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.Comment: 31 pages, Late

The two phases of topologically massive compact U(1) theory

The mean field like gauge invariant variational method formulated recently, is applied to a topologically massive QED in 3 dimensions. We find that the theory has a phase transition in the Chern Simons coefficient n. The phase transition is of the Berezinsky-Kosterlitz - Thouless type, and is triggered by the liberation of Polyakov monopoles, which for n>8 are tightly bound into pairs. In our Hamiltonian approach this is seen as a similar behaviour of the magnetic vortices, which are present in the ground state wave functional of the compact theory. For n>8, the low energy behavior of the theory is the same as in the noncompact case. For n<8 there are no propagating degrees of freedom on distance scales larger than the ultraviolet cutoff. The distinguishing property of the n<8 phase, is that the magnetic flux symmetry is spontaneoously broken

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.Comment: 26 pages, 1 figure, discussion about spatial Wilson loops added, to appear in JHE

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

Dense-Dilute Duality at work: dipoles of the target

We explore the properties of the QCD high energy evolution in the limit of a dilute target. Using the recently established property of selfduality of the evolution operator (hep-ph/0502119), we show how to properly define the target gluon and dipole creation operators in terms of dual Wilson lines (dual eikonal factors). We explain how to expand these operators in terms of the functional derivatives of the color charge density, in the situation when they act on the eikonal factors of the projectile partons. We explicitly calculate the expansion of the high energy evolution operator to fourth order in the functional derivatives. Our result is infrared and ultraviolet finite, but does not coincide with the formula given in hep-ph/0501088. We resolve this discrepancy by showing that the identification of the dipole creation and annihilation operators used in hep-ph/0501088 is incomplete, and provide the required corrections to these definitions. The use of the corrected operators in the calculational framework of hep-ph/0501088 reproduces our result. We also prove that there is no discrepancy between the expansion of the JIMWLK equation and the dualization of the expansion of the weak field limit.Comment: 18 pages, Explanations added. Version to appear in PR

Relativistic Winds from Compact Gamma-Ray Sources: II. Pair Loading and Radiative Acceleration in Gamma-ray Bursts

We consider the effects of rapid pair creation by an intense pulse of gamma-rays propagating ahead of a relativistic shock. Side-scattered photons colliding with the main gamma-ray beam amplify the density of scattering charges. The acceleration rate of the pair-loaded medium is calculated, and its limiting bulk Lorentz factor related to the spectrum and compactness of the photon source. One obtains, as a result, a definite prediction for the relative inertia in baryons and pairs. The deceleration of a relativistic shock in the moving medium, and the resulting synchrotron emissivity, are compared with existing calculations for a static medium. The radiative efficiency is increased dramatically by pair loading. When the initial ambient density exceeds a critical value, the scattering depth traversed by the main gamma-ray pulse rises above unity, and the pulse is broadened. These considerations place significant constraints on burst progenitors: a pre-burst mass loss rate exceeding 10^{-5} M_\odot per year is difficult to reconcile with individual pulses narrower than 10 s, unless the radiative efficiency is low. An anisotropic gamma-ray flux (on an angular scale \Gamma^{-1} or larger) drives a large velocity shear that greatly increases the energy in the seed magnetic field forward of the propagating shock.Comment: 19 pp., LaTeX (aaspp4.sty), revised 12/23/99, Ap. J. in press; summary section added and several minor improvements in presentatio

Treading on the cut: Semi inclusive observables at high energy

We develop the formalizm for calculating semi inclusive observables at high energy in the JIMWLK/KLWMIJ approach. We consider several examples including diffractive processes, elastic and inclusive over the target degrees of freedom, scattering with fixed total transverse momentum transfer and inclusive gluon production. We discuss evolution of these observables with respect to various rapidity variables involved in their definitions (total rapidity, rapidity gap, width of diffractive interval etc.). We also discuss the dipole model limit of these observables and derive closed simple (as opposed to functional) differential equations in this approximation. We point out that there are some interesting differences between the full JIMWLK/KLWMIJ evolution and the dipole model evolution of diffractive cross section. In particular we show that in the dipole approximation the target does not diffract beyond the valence rapidity interval, consistently with the intuition suggested by the Pomeron fan diagramms. On the other hand such diffractive processes do exist in the full JIMWLK/KLWMIJ approach, albeit suppressed by the factor 1/N_c^2.Comment: 37 pages, 3 figures. A few remarks added. To appear in PR

Relativistic Winds from Compact Gamma-ray Sources: I. Radiative Acceleration in the Klein-Nishina Regime

We consider the radiative acceleration to relativistic bulk velocities of a cold, optically thin plasma which is exposed to an external source of gamma-rays. The flow is driven by radiative momentum input to the gas, the accelerating force being due to Compton scattering in the relativistic Klein-Nishina limit. The bulk Lorentz factor of the plasma, Gamma, derived as a function of distance from the radiating source, is compared with the corresponding result in the Thomson limit. Depending on the geometry and spectrum of the radiation field, we find that particles are accelerated to the asymptotic Lorentz factor at infinity much more rapidly in the relativistic regime; and the radiation drag is reduced as blueshifted, aberrated photons experience a decreased relativistic cross section and scatter preferentially in the forward direction. The random energy imparted to the plasma by gamma-rays can be converted into bulk motion if the hot particles execute many Larmor orbits before cooling. This `Compton afterburn' may be a supplementary source of momentum if energetic leptons are injected by pair creation, but can be neglected in the case of pure Klein-Nishina scattering. Compton drag by side-scattered radiation is shown to be more important in limiting the bulk Lorentz factor than the finite inertia of the accelerating medium. The processes discussed here may be relevant to a variety of astrophysical situations where luminous compact sources of hard X- and gamma-ray photons are observed, including active galactic nuclei, galactic black hole candidates, and gamma-ray bursts.Comment: LateX, 20 pages, 5 figures, revised version accepted for publication in the Ap

Supersymmetric Yang-Mills theory on the lattice

Recent development in numerical simulations of supersymmetric Yang-Mills (SYM) theories on the lattice is reviewed.Comment: 37 pages, 10 figure