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 ($\gamma$ and Z) and their Kaluza-Klein modes in the dilepton final state $pp\to l^+l^-X$. It is shown that LHC with 100$fb^{-1}$ of luminosity can discover Kaluza-Klein modes up to compactification scales of $\approx 6$ 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 $Z_2\times Z_2, Z_3$, and $Z_6$ orbifold compactifications.Comment: 17 pages, 6 figure

Flux Compactification

We review recent work in which compactifications of string and M theory are constructed in which all scalar fields (moduli) are massive, and supersymmetry is broken with a small positive cosmological constant, features needed to reproduce real world physics. We explain how this work implies that there is a ``landscape'' of string/M theory vacua, perhaps containing many candidates for describing real world physics, and present the arguments for and against this idea. We discuss statistical surveys of the landscape, and the prospects for testable consequences of this picture, such as observable effects of moduli, constraints on early cosmology, and predictions for the scale of supersymmetry breaking.Comment: 66 pages, 3 figures, Latex with revtex4 macros. v3: version to appear in RM

Compactification of closed preordered spaces

A topological preordered space admits a Hausdorff closed preorder compactification if and only if it is Tychonoff and the preorder is represented by the family of continuous isotone functions. We construct the largest Hausdorff closed preorder compactification for these spaces and clarify its relation with Nachbin's compactification. Under local compactness the problem of the existence and identification of the smallest Hausdorff closed preorder compactification is considered.Comment: 17 pages, Latex2e. v2: fixed minor typo

A Topological Approach to Unifying Compactifications of Symmetric Spaces

In this paper we present a topological way of building a compactification of a symmetric space from a compactification of a Weyl Chamber

Shadows of the Planck Scale: The Changing Face of Compactification Geometry

By studying the effects of the shape moduli associated with toroidal compactifications, we demonstrate that Planck-sized extra dimensions can cast significant ``shadows'' over low-energy physics. These shadows can greatly distort our perceptions of the compactification geometry associated with large extra dimensions, and place a fundamental limit on our ability to probe the geometry of compactification simply by measuring Kaluza-Klein states. We also discuss the interpretation of compactification radii and hierarchies in the context of geometries with non-trivial shape moduli. One of the main results of this paper is that compactification geometry is effectively renormalized as a function of energy scale, with ``renormalization group equations'' describing the ``flow'' of geometric parameters such as compactification radii and shape angles as functions of energy.Comment: 7 pages, LaTeX, 2 figure

A compactification of outer space which is an absolute retract

We define a new compactification of outer space $CV_N$ (the \emph{Pacman compactification}) which is an absolute retract, for which the boundary is a $Z$-set. The classical compactification $\overline{CV_N}$ made of very small $F_N$-actions on $\mathbb{R}$-trees, however, fails to be locally $4$-connected as soon as $N\ge 4$. The Pacman compactification is a blow-up of $\overline{CV_N}$, obtained by assigning an orientation to every arc with nontrivial stabilizer in the trees.Comment: Final version. To appear in Annales de l'Institut Fourie

On the metric compactification of infinite-dimensional ℓp\ell_{p} spaces

The notion of metric compactification was introduced by Gromov and later rediscovered by Rieffel; and has been mainly studied on proper geodesic metric spaces. We present here a generalization of the metric compactification that can be applied to infinite-dimensional Banach spaces. Thereafter we give a complete description of the metric compactification of infinite-dimensional $\ell_{p}$ spaces for all $1\leq p < \infty$. We also give a full characterization of the metric compactification of infinite-dimensional Hilbert spaces.Comment: Minor typos corrected. References updated. Title changed. Results unchange