Conformally invariant fractals and potential theory

The multifractal (MF) distribution of the electrostatic potential near any conformally invariant fractal boundary, like a critical O(N) loop or a Q-state Potts cluster, is solved in two dimensions. The dimension &fcirc;(straight theta) of the boundary set with local wedge angle straight theta is &fcirc;(straight theta) = pi / straight theta-25-c / 12 (pi-straight theta)(2) / straight theta(2pi-straight theta), with c the central charge of the model. As a corollary, the dimensions D(EP) of the external perimeter and D(H) of the hull of a Potts cluster obey the duality equation (D(EP)-1) (D(H)-1) = 1 / 4. A related covariant MF spectrum is obtained for self-avoiding walks anchored at cluster boundaries.     

Conformally invariant equations of the quantum field theory

The equations invariant under the transformation of the conformal algebra are obtained using the Casimir operators. The connections among the components of the field are explicitly derived in the case of indecomposable representations of the conformal algebra which give rise to e.g. the Maxwell equations with currents. The free field equations are also incorporated in the conformally covariant scheme.     

Gauge invariant geometric variables for Yang-Mills theory

In a previous publication, local gauge invariant geometric variables were introduced to describe the physical Hilbert space of Yang-Mills theory. In these variables, the electric energy involves the inverse of an operator which can generically have zero-modes, and thus its calculation is subtle. In the present work, we resolve these subtleties by considering a small deformation in the definition of these variables, which in the end is removed. The case of spherical configurations of the gauge invariant variables is treated in detail, as well as the inclusion of infinitely heavy point color sources, and the expression for the associated electric field is found explicitly. These spherical geometries are seen to correspond to the spatial components of instanton configurations. The related geometries corresponding to Wu-Yang monopoles and merons are also identified.     

Conformally invariant gravitational waves in a modified gravitational theory

International Journal of Theoretical Physics - An attempt is made to obtain a conformally invariant gravitational wave equation in an isotropic background universe by modifying the Einstein field...     

Conformally invariant scalar field in charge-asymmetric cosmological models

Within a statistical approach to the general theory of relativity, we have constructed isotropic-charge-asymmetric cosmological models with an ultrarelativistic mixture of baryons and antibaryons and a conformally invariant scalar field. We have determined the role of the scalar field in the models obtained. We have investigated the evolution of small perturbations on the background of the spatially flat nonsingular model.Donets Polytechnical Institute. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 71–75, January, 1994.     

The Poisson algebra of the invariant charges of the Nambu-Goto theory: Casimir elements

The reparametrization invariant non-local conserved charges of the Nambu-Goto theory form an algebra under Poisson bracket operation. The center of the formal closure of this algebra is determined. The relation of the central elements to the constraints of the Nambu-Goto theory is clarified.On leave of absence from Physics Faculty, University of Freiburg, Federal Republic of GermanyThis work was supported by Stiftung Volkswagenwerk, Deutsche Forschungsgemeinschaft and by the Director, Office of Energy Research, Office of High Energy and Nuclear Physics, Division of High Energy Physics of the U.S. Department of Energy under Contract De-AC03-76SF0098     

Conformally invariant thermodynamics of a Maxwell-Dilaton black hole

The thermodynamics of Maxwell-Dilaton black holes has been extensively studied. It has served as a fertile ground to test ideas about temperature through various definitions of surface gravity. In this paper, we make an independent analysis of this black hole solution in both, Einstein and Jordan, frames. We explore a set of definitions for the surface gravity and observe the different predictions they make for the near extremal configuration of this black hole. Finally, motivated by the singularity structure in the interior of the event horizon, we use a holographic argument to remove the micro-states from the disconnected region of this solution. In this manner, we construct a frame independent entropy from which we obtain a temperature which agrees with the standard results in the non-extremal regime, and has a desirable behaviour around the extremal configurations according to the third law of black hole mechanics.     

Gauge invariant regularization of Yang-Mills wave functionals

We present a gauge invariant nonperturbative regularization of gauge theories in the temporal gauge. We use the Schrödinger representation for field theory. An example is given to illustrate regularization using wave functionals.     

Exact solutions of supergauge invariant Yang-Mills equations

We point our a new class of solutions of the supersymmetric Yang-Mills equations. This class provides solutions which cannot be generated from the solutions of the ordinary Yang-Mills equations by finite supersymmetry transformations and contains the supersymmetric generalization of the non-abelian plane waves.     

Half-monopoles in the Yang-Mills theory

Using a gauge-invariant characterization of monopoles defined via their centres, we investigate the generic topological field pattern for the three-dimensional Yang-Mills theory. This leads to field patterns with one-half winding number. After presenting the main features through the simpler case of half-vortices, we consider half-monopoles in detail.     

Yang-Mills theory and uniformization

We define a notion of a stable system of Hodge bundles. A stable system of Hodge bundles has a Hermitian-Yang-Mills metric and, if certain Chern classes vanish, this gives a complex variation of Hodge structure. We use these ideas to obtain a criterion for a variety to be uniformized by a bounded symmetric domain.     

Elliptic-type solutions to the scale invariant Yang-Mills and sigma-model hierarchies

We outline the construction of non-self-dual elliptic solutions by relating the spherically symmetric subsystem of the (scale invariant) Yang-Mills and sigmamodel hierarchies to the hierarchies of ⁴ and Sine-Gordon models in one dimension respectively. The construction is carried out explicitly for the usual Yang-Mills model on ₄, and the first two sigma-models on ₂ and ₄. The solution to the first member of the Yang-Mills hierarchy is related to elliptic solutions found previously.     

Conformally invariant gauge fixed actions for 2-D topological gravity

We show that invariants of Mumford for moduli spaces of curves are obtainable from a gauge fixed action of a topological quantum field theory in two dimensions. The method is completely analogous to the relation of Donaldson invariants with the topological quantum field theory for gauge theories in four dimensions.Supported by D.O.E. Grant DE-FG02-88ER 25066     

Conformally invariant pomeron interaction in perturbative QCD with large Nc

An effective non-local quantum field theory is constructed, which describes the interaction of pomerons in high-colored QCD. The theory includes both splitting and merging triple pomeron vertexes and diagrams with pomeronic loops. The Schwinger–Dyson equations for the ‘physical’ pomeron are written. Conformal invariance allows one to reduce the theory to the old-fashioned Gribov pomeron theory with an infinite number of pomerons, one of which is supercritical.