Igor P. Volobuev

Effective Lagrangians for physical degrees of freedom in the Randall–Sundrum model

We derive the second variation Lagrangian of the Randall–Sundrum model with two branes, study its gauge invariance and diagonalize it in the unitary gauge. We also show that the effective four-dimensional theory looks different on different branes and calculate the observable mass spectra and the couplings of the physical degrees of freedom of five-dimensional gravity to matter.

Constructing stabilized brane world models in five-dimensional Brans–Dicke theory

We consider brane world models, which can be constructed in the five-dimensional Brans–Dicke theory with bulk scalar field potentials suggested by the supergravity theory. For different choices of the potentials and parameters, we get (i) an unstabilized model with the Randall–Sundrum solution for the metric and constant solution for the scalar field; (ii) models with a flat background and tension-full branes; (iii) stabilized brane world models, one of which reproduces the Randall–Sundrum solution for the metric and gives an exponential solution for the scalar field. We also discuss the relationship between solutions in different frames, with non-minimal and minimal couplings of the scalar field.

PHYSICAL DEGREES OF FREEDOM IN STABILIZED BRANE WORLD MODELS

We consider brane world models with interbrane separation stabilized by the Goldberger–Wise scalar field. For arbitrary background, or vacuum configurations of the gravitational and scalar fields in such models, we construct the second variation Lagrangian, study its gauge invariance, find the corresponding equations of motion and decouple them in a suitable gauge. We also derive an effective four-dimensional Lagrangian for such models, which describes the massless graviton, a tower of massive gravitons and a tower of massive scalars. It is shown that for a special choice of the background solution the masses of the graviton excitations may be of the order of 1 TeV, the radion mass of the order of 100 GeV, the inverse size of the extra dimension being 1 TeV. In this case the coupling of the radion to matter on the negative tension brane is approximately ten times weaker than in the unstabilized model with the same values of the fundamental five-dimensional energy scale and the interbrane distance.

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.

On the gauge orbit space stratification: a review

First, we review the basic mathematical structures and results concerning the gauge orbit space stratification. This includes general properties of the gauge group action, fibre bundle structures induced by this action, basic properties of the stratification and the natural Riemannian structures of the strata. In the second part, we study the stratification for theories with gauge group SU(n) in spacetime dimension 4. We develop a general method for determining the orbit types and their partial ordering, based on the 1–1 correspondence between orbit types and holonomy-induced Howe subbundles of the underlying principal SU(n)-bundle. We show that the orbit types are classified by certain cohomology elements of spacetime satisfying two relations and that the partial ordering is characterized by a system of algebraic equations. Moreover, operations for generating direct successors and direct predecessors are formulated, which allow one to construct the set of orbit types, starting from the principal type. Finally, we discuss an application to nodal configurations in Yang–Mills–Chern–Simons theory.

Higgs-radion mixing in stabilized brane world models

We consider a quartic interaction of the Higgs and Goldberger-Wise fields, which connects the mechanism of the extra dimension size stabilization with spontaneous symmetry breaking on our brane and gives rise to a coupling of the Higgs field to the radion and its KK tower. We estimate a possible influence of this coupling on the Higgs-radion mixing and study restrictions on model parameters from the LHC data.

Partial ordering of gauge orbit types for SU(n) gauge theories

The natural partial ordering of the orbit types of the action of the group of local gauge transformations on the space of connections in space–time dimension d≤4 is investigated. For that purpose, a description of orbit types in terms of cohomology elements of space–time, derived earlier, is used. It is shown that on the level of these cohomology elements, the partial ordering relation is characterized by a system of algebraic equations. Moreover, operations to generate direct successors and direct predecessors are formulated. The latter allow to successively reconstruct the set of orbit types, starting from the principal type.

Classification of Gauge Orbit Types for SU(n)-Gauge Theories

A method for determining the orbit types of the action of the group of gauge transformations on the space of connections for gauge theories with gauge group SU(n) in spacetime dimension d≤4 is presented. The method is based on the one-to-one correspondence between orbit types and holonomy-induced reductions of the underlying principal SU(n)-bundle. It is shown that the orbit types are labelled by certain cohomology elements of spacetime satisfying two relations. Thus, for every principal SU(n)-bundle the corresponding stratification of the gauge orbit space can be explicitly determined. As an application, a criterion characterizing kinematical nodes for physical states in Yang–Mills theory with the Chern–Simons term proposed by Asorey et al. is discussed.