Type Of Compactification Research Articles

On one type of compactification of positive integers

The object of observation is a compact metric ring containing positive integers as dense subset. It is proved that this ring is isomorphic with a ring of reminder classes of polyadic integers.

A class of models with spontaneous compactification of the Freund-Rubin type and a nontrivial solution for the vector field

A theory of interacting gravity, vector, and antisymmetric third-rank tensor fields with self-consistent spontaneous compactification solutions of the Freund-Rubin type in seven-dimensional space-time is considered. A class of models is studied, which allow the same type of compactification and possess nontrivial solutions for the vector field. A subclass of the models is separated in which the four-dimensional Lorentz invariance is either unbroken or weakly broken.

BPS-like potential for compactifications of heterotic M-theory?

We analyze the possibility to rewrite the action of Horava-Witten theory in a BPS-like form, which means that it is given as a sum of squares of the supersymmetry conditions. To this end we compactify the theory on a seven dimensional manifold of SU(3) structure and rewrite the scalar curvature of the compactification manifold in terms of the SU(3) structure forms. This shows that a BPS-like form cannot be obtained in general, but only for certain types of compactifications.

Gravity waves and linear inflation from axion monodromy

Wrapped branes in string compactifications introduce a monodromy that extends the field range of individual closed-string axions to beyond the Planck scale. Furthermore, approximate shift symmetries of the system naturally control corrections to the axion potential. This suggests a general mechanism for chaotic inflation driven by monodromy-extended closed-string axions. We systematically analyze this possibility and show that the mechanism is compatible with moduli stabilization and can be realized in many types of compactifications, including warped Calabi-Yau manifolds and more general Ricci-curved spaces. In this broad class of models, the potential is linear in the canonical inflaton field, predicting a tensor to scalar ratio $r\ensuremath{\approx}0.07$ accessible to upcoming cosmic microwave background observations.

Constraints on modular inflation in supergravity and string theory

We perform a general algebraic analysis on the possibility of realising slow-roll inflation in the moduli sector of string models. This problem turns out to be very closely related to the characterisation of models admitting metastable vacua with non-negative cosmological constant. In fact, we show that the condition for the existence of viable inflationary trajectories is a deformation of the condition for the existence of metastable de Sitter vacua. This condition depends on the ratio between the scale of inflation and the gravitino mass and becomes stronger as this parameter grows. After performing a general study within arbitrary supergravity models, we analyse the implications of our results in several examples. More concretely, in the case of heterotic and orientifold string compactifications on a Calabi-Yau in the large volume limit we show that there may exist fully viable models, allowing both for inflation and stabilisation. Additionally, we show that subleading corrections breaking the no-scale property shared by these models always allow for slow-roll inflation but with an inflationary scale suppressed with respect to the gravitino scale. A scale of inflation larger than the gravitino scale can also be achieved under more restrictive circumstances and only for certain types of compactifications.

De Sitter vacua in no-scale supergravities and Calabi-Yau string models

We perform a general analysis on the possibility of obtaining metastable vacua with spontaneously broken N = 1 supersymmetry and non-negative cosmological constant in the moduli sector of string models. More specifically, we study the condition under which the scalar partners of the Goldstino are non-tachyonic, which depends only on the Kahler potential. This condition is not only necessary but also sufficient, in the sense that all of the other scalar fields can be given arbitrarily large positive square masses if the superpotential is suitably tuned. We consider both heterotic and orientifold string compactifications in the large-volume limit and show that the no-scale property shared by these models severely restricts the allowed values for the 'sGoldstino' masses in the superpotential parameter space. We find that a positive mass term may be achieved only for certain types of compactifications and specific Goldstino directions. Additionally, we show how subleading corrections to the Kahler potential which break the no-scale property may allow to lift these masses.

Pure-spinor superstrings ind= 2,4,6

We continue the study of the d=2,4,6 pure-spinor superstring models introduced in [1]. By explicitly solving the pure-spinor constraint we show that these theories have vanishing central charge and work out the (covariant) current algebra for the Lorentz currents. We argue that these super-Poincare covariant models may be thought of as compactifications of the superstring on CY_{4,3,2}, and take some steps toward making this precise by constructing a map to the RNS superstring variables. We also discuss the relation to the so called hybrid superstrings, which describe the same type of compactifications.

Curvatures and potential of M–theory inD= 4 with fluxes and twist

We give the curvatures of the free differential algebra (FDA) of M--theory compactified to D=4 on a twisted seven--torus with the 4--form flux switched on. Two formulations are given, depending on whether the 1--form field strengths of the scalar fields (originating from the 3--form gauge field $\hat{A}^{(3)}$) are included or not in the FDA. We also give the bosonic equations of motion and discuss at length the scalar potential which emerges in this type of compactifications. For flat groups we show the equivalence of this potential with a dual formulation of the theory which has the full $\rE_{7(7)}$ symmetry.

Probing the nature of compactification with Kaluza–Klein excitations at the Large Hadron Collider

It is shown that the nature of compactification of extra dimensions in theories of large radius compactification can be explored in several processes at the Large Hadron Collider (LHC). Specifically it is shown that the characteristics of the Kaluza–Klein (KK) excitations encode information on the nature of compactification, i.e., on the number of compactified dimensions as well as on the type of compactification, e.g., of the specific orbifold compactification. The most dramatic signals arise from the interference pattern involving the exchange of the Standard Model spin 1 bosons ( γ and Z) and their Kaluza–Klein modes in the dilepton final state pp→ l + l − X. It is shown that LHC with 100 fb −1 of luminosity can discover Kaluza–Klein modes up to compactification scales of ≈6 TeV as well as identify the nature of compactification. Effects of the Kaluza–Klein excitations of the W boson and of the gluon are also studied. Exhibition of these phenomena is given for the case of one extra dimension and for the case of two extra dimensions with Z 2× Z 2, Z 3, and Z 6 orbifold compactifications.

Orbifolds with Continuous Wilson Lines and Soft Terms

Orbifold compactifications with continuous Wilson lines have very interesting characteristics and as a consequence they are candidates for obtaining realistic models. We perform an analysis of the soft supersymmetry-breaking terms arising in this type of compactifications. We also compare these results with those of orbifolds without including continuous Wilson lines. Their phenomenological properties turn out to be similar.

ETERNAL CHAOTIC INFLATION

It is shown that the evolution of the universe in the chaotic inflation scenario has no end and may have no beginning. According to this scenario, the universe consists of an exponentially large number of different mini-universes inside which all possible metastable vacuum states and all possible types of compactifications are realized.

General rings of functions

Several authors have studied various types of rings of continuous functions on Tychonoff spaces and have used them to study various types of compactifications (See for example Hager (1969), Isbell (1958), Mrowka (1973), Steiner and Steiner (1970)). However many important results and properties pertaining the Stone-Čech compactification and the Hewitt realcompactification can be extended to a more general setting by considering appropriate lattices of sets, generalizing that of the lattice of zero sets in a Tychonoff space. This program was first considered by Wallman (1938) and Alexandroff (1940) and has more recently appeared in Alo and Shapiro (1970), Banachewski (1962), Brooks (1967), Frolik (1972), Sultan (to appear) and others.