Yu. A. Kubyshin

Effective Lagrangians of the Randall–Sundrum Model

We construct the second variation Lagrangian for the Randall*Sundrum model with two branes, study its gauge invariance, and introduce and decouple the corresponding equations of motion. For the physical degrees of freedom in this model, we find the effective four-dimensional Lagrangians describing the massless graviton, massive gravitons, and the massless scalar radion. We show that the masses of these fields and their matter coupling constants are different on the different branes.

Higgs potentials as “inheritance” from higher space-time dimensions. II. Construction of Higgs models

A study is made of gauge theories obtained by dimensional reduction of multidimensional free gauge theories with symmetry. A sufficient condition for the reduced theory to contain only one irreducible multiplet of scalar fields is found. For the classes of such theories the potentials of scalar fields, Higgs potentials, are calculated explicitly. It is shown that in this approach the boson sector of the Weinberg-Salam model can be obtained. Stringent predictions for the mass of the Higgs boson and the Weinberg angle then arise - they can take only a discrete series of values.

SCALAR FIELDS IN THE DIMENSIONAL REDUCTION SCHEME FOR SYMMETRIC SPACES

We study the general features of the dimensional reduction scheme for multi-dimensional spaces of the type M4 × S/R, S/R being a symmetric coset space. The properties of the scalar potentials of the reduced theories are investigated and an effective method of explicit calculation of these potentials is elaborated. We consider also a wide class of embeddings of Lie subalgebras into simple Lie algebras resulting in reduced theories of physical interst.

Multidimensional Einstein-Yang-Mills theories: Dimensional reduction, spontaneous compactification, and all that

Abstract We study some new aspects of dimensional reduction and spontaneous compactification in multidimensional Einstein-Yang-Mills theories. Relations between physical properties (spontaneous sy symmetry breaking, absence of ghosts and tachyons) of the reduced theory and the metric on the multidimensional space and its symmetries are established. Assuming the space of extra dimensions to be a generic coset space we find an effective potential for the spontaneous compactification equations and investigate a class of models possessing compactifying solutions with remarkable properties: (a) the multidimensional vacuum states correspond to the phase with spontaneous symmetry breaking of the reduced theory, (b) there exist solutions with compact time-like extra-dimensions, (c) one of the solutions leads to enlargement of the initial symmetry group of the metric of the internal space.

Spontaneous Compactification and Dimensional Reduction

Abstract A connection between dimensional reduction and spontaneous compactification is studied. It is shown that the methods of the coset-space dimensional-reduction scheme can be effectively used for constructing solutions of multidimensional Einstein-Yang-Mills equations and for interpreting from the viewpoint of the four-dimensional theory.

Exact Renormalization Group Approach in Scalar and Fermionic Theories

The Polchinski version of the exact renormalization group equation is discussed and its applications in scalar and fermionic theories are reviewed. Relation between this approach and the standard renormalization group is studied, in particular the relation between the derivative expansion and the perturbation theory expansion is worked out in some detail.

Invariant connections on homogeneous spaces

G‐invariant metric compatible linear connections on homogeneous spaces G/H are investigated herein. For certain classes of homogeneous spaces the most general form of G‐invariant metric and torsion are found.

On the equations of spontaneous compactification for Gauss-Bonnet extended Einstein-Cartan theory

Abstract We show for a broad class of homogeneous spaces that the equations of spontaneous compactification for Gauss-Bonnet extended Einstein-Cartan theory are equivalent to the system of equations obtained by the dimensional reduction procedure.

Instanton propagator and instanton induced processes in scalar model

The propagator in the instanton background in the

Metric space as a model of spacetime: Classical theory and quantization

(- \lambda \phi^{4})