Potential for the slow-roll inflation, mass scale hierarchy and Dark Energy from the Type IIA supergravity

The magnetic fluxbrane solution with a strongly warped throat is studied in the Type IIA supergravity theory with co-dimension one local source which surves as $Z_{2}$-symmetric UV boundary of the throat. Overall volume of extra space is stabilized since introduction of the local source breaks the no-scale structure of the theory and evades the no-go theorem. Radion field is defined as the position of UV boundary "moved" from its stable value fixed by the anisotropic Israel junction conditions. Analytical expression for the radion effective potential is received. Potential decreases exponentially (exponent is equal to 0,21 in Planck units) in the slow-roll region and apparently meets other demands of the early inflation. Reissner-Nordstrom type deformation of the elementary fluxbrane solution permits to construct the IR end of the throat and results in tiny positive non-zero value of the radion potential in its extremal point seen today as Dark Energy $\rho_{D.E.}$. Expressions for the mass scale hierarchy and for the "acceleration hierarchy" received in the paper give the physically interesting relation between two hierarchies: $\rho_{D.E.} \sim G_{N}^{2}m^{8}$.Comment: 32 pages, Late

II. Calculation of large mass hierarchy from number of extra dimensions

The higher-dimensional generalization of Randall-Sundrum approach with additional positive curvature $n$-dimensional and Ricci-flat $m$-dimensional compuct subspaces is considered in pure gravity theory with metric of space-time and $(p+1)$-form potential as basic fields. Introduction of mass term of $(p+1)$-form potential into the action of co-dimension one brane permits to stabilize brane's position and hence to calculate the value of Planck/electroweek scales ratio. There are no ad hoc too large or too small parameters in the theory; calculated mass hierarchy strongly depends on dimensionalities $m$, $n$ of additional subspaces and its observed large value in 4 dimensions (i.e. for $p=3$) is received in particular in $D13$ ($m=1$, $n=7$) or $D16$ ($m=2$, $n=9$) space-times.Comment: 11 pages, Late

Calculation of the Observationally Small Cosmological Constant in the Model of Six-Dimensional Warped Brane-Bolt World

In the 6-dimensional model of warped compactification based on the euclidean AdS Reissner-Nordstrom metric it is possible to escape artificial 4-brane's stress-energy tensor anistropy necessary for fulfillment of Israel junction conditions by introducing in 3+1 spacetime of the cosmological constant which turns out to be ${}\sim G^2$ ($G$ - Newton's constant) and acquires the value compatible with observations.Comment: 8 pages, LaTeX-2

Higgs mechanism from fluxes and two mass hierarchies in the "fat" throat solution of Type IIA supegravity

Spectra of Kaluza-Klein gauge fields are calculated at the background of the magnetic fluxbrane throat-like solution of the Type IIA supergravity equations. Magnetic flux plays the role of Higgs scalar generating the electroweak scale mass of non-abelian KK gauge field. The same "flux-Higgs" mechanism gives the scale of the "second mass hierarchy", 0.001 eV, in the spectrum of KK excitations at the background of the throat deformed in a Reissner-Nordstrom way. Gauge coupling constants in 4 dimensions are calculated; they prove to be of the physically sensible values for the EW scale massive modes of the gauge fields and are extremely small for the long range gauge fields. 5D effective Action with the flux-generated mass terms of the KK gauge fields associated with isometries of compactified subspaces is put down, correspondence of the "classical" KK approach and dual holography approach to the low-dimensional gauge theories is discussed, and idea of Bootstrap Holography is set forth.Comment: 24 page

I. Calculation of the observed value of large mass hierarchy in modified RS model

In generalized Randall-Sundrum (RS) model with dilaton where bulk potential is generated by the antisymmetric tensor field the mass term of this field is introduced into the brane's Action. This permits to stabilize brane's position and hence to calculate the Planck/electroweek scales ratio which proves to depend non-analytically on the dilaton-antisymmetric tensor field coupling constant. The large observed number of mass hierarchy is achieved for the moderate value of this coupling constant of order 0,3. In the subsequent Paper II it is shown that the same approach in a higher dimensional theory without dilaton permits to express mass hierarchy only through number of extra dimensions.Comment: 10 pages, Late

"Old" Conformal Bootstrap in the AdS/CFT Context

The Schwinger-Dyson equations for Green functions and 3-vertexes in planar approximation used 50 years ago in the earlier theory of conformal bootstrap are written in frames of the AdS/CFT correspondence. The technique of "Wightman-Witten" diagrams is used in calculations of the bubble bulk diagrams that permitted to obtain the values of conformal dimensions of primary operators in two models of the interacting bulk scalar fields which conformal dimensions obey "extremal" relation. Simple expressions for the four-point tree "Wightman-Witten" correlators of these primary operators are obtained and spectra of corresponding Bethe-Salpeter equations are calculated.Comment: 24 page

Scalar field on AdS: quantum one loop "in one line"

It is shown that quantum one-loop potentials of the bulk fields in the Randall and Sundrum (RS) model may be immediately expressed in integrals with use of Barvinsky-Nesterov or equivalently Gelfand-Yaglom methods of calculation of quantum determinants. Simple expression is obtained for the UV-finite difference of one-loop quantum energies for two arbitrary values of parameter of the double-trace asymptotic boundary condition in one-brane and two-brane RS-models. Compact formula for Schwinger-DeWitt expansion gives values of induced Planck mass and induced gauge coupling constant in transverse space. S-DW expansion is plagued by IR-divergences in one-brane RS-model and makes sense in two-brane model.Comment: 19 pages, Report at the Ginzburg Centennial Conference, Lebedev Institute, Moscow, 29 May - 03 June 201

Sakharov's induced gravity on the AdS background: SM scale as inverse mass parameter of the Schwinger-DeWitt expansion

One loop quantum effective action W of scalar field 'living' on the AdS background of the Randall-Sundrum model is defined here by now popular way which excludes bulk UV divergencies; thus induced Planck mass is given not by the UV regularization parameter, like in Sakharov's pioneer work, but by the location of the UV-cut of AdS space. Resummation of Schwinger-DeWitt expansion of the action W is performed by the novel 'auxiliary mass' method. The inverse mass squared parameter of this expansion is determined by the location of the 'visible' IR-brane of the RS-model. Obtained expression for induced vacuum energy density coincides with the independently calculated VEV of the stress-energy tensor. Corresponding potential in 4 dimensions possesses a non-trivial extremum which hopefully will permit us to stabilize IR brane and hence to fix the observed small value of mass hierarchy in analogy with the Coleman-Weinberg mechanism. It is demonstrated that naive equating of values of the induced Planck mass and vacuum energy density to those of the RS-model determines otherwise arbitrary constants of the model. A principle of quantum self-consistency generalizing this approach is proposed.Comment: 26 pages, Latex; Contents and Section 5.4 adde

String theory provides landmarks fixing RS branes' positions: Possibility to deduce large mass hierarchy from small numbers

Two-branes RS-I 5-dimensional model is generalized in higher dimensional string-induced theory with dilaton and $n$-form field. It is supposed that "hidden" and "visible" Randall-Sundrum branes are located at the boundaries of region of space-time where low-energy supergravity description is valid. This permits to determine mass scale hierarchy which calculated value proves to be strongly dependent on dimensionalities of subspaces.Comment: 12 pages, Late

Mach's Principle selects 4 space-time dimensions

Bi-tensor kernel in integral form of Einstein equations realizing Mach's idea of non-existence of empty space-times is taken as an inverse of differential operator ("Mach operator") defined conventionally as a second variation of Einstein's gravity Action over contravariant components of metric tensor. The choice of transverse gauge condition used in this definition does not influence results of the paper since only transverse and traceless tensor modes written on different background space-times are studied. Presence of ghosts among modes of Mach operator invalidates the integral formulation of Einstein equations. And the demand of absence of these ghosts proves to be a selection rule for dimensionality of the background space-time. In particular Mach operator written on De Sitter background or on the background of so called "Einstein Universe" does not possess tensor ghosts only in 4-dimensions. The similar demand gives non-trivial formula for dimensionalities of subspaces of the Freund-Rubin background.Comment: 15 page