Infrared behaviour of Yang-Mills theory at high temperatures

We employ Monte Carlo methods to probe the infrared structure of SU(2) Yang-Mills theory at high temperatures. In particular, we study the free energy of the gauge invariant non-abelian magnetic flux. The Monte Carlo support the conjecture that the magnetic flux is screened. The inverse magnetic screening length provides a non-perturbative infrared cut-off for the quantum statistics of the SU(2) gauge theory and is estimated to be about 0.24 g²T.     

Perturbative infrared finiteness of Yang-Mills theory from renormalization group flow

It is commonly believed that a Yang-Mills theory (and in general a massless theory) with a nonvanishing subtraction point is infrared finite, i.e. the vertex functions at non-exceptional momenta are finite. We give a simple perturbative proof of this fact by using the Wilson renormalization group formulation. The proof requires the control of the singular behaviour of vertex functions only for a restricted class of exceptional configurations of momenta.     

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.     

Combining infrared and low-temperature asymptotes in Yang-Mills theories

We demonstrate that the powerlike nonperturbative behavior of gluon and ghost propagators in the infrared limit of Yang-Mills theories can provide at finite temperatures T a negative T4 contribution to the pressure and energy density. The existence of a mass gap then implies new relations between the infrared critical exponents of gluon and ghost propagators.     

Two-loop diagrams in Yang-Mills theory

A calculation of the renormalisation constants of the Yang-Mills field to O(g⁴) is presented. The function β(g) is hence evaluated to O(g⁵) and possible implications for gauge theories of the strong interactions discussed.     

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.     

String-like phase in Yang-Mills theory

A dynamical mechanism is discussed leading to the phase where the string of the color flux tube is formed in Yang-Mills theory. The pairing force between massless gauge fields in the color single channel forms a tachyon or a Cooper state and leads to the instability of the normal vacuum. A stable vacuum is required to remain massless after the condensation of pairs. Then the stability of the new vacuum leads to the condition on the 't Hooft index α which is equivalent to the condition of the existence of the string solutions.     

Yang-Mills gauge theory and gravitation

We point out that Yang's and Einstein's gravitational equations can be obtained from a geometric approach of Yang-Mills gauge theory in a sourceless case, under a decomposition of the Poincaré algebra. Otherwise, Einstein's equations cannot be derived from a Yang-Mills gauge equation when sources are inserted in the rotational sector of that algebra. A gauge Lagrangian structure is also discussed.     

Liquid-crystal defects and confinement in Yang-Mills theory

It has been shown that, in the Landau gauge of the SU(2) Yang-Mills theory, the residual global symmetry supports the existence of topological vortices which resemble disclination defects in nematic liquid crystals and Alice (half-quantum) vortices in superfluid ³He in the A-phase. The theory also possesses half-integer and integer-charged monopoles, which are analogous to the point-like defects in nematic crystal and in liquid helium. We argue that the deconfinement phase transition in the Yang-Mills theory in the Landau gauge is associated with the proliferation of these vortices and/or monopoles. The text was submitted by the author in English.     

Infrared behaviour of on shell form factors in anN=4 supersymmetric Yang-Mills field theory

We discuss the infrared and mass singular behaviour of some on shell form factors which are calculated up to the two loop level in anN=4 supersymmetric Yang-Mills field theory. One of the outcomes of our investigation is that the finite terms in the perturbation series of the form factor are determined by exponentiating the lowest order term. The same phenomeno has been discovered in some infrared and mass finite quantities.     

Functional determinants in euclidean Yang-Mills theory

We study functional determinants entering the path integral for topologically non-trivial sectors of Euclidean SU(2) Yang-Mills theory and we derive some results in exact closed form.This work is supported through funds provided by the US Department of Energy (DOE) under Contract EY-76-C-02-3069 and by the National Science Foundation through funds provided under Contract PHY 79-16812     

Large volume behaviour of Yang-Mills propagators

We investigate finite volume effects in the propagators of Landau gauge Yang-Mills theory using Dyson-Schwinger equations on a 4-dimensional torus. In particular, we demonstrate explicitly how the solutions for the gluon and the ghost propagator tend towards their respective infinite volume forms in the corresponding limit. This solves an important open problem of previous studies where the infinite volume limit led to an apparent mismatch, especially of the infrared behaviour, between torus extrapolations and the existing infinite volume solutions obtained in 4-dimensional Euclidean space-time. However, the correct infinite volume limit is approached rather slowly. The typical scales necessary to see the onset of the leading infrared behaviour emerging already imply volumes of at least 10-15 fm in lengths. To reliably extract the infrared exponents of the infinite volume solutions requires even much larger ones. While the volumes in the Monte-Carlo simulations available at present are far too small to facilitate that, we obtain a good qualitative agreement of our torus solutions with recent lattice data in comparable volumes.     

Gravity as Yang-Mills gauge theory

We propose a Yang-Mills field theory of gravity based on a unitary phase-gauge-invariance of the lagrangian where the gauge transformations are those of the SU(2) × U(1) symmetry of the 2-spinors. In the classical limit this microscopic theory results in Einstein's metrical theory of gravity, where we restrict ourselves in a first step to its linearized version.     

Geometric regularization of Yang-Mills theory

A continuum regularization of Yang-Mills theory with a possible non-perturbative interpretation is introduced in the euclidean formalism. The regularization preserves Lorentz covariance and gauge invariance and involves not only a regularization of the action but also a regularization of the functional measure in terms of a nuclear-riemannian structure of the space of gauge orbits.