arXiv subjects

Alex Kovner

Publications and source records attributed to Alex Kovner.

At least 91 records · Page 5Linked to original sources

arXiv2005

Remarks on High Energy Evolution

We make several remarks on the B-JIMWLK hierarchy. First, we present a simple and instructive derivation of this equation by considering an arbitrary projectile wave function with small number of valence gluons. We also generalize the equation by including corrections which incorporate effects of high density in the projectile wave function. Second, we systematically derive the dipole model approximation to the hierarchy. We show that in the dipole approximation the hierarchy has a simplifying property that allows its solution by solving the classical equation followed by averaging over the ensemble of initial conditions.

hep-ph↗

arXiv2004

Variational techniques in non-perturbative QCD

We review attempts to apply the variational principle to understand the vacuum of non-abelian gauge theories. In particular, we focus on the method explored by Ian Kogan and collaborators, which imposes exact gauge invariance on the trial Gaussian wave functional prior to the minimization of energy. We describe the application of the method to a toy model -- confining compact QED in 2+1 dimensions -- where it works wonderfully and reproduces all known non-trivial results. We then follow its applications to pure Yang-Mills theory in 3+1 dimensions at zero and finite temperature. Among the results of the variational calculation are dynamical mass generation and the analytic description of the deconfinement phase transition.

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arXiv2004

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.

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arXiv2003

Energy Dependence of the Cronin Effect from Non-Linear QCD Evolution

The non-linear evolution of dense partonic systems has been suggested as one of the novel physics mechanisms relevant to the dynamics of hadron-nucleus and nucleus-nucleus collisions at collider energies. Here we study to what extent the description of Cronin enhancement in the framework of this non-linear evolution is consistent with the recent observation in 200 AGeV d--Au collisions at the Relativistic Heavy Ion Collider. We solve the Balitsky-Kovchegov evolution equation numerically for several initial conditions encoding Cronin enhancement. We find that the properly normalized nuclear gluon distribution is suppressed at all momenta relative to that of a single nucleon. Calculating the resulting spectrum of produced gluons in p-A and A-A collisions, we establish that the nonlinear QCD evolution is unable to generate a Cronin type enhancement, and that it quickly erases any such enhancement which may be present at lower energies.

hep-ph↗

arXiv2002

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.

hep-th↗

arXiv2002

Fundamental Matter and the Deconfining Phase Transition in 2+1 D

We analyze the effect of heavy fundamentally charged particles on the finite temperature deconfining phase transition in the 2+1 dimensional Georgi-Glashow model. We show that in the presence of fundamental matter the transition turns into a crossover. The near critical theory is mapped onto the 2 dimensional Ising model in an external magnetic field. Using this mapping we determine the width of the crossover region as well as the specific heat as a function of the fundamental mass.

hep-th↗

arXiv2002

Monopoles, Vortices and Strings: Confinement and Deconfinement in 2+1 Dimensions at Weak Coupling

We consider, from several complementary perspectives, the physics of confinement and deconfinement in the 2+1 dimensional Georgi-Glashow model. Polyakov's monopole plasma and 't Hooft's vortex condensation are discussed first. We then discuss the physics of confining strings at zero temperature. We review the Hamiltonian variational approach and show how the linear confining potential arises in this framework. The second part of this review is devoted to study of the deconfining phase transition. We show that the mechanism of the transition is the restoration of 't Hooft's magnetic symmetry in the deconfined phase. The heavy charged $W$ bosons play a crucial role in the dynamics of the transition, and we discuss the interplay between the charged $W$ plasma and the binding of monopoles at high temperature. Finally we discuss the phase transition from the point of view of confining strings. We show that from this point of view the transition is not driven by the Hagedorn mechanism (proliferation of arbitrarily long strings), but rather by the "disintegration" of the string due to the proliferation of 0 branes.

hep-th↗

arXiv2002

Perturbative Saturation and the Soft Pomeron

We show that perturbation theory provides two distinct mechanisms for the power like growth of hadronic cross sections at high energy. One, the leading BFKL effect is due to the growth of the parton density, and is characterized by the leading BFKL exponent. The other mechanism is due to the infrared diffusion, or the long range nature of the Coulomb field of perturbatively massless gluons. When perturbative saturation effects are taken into account, the first mechanism is rendered ineffective but the second one persists. We suggest that these two distinct mechanisms are responsible for the appearance of two pomerons. The density growth effects are responsible for the hard pomeron and manifest themselves in small systems (e.g. gamma^* or small size fluctuations in the proton wave function) where saturation effects are not important. The soft pomeron is the manifestation of the exponential growth of the black saturated regions which appear in typical hadronic systems. We point out that the nonlinear generalization of the BFKL equation which takes into account wave function saturation effects ("pomeron loops") provides a well defined perturbative framework for the calculation of the soft pomeron intercept. The conjecture of a perturbative soft pomeron is consistent with picturing the proton as a loosely bound system of several small black regions corresponding e.g. to constituent quarks of size about 0.3 fm. Phenomenological implications of this picture are compatible with the main qualitative features of data on p-p scattering.

hep-ph↗

arXiv2001

Eikonal Evolution and Gluon Radiation

We give a simple quantum mechanical formulation of the eikonal propagation approximation, which has been heavily used in recent years in problems involving hadronic interactions at high energy. This provides a unified framework for several approaches existing in the literature. We illustrate this scheme by calculating the total, elastic, inelastic and diffractive DIS cross sections, as well as gluon production in high energy hadronic collisions. From the q-qbar-g-component of the DIS cross sections, we straightforwardly derive low x evolution equations for inelastic and diffractive DIS distribution functions. In all calculations, we provide all order 1/N corrections to the results existing in the literature.

hep-ph↗

arXiv2001

Instanton molecules at high temperature - the Georgi-Glashow model and beyond

We show that correlators of some local operators in gauge theories are sensitive to the presence of the instantons even at high temperature where the latter are bound into instanton-anti-instanton "molecules". We calculate correlation functions of such operators in the deconfined phase of the 2+1 dimensional Georgi-Glashow model and discuss analogous quantities in the chirally symmetric phase of QCD. We clarify the mechanism by which the instanton-anti-instanton molecules contribute to the anomaly of axial U(1) at high temperature.

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arXiv2001

The chicken or the egg; or Who ordered the chiral phase transition?

We draw an analogy between the deconfining transition in the 2+1 dimensional Georgi-Glashow model and the chiral phase transition in 3+1 dimensional QCD. Based on the detailed analysis of the former (hep-th/0010201) we suggest that the chiral symmetry restoration in QCD at high temperature is driven by the thermal ensemble of baryons and anti-baryons. The chiral symmetry is restored when roughly half of the volume is occupied by the baryons. Surprisingly enough, even though baryons are rather heavy, a crude estimate for the critical temperature gives $T_c=180$ Mev. In this scenario the binding of the instantons is not the cause but rather a consequence of the chiral symmetry restoration.

hep-ph↗

arXiv2001

Deconfinement at N>2: SU(N) Georgi-Glashow model in 2+1 dimensions

We analyse the deconfining phase transition in the SU(N) Georgi-Glashow model in 2+1 dimensions. We show that the phase transition is second order for any N, and the universality class is different from the Z(N) invariant Villain model. At large N the conformal theory describing the fixed point is a deformed SU(N)_1 WZNW model which has N-1 massless fields. It is therefore likely that its self-dual infrared fixed point is described by the Fateev-Zamolodchikov theory of Z(N) parafermions.

hep-th↗

arXiv2001

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.

hep-th↗

arXiv2001

Z(N) wall junctions: Monopole fossils in hot QCD

We point out that the effective action of hot Yang--Mills theories has semi-classical solutions, which are naturally identified with monopole world lines, ``frozen'' into the short imaginary time dimension. The solutions look like wall junctions: lines along which N electric Z(N) domain walls come together. They are instrumental in reconciling explicit perturbative calculations at high temperature with the magnetic Z(N) symmetry.

hep-ph↗

arXiv2001

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.

hep-th↗

arXiv2000

Confinement, magnetic Z(N) symmetry and low energy effective theory of gluodynamics

In these notes I explain the idea how one could understand confinement by studying the low energy effective dynamics of non Abelian gauge theories. I argue that under some mild assumptions, the low energy dynamics is determined universally by the spontaneous breaking of the magnetic symmetry introduced by 't Hooft more than 20 years ago. The degrees of freedom in the effective theory are magnetic vortices. They play a similar role in confining dynamics to the role played by pions and sigma in the chiral symmetry breaking dynamics. I give explicit derivation of the effective theory in 2+1 dimensional weekly coupled confining models and give arguments 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 long range interaction between topological solitons, which follows by a simple direct classical calculation from the structure of the effective Lagrangian. I discuss the elements of this picture which generalize to 3+1 dimensions and point to the open questions still remaining.

hep-ph↗

arXiv2000

Vortices and bags in 2+1 dimension

We consider the effect of the (heavy) fundamental quarks on the low energy effective Lagrangian description of nonabelian gauge theories in 2+1 dimensions. We show that in the presence of the fundamental charges, the magnetic $Z_N$ symmetry becomes local. We construct the effective Lagrangian representing this local symmetry in terms of magnetic vortex fields, and discuss its physical consequences. We show that the finite energy states described by this Lagrangian have distinct bag-like structure. The point-like quarks are confined to the region of space where the value of the vortex field is much smaller than in the surrounding vacuum.

hep-th↗

arXiv2000

Magnetic Symmetries and Vortices In Chern-Simons Theories

We study the locality properties of the vortex operators in compact U(1) Maxwell-Chern-Simons and SU(N) Yang-Mills-Chern-Simons theories in 2+1 dimensions. We find that these theories do admit local vortex operators and thus in the UV regularized versions should contain stable magnetic vortices. In the continuum limit however the energy of these vortex excitations generically is logarithmically UV divergent. Nevertheless the classical analysis shows that at small values of CS coefficient $κ$ the vortices become light. It is conceivable that they in fact become massless and condense due to quantum effects below some small $κ$. If this happens the magnetic symmetry breaks spontaneously and the theory is confining.

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