One gluon, two gluon: multigluon production via high energy evolution

We develop an approach for calculating the inclusive multigluon production within the JIMWLK high energy evolution. We give a formal expression of multigluon cross section in terms of a generating functional for arbitrary number of gluons $n$. In the dipole limit the expression simplifies dramatically. We recover the previously known results for single and double gluon inclusive cross section and generalize those for arbitrary multigluon amplitude in terms of Feynman diagramms of Pomeron - like objects coupled to external rapidity dependent field $s(\eta)$. We confirm the conclusion that the AGK cutting rules in general are violated in multigluon production. However we present an argument to the effect that for doubly inclusive cross section the AGK diagramms give the leading contribution at high energy, while genuine violation only occurs for triple and higher inclusive gluon production. We discuss some general properties of our expressions and suggest a line of argument to simplify the approach further.Comment: 32 pages, one reference corrected. to appear in JHE

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.Comment: 71 pages, 1 figure. To be published in the memorial volume "From Fields to Strings: Cirvumnavigating Theoretical Physics", World Scientific, 2004. Dedicated to the memory of Ian Koga

From bubbles to foam: dilute to dense evolution of hadronic wave function at high energy

We derive the evolution of a hadronic light cone wave function with energy at weak coupling. Our derivation is valid both in the high and the low partonic density limit, and thus encompasses both the JIMWLK and the KLWMIJ evolution. The hadronic wave function is shown to evolve by the action of the Bogoliubov-type operator, which diagonalizes on the soft gluon sector the light-cone hamiltonian in the presence of an arbitrary valence charge density. We find explicitly the action of this operator on the soft as well as the valence degrees of freedom of the theory.Comment: 30 page

First correction to JIMWLK evolution from the classical equations of motion

We calculate some ${\cal O}(\alpha_s^2)$ corrections to the JIMWLK kernel in the framework of the light-cone wave function approach to the high energy limit of QCD. The contributions that we consider originate from higher order corrections in the strong coupling and in the density of the projectile to the solution of the classical Yang-Mills equations of motion that determine the Weizs\"acker-Williams fields of the projectile. We study the structure of these corrections in the dipole limit, showing that they are subleading in the limit of large number of colours $N$, and that they cannot be fully recast in the form of dipole degrees of freedom.Comment: 4 pages, LaTeX, 2 eps figures included using graphicx, uses enclosed iopart.cls; contribution to the proceedings of Quark Matter 2006 (Shanghai, November 14th-20th 2006

Classicalization and Unitarity

We point out that the scenario for UV completion by "classicalization", proposed recently is in fact Wilsonian in the classical Wilsonian sense. It corresponds to the situation when a field theory has a nontrivial UV fixed point governed by a higher dimensional operator. Provided the kinetic term is a relevant operator around this point the theory will flow in the IR to the free scalar theory. Physically, "classicalization", if it can be realized, would correspond to a situation when the fluctuations of the field operator in the UV are smaller than in the IR. As a result there exists a clear tension between the "classicalization" scenario and constraints imposed by unitarity on a quantum field theory, making the existence of classicalizing unitary theories questionable.Comment: Some clarifications and refs added. Accepted as a JHEP publication; 12 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

On Nonexistence of Magnetic Charge in Pure Yang-Mills Theories

We prove that magnetic charge does not exist as a physical observable on the physical Hilbert space of the pure SU(2) gauge theory. The abelian magnetic monopoles seen in lattice simulations are then interpreted as artifacts of gauge fixing. The apparent physical scaling properties of the monopole density in the continuum limit observed on the lattice are attributed to the correct scaling properties of physical objects - magnetic vortices, as first argued by Greensite et. al. We can show that a local gauge transformation of a certain type can " create" abelian monopole-antimonopole pairs along magnetic vortices. This gauge transformation exists in pure SU(N) gauge theory at any $N$.Comment: Some references and comments adde

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