Topological field patterns in the Yang-Mills theory

We present a formalism where the topological configurations of pure Yang-Mills theory are characterised using gauge fields alone. Here, we obtain an expression for the charges of these topologicalSO(3) gauge field configurations in terms of the Abelian vector potentials. In this formalism we analyse the ’t Hooft-Polyakov monopole solution.     

Topological susceptibility in the Yang-Mills theory in the vacuum correlator method

It is proven that no wormholes can be formed in viable scalar-tensor models of dark energy admitting its phantom-like (w < −1) behavior in cosmology, even in the presence of electric or magnetic fields, if the nonminimal coupling function f(Φ) is positive everywhere and the scalar field Φ itself is not a ghost. Some special static, spherically symmetric wormhole solutions may exist if f(Φ) is allowed to reach zero or to become negative, so that the effective gravitational constant becomes negative in some region making the graviton a ghost. If f remains non-negative, such solutions require severe fine-tuning and a very peculiar kind of model. If f < 0 is allowed, it is argued (and confirmed by previous investigations) that such solutions are generically unstable under nonstatic perturbations, the instability appearing right near transition surfaces to negative f. The text was submitted by the authors in English.     

Part 1 : Topological aspects of Yang-Mills fields in curved spaces. (Exact solutions)

To explore in its full richness the topological possibilities of gauge fields one should allow for simultaneous presence of gravitational and Yang-Mills ones. Thus if the integral topological indices of the Yang-Mills field for a flat Euclidean base space is associated with the structure of the vacuum, one may ask among other questions of interest, how this spectrum might be modified when the base space itself has non trivial indices. Exact solutions of SU(2) Yang-Mills fields are presented for metrics corresponding to well-known gravitational instantons. Such selfdual solutions, with vanishing energy monien-tunl tensor T_μv for Euclidean signature of the base space, do not perturb the metric. Thus they provide solutions of the combined gravitational-Y.M. system. New topological possibilities, such as finite action SU(2) fields with fractional indices for many centre inetrics are displayed explicitly. As another type of possibility non selfdual, finite action solutions are constructed explicitly on Schwarzschild and de Sitter metrics, the solution being real in the first and complex in second case respectively. It is also shown how various meron type solutions in flat space can be derived systematically from a very simple static solution in de Sitter.     

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.     

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.     

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.     

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.     

Yang-Mills theory on a cylinder

Yang-Mills theory on a two dimensional cylinder is studied in the hamiltonian formalism, without using gauge conditions. Since the only gauge invariant variable is the Wilson loop (holonomy) this system is equivalent to a finite dimensional system. The eigenstates and eigenvalues of the hamiltonian are found exactly.     

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.     

Topological vacua and spontaneous CP violations in Yang-Mills theories

Zeitschrift für Physik C Particles and Fields - From the consideration of the topological structures of Yang-Mills theories, we obtain the results thatSU(2) Yang-Mills theory in the Minkowski...     

Double field formulation of Yang-Mills theory

Based on our previous work on the differential geometry for the closed string double field theory, we construct a Yang-Mills action which is covariant under O(D,D) T-duality rotation and invariant under three-types of gauge transformations: non-Abelian Yang-Mills, diffeomorphism and one-form gauge symmetries. In double field formulation, in a manifestly covariant manner our action couples a single O(D,D) vector potential to the closed string double field theory. In terms of undoubled component fields, it couples a usual Yang-Mills gauge field to an additional one-form field and also to the closed string background fields which consist of a dilaton, graviton and a two-form gauge field. Our resulting action resembles a twisted Yang-Mills action.