Mikhail N. Smolyakov

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.

Analytic

Explicit solutions for extended objects of a Q-ball type were found analytically in a model describing complex scalar field with piecewise parabolic potential in (3+1)- and (1+1)-dimensional space-times. Such a potential provides a variety of solutions which were thoroughly examined. It was shown that, depending on the values of the parameters of the model and according to the known stability criteria, there exist stable and unstable solutions. The classical stability of solutions in (1+1)-dimensional space-time was examined in the linear approximation and it was shown explicitly that the spectrum of linear perturbations around some solutions contains exponentially growing modes while it is not so for other solutions.

Q

In this paper, the main properties of (3+1)-dimensional

-ball solutions and their stability in a piecewise parabolic potential

U(1)

Theory of

gauged Q-balls are examined. In particular, it is shown that the relation

U(1)

\frac{dE}{dQ}=\omega

gauged Q-balls revisited

holds for such gauged Q-balls in the general case. As a consequence, it is shown that the well-known estimate for the maximal charge of stable gauged Q-balls was derived by means of an inconsistent procedure and can not be considered as correct. A simple method for obtaining the main characteristics of gauged Q-balls using only the nongauged background solution for the scalar field in the case, when the back-reaction of the gauge field on the scalar field is small and the linearized theory can be used, is proposed. The criteria of applicability of the linearized theory, which do not reduce to the demand of the smallness of the coupling constant, are established. Some interesting properties of gauged Q-balls, as well as the advantages of the proposed method, are demonstrated by the example of two models, admitting, in the linear approximation in the perturbations, exact analytic solutions for gauged Q-balls.