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Alex Kovner

Publications and source records attributed to Alex Kovner.

At least 109 records · Page 6Linked to original sources
arXiv2000

Relating different approaches to nonlinear QCD evolution at finite gluon density

We analyze the relation between evolution equations at low x that have been derived in different approaches in the last several years. We show that the equation derived by Balitsky and Kovchegov is obtained from the Jalilian-Marian-Kovner-Leonidov-Weigert (JKLW) equation in the limit of small induced charge density. We argue that the higher nonlinearities resummed by the JKLW equation correspond, in physical terms, to the breakdown of the eikonal approximation when the gluon fields in the target are large.

hep-ph↗
arXiv1999

Gauge Invariant Variational Approach with Fermions: the Schwinger Model

We extend the gauge invariant variational approach of Phys. Rev. D52 (1995) 3719, hep-th/9408081, to theories with fermions. As the simplest example we consider the massless Schwinger model in 1+1 dimensions. We show that in this solvable model the simple variational calculation gives exact results.

hep-th↗
arXiv1999

Vector potential versus colour charge density in low-x evolution

We reconsider the evolution equations for multigluon correlators derived in hep-ph/9709432. We show how to derive these equations directly in terms of vector potentials (or colour field strength) avoiding the introduction of the concept of colour charge density in the intermediate steps. The two step procedure of deriving the evolution of the charge density correlators followed by the solution of classical equations for the vector potentials is shown to be consistent with direct derivation of evolution for vector potentials. In the process we correct some computational errors of hep-ph/9709432 and present the corrected evolution equations which have a somewhat simpler appearance.

hep-ph↗
arXiv1999

Interaction potential in compact three-dimensional QED with mixed action

We use a variational wave function to calculate the energy of the interaction between external charges in the compact Abelian gauge theory in 2+1 dimensions with mixed action. Our variational wave functions preserve the compact gauge invariance of the theory both in the vacuum and in the charged sectors. We find that a good estimate of the interaction energy is obtained only when we allow more variational parameters in the charged sector than in the vacuum sector. These extra parameters are the profile of an induced electric field. We find that the theory has a two-phase structure: When the charge-2 coupling is large and negative there is no mass gap in the theory and no confinement, while otherwise a mass gap is generated dynamically and the theory confines charges. The pure Wilson theory is in the confining phase.

hep-lat↗
arXiv1998

Instantons and the QCD Vacuum Wavefunctional

We analyze the instanton transitions in the framework of the gauge invariant variational calculation in the pure Yang-Mills theory. Instantons are identified with the saddle points in the integration over the gauge group which projects the Gaussian wave functional onto the gauge invariant physical Hilbert space. We show that the dynamical mass present in the best variational state provides an infrared cutoff for the instanton sizes. The instantons of the size $ρ<1/M$ are suppressed and the large size instanton problem arising in the standard WKB calculation is completely avoided in the present variational framework.

hep-ph↗
arXiv1998

Unitarization of Gluon Distribution in the Doubly Logarithmic Regime at High Density

We analyze the general nonlinear evolution equations for multi gluon correlators derived in hep-ph/9709432 by restricting ourselves to a double logarithmic region. In this region our evolution equation becomes local in transverse momentum space and amenable to simple analysis. It provides a complete nonlinear generalization of the GLR equation. We find that the full double log evolution at high density becomes strikingly different from its linear doubly logarithmic DGLAP counterpart. An effective mass is induced by the nonlinear corrections which at high densities slows down the evolution considerably. We show that at small values of impact parameter the gluonic density grows as a logarithm of energy. At higher values of impact parameter the growth is faster, since the density of gluons is lower and nonlinearities are less important.

hep-ph↗
arXiv1998

Strings and string breaking in 2+1 dimensional nonabelian theories

We consider properties of confining strings in 2+1 dimensional SU(2) nonabelian gauge theory with the Higgs field in adjoint representation. The analysis is carried out in the context of effective dual Lagrangian which describes the dynamics of t'Hooft's $Z_{N}$ vorices. We point out that the same Lagrangian should be interpreted as an effective Lagrangian for the lightest glueballs. It is shown how the string tension for a fundamental string arises in this description. We discuss the properties of the adjoint string and explain how its breaking occurs when the distance between the charges exceeds a critical value. The interaction between the fundamental strings is studied. It is shown that they repel each other in the weak coupling regime. We argue that in the confining regime (pure Yang-Mills theory, or a theory with a heavy Higgs field) the strings actually attract each other and the crossover between the two regimes corresponds to the crossover between the dual superconductors of first and second kind.

hep-th↗
arXiv1998

Chiral Symmetry Breaking without Bilinear Condensates, Unbroken Axial Z_N Symmetry, and Exact QCD Inequalities

An alternative pattern of the chiral symmetry breaking, suggested recently by Stern, is investigated. It could be self-consistent provided that the chiral $SU(N_f) \times SU(N_f)$ symmetry is broken spontaneously down to $SU(N_f) \times Z_{N_f}$ rather than to $SU(N_f)_V$. The discrete axial $Z_{N_f}$ then would play a custodial role preventing the quark bilinears from condensation. It is shown that this pattern of the chiral symmetry breaking is ruled out in QCD by exact inequalities. It is not ruled out, however, in other gauge theories with scalar quarks and/or Yukawa couplings.

hep-ph↗
arXiv1998

More on Supersymmetric Domain Walls, N Counting and Glued Potentials

Various features of domain walls in supersymmetric gluodynamics are discussed. We give a simple field-theoretic interpretation of the phenomenon of strings ending on the walls recently conjectured by Witten. An explanation of this phenomenon in the framework of gauge field theory is outlined. The phenomenon is argued to be particularly natural in supersymmetric theories which support degenerate vacuum states with distinct physical properties. The issue of existence (or non-existence) of the BPS saturated walls in the theories with glued (super)potentials is addressed. The amended Veneziano-Yankielowicz effective Lagrangian belongs to this class. The physical origin of the cusp structure of the effective Lagrangian is revealed, and the limitation it imposes on the calculability of the wall tension is explained. Related problems are considered. In particular, it is shown that the so called discrete anomaly matching, when properly implemented, does not rule out the chirally symmetric phase of supersymmetric gluodynamics, contrary to recent claims.

hep-th↗
arXiv1997

The Wilson renormalization group for low x physics: towards the high density regime

We continue the study of the effective action for low $x$ physics based on a Wilson renormalization group approach. We express the full nonlinear renormalization group equation in terms of the average value and the average fluctuation of extra color charge density generated by integrating out gluons with intermediate values of $x$. This form clearly exhibits the nature of the phenomena driving the evolution and should serve as the basis of the analysis of saturation effects at high gluon density at small $x$.

hep-ph↗
arXiv1997

The BFKL Equation from the Wilson Renormalization Group

We discuss the Wilson renormalization group approach to the effective action for low $x$ physics. It is shown that in the linearized, weak field regime the RG equation reduces to the BFKL equation for the evolution of the unintegrated gluon density. We discuss the relation of this approach with that of Lipatov.

hep-ph↗
arXiv1996

Dual Superconductivity. Variations on a Theme

It is pointed out that the low energy effective theory that describes the low lying glueballs of the pure Yang Mills theory sustains static classical stringlike solutions. We suggest that these objects can be identified with the QCD flux tubes and their energy per unit length with the string tension.

hep-ph↗
arXiv1996

The Intrinsic Glue Distribution at Very Small x

We compute the distribution functions for gluons at very small x and not too large values of transverse momenta. We extend the McLerran-Venugopalan model by using renormalization group methods to integrate out effects due to those gluons which generate an effective classical charge density for Weizsäcker-Williams fields. We argue that this model can be extended from the description of nuclei at small x to the description of hadrons at yet smaller values of x. This generates a Lipatov like enhancement for the intrinsic gluon distribution function and a non-trivial transverse momentum dependence as well. We estimate the transverse momentum dependence for the distribution functions, and show how the issue of unitarity is resolved in lepton-nucleus interactions.

hep-ph↗
arXiv1995

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.

hep-th↗
arXiv1995

Gluon Production from Non-Abelian Weizsäcker-Williams Fields in Nucleus-Nucleus Collisions

We consider the collisions of large nuclei using the theory of McLerran and Venugopalan. The two nuclei are ultra-relativistic and sources of non-abelian Weizsäcker-Williams fields. These sources are in the end averaged over all color orientations locally with a Gaussian weight. We show that there is a solution of the equations of motion for the two nucleus scattering problem where the fields are time and rapidity independent before the collision. After the collision the solution depends on proper time, but is independent of rapidity. We show how to extract the produced gluons from the classical evolution of the fields.

hep-ph↗
arXiv1994

Compact QED$_3$ - a simple example of a variational calculation in a gauge theory

We apply a simple mean field like variational calculation to compact QED in 2+1 dimensions. Our variational ansatz explicitly preserves compact gauge invariance of the theory. We reproduce in this framework all the known results, including dynamical mass generation, Polyakov scaling and the nonzero string tension. It is hoped that this simple example can be a useful reference point for applying similar approximation techniques to nonabelian gauge theories.

hep-th↗