the ultraviolet behaviour of the vortex operator in the Georgi-Glashow model is independent of the Higgs mass.Comment: 14 page

Gluon production and diffraction in the dipole picture

Using the eikonal approximation, we show that inclusive gluon production is related to the scattering of a gluon-gluon dipole while diffractive gluon production in DIS is related to a two-$q\bar q$ dipole scattering amplitude. Hence diffractive photon dissociation cross-sections are observables that provide potential information on dipole correlations, which represent an open issue in high-energy QCD.Comment: 4 pages, 2 figures, Proceedings of the 10th International Baryons Conference (Baryons04), Ecole Polytechnique, Palaiseau, France, October 25-29 200

Magnetic Z(N) symmetry in 2+1 dimensions

This review describes the role of magnetic symmetry in 2+1 dimensional gauge theories. In confining theories without matter fields in fundamental representation the magnetic symmetry is spontaneously broken. Under some mild assumptions, the low-energy dynamics is determined universally by this spontaneous breaking phenomenon. The degrees of freedom in the effective theory are magnetic vortices. Their role in confining dynamics is similar to that played by pions and sigma in the chiral symmetry breaking dynamics. I give an explicit derivation of the effective theory in (2+1)-dimensional weakly coupled confining models and argue that it remains qualitatively the same in strongly coupled (2+1)-dimensional gluodynamics. Confinement in this effective theory is a very simple classical statement about the long range interaction between topological solitons, which follows (as a result of a simple direct classical calculation) from the structure of the effective Lagrangian. I show that if fundamentally charged dynamical fields are present the magnetic symmetry becomes local rather than global. The modifications to the effective low energy description in the case of heavy dynamical fundamental matter are discussed. This effective lagrangian naturally yields a bag like description of baryonic excitations. I also discuss the fate of the magnetic symmetry in gauge theories with the Chern-Simons term

Charge and Magnetic Flux Correlations in Chern-Simons Theory with Fermions

Charge and magnetic flux bearing operators are introduced in Chern-Simons theory both in its pure form and when it is coupled to fermions. The magnetic flux creation operator turns out to be the Wilson line. The euclidean correlation functions of these operators are shown to be local and are evaluated exactly in the pure case and through an expansion in the inverse fermion mass whenever these are present. Physical states only occur in the presence of fermions and consist of composite charge-magnetic flux carrying states which are in general anyonic. The large distance behavior of the correlation functions indicates the condensation of charge and magnetic flux.Comment: Latex, 17 page

Critical Exponents of the Superconducting Phase Transition

We study the critical exponents of the superconducting phase transition in the context of renormalization group theory starting from a dual formulation of the Ginzburg-Landau theory. The dual formulation describes a loop gas of Abrikosov flux tubes which proliferate when the critical temperature is approached from below. In contrast to the Ginzburg-Landau theory, it has a spontaneously broken global symmetry and possesses an infrared stable fixed point. The exponents coincide with those of a superfluid with reversed temperature axis.Comment: Postscript file. For related work see www adress http://www.physik.fu-berlin.de/kleiner_re.html in our homepage http://www.physik.fu-berlin.de/kleinert.htm

Small-x QCD effects in forward-jet and Mueller-Navelet jet production

We investigate small-x QCD effects in forward-jet production in deep inelastic scattering in the kinematic regime where the virtuality of the photon and the transverse momentum of the jet are two hard scales of about the same magnitude. We show that the data from HERA published by the H1 and ZEUS collaborations are well described by leading-logarithmic BFKL predictions. Parametrizations containing saturation effects expected to be relevant at higher energies also compare well to the present data. We extend our analysis to Mueller-Navelet jets at the LHC and discuss to what extent this observable could test these small-x effects and help distinguishing between the different descriptions.Comment: 18 pages, 9 figures, minor changes, published versio

Aspects of Duality in Nodal Liquids

Starting from a microscopic t-J like model and a SU(2) spin-charge separation ansatz, a relativistic continuum gauge lagrangian is obtained in the vicinity of a nodal point of the Fermi surface. The excitations in the pseudogap phase are described by topological excitations in the dual model which has a Z_2 global symmetry due to the effect of instantons. Confinement of spinon and holons emerge from this picture. The adjoint and fundamental strings are associated with stripes. As the spin gap decreases a local Z_2 symmetry emerges.Comment: 15 pages revtex, no figure