Stabilization of Sub-Millimeter Dimensions: The New Guise of the Hierarchy Problem

A new framework for solving the hierarchy problem was recently proposed which does not rely on low energy supersymmetry or technicolor. The fundamental Planck mass is at a \tev and the observed weakness of gravity at long distances is due the existence of new sub-millimeter spatial dimensions. In this picture the standard model fields are localized to a $(3+1)$-dimensional wall or ``3-brane''. The hierarchy problem becomes isomorphic to the problem of the largeness of the extra dimensions. This is in turn inextricably linked to the cosmological constant problem, suggesting the possibility of a common solution. The radii of the extra dimensions must be prevented from both expanding to too great a size, and collapsing to the fundamental Planck length \tev^{-1}. In this paper we propose a number of mechanisms addressing this question. We argue that a positive bulk cosmological constant $\bar\Lambda$ can stabilize the internal manifold against expansion, and that the value of $\bar\Lambda$ is not unstable to radiative corrections provided that the supersymmetries of string theory are broken by dynamics on our 3-brane. We further argue that the extra dimensions can be stabilized against collapse in a phenomenologically successful way by either of two methods: 1) Large, topologically conserved quantum numbers associated with higher-form bulk U(1) gauge fields, such as the naturally occurring Ramond-Ramond gauge fields, or the winding number of bulk scalar fields. 2) The brane-lattice-crystallization of a large number of 3-branes in the bulk. These mechanisms are consistent with theoretical, laboratory, and cosmological considerations such as the absence of large time variations in Newton's constant during and after primordial nucleosynthesis, and millimeter-scale tests of gravity.Comment: Corrected referencing to important earlier work by Sundrum, errors fixed, additional discussion on radion phenomenology, conclusions unchanged, 23 pages, LaTe

On Effective Theory of Brane World with Small Tension

The five dimensional theory compactified on $S^1$ with two ``branes'' (two domain walls) embedded in it is constructed, based on the field-theoretic mechanism to generate the ``brane''. Some light states localized in the ``brane'' appear in the theory. One is the Nambu-Goldstone boson, which corresponds to the breaking of the translational invariance in the transverse direction of the ``brane''. In addition, if the tension of the ``brane'' is smaller than the fundamental scale of the original theory, it is found that there may exist not only massless states but also some massive states lighter than the fundamental scale in the ``brane''. We analyze the four dimensional effective theory by integrating out the freedom of the fifth dimension. We show that some effective couplings can be explicitly calculated. As one of our results, some effective couplings of the state localized in the ``brane'' to the higher Kaluza-Klein modes in the bulk are found to be suppressed by the width of the ``brane''. The resultant suppression factor can be quantitatively different from the one analyzed by Bando et al. using the Nambu-Goto action, while they are qualitatively the same.Comment: 17 pages, uses REVTEX macr

Statistics in the Landscape of Intersecting Brane Models

An approach towards a statistical survey of four dimensional supersymmetric vacua in the string theory landscape is described and illustrated with three examples of ensembles of intersecting D-brane models. The question whether it is conceivable to make predictions based on statistical distributions is discussed. Especially interesting in this context are possible correlations between low energy observables. As an example we look at correlations between properties of the gauge sector of intersecting D-brane models and Gepner model constructions.Comment: Submitted for the SUSY07 proceedings, 4 pages, 2 figure

Search for solar Kaluza-Klein axions in theories of low-scale quantum gravity

We explore the physics potential of a terrestrial detector for observing axionic Kaluza-Klein excitations coming from the Sun within the context of higher-dimensional theories of low-scale quantum gravity. In these theories, the heavier Kaluza-Klein axions are relatively short-lived and may be detected by a coincidental triggering of their two-photon decay mode. Because of the expected high multiplicity of the solar axionic excitations, we find experimental sensitivity to a fundamental Peccei-Quinn axion mass up to $10^{-2}$ eV (corresponding to an effective axion-photon coupling $g_{a\gamma \gamma} \approx 2.\times 10^{-12}$ GeV$^{-1}$) in theories with 2 extra dimensions and a fundamental quantum-gravity scale $M_{\rm F}$ of order 100 TeV, and up to $3.\times 10^{-3}$ eV (corresponding to $g_{a\gamma \gamma} \approx 6.\times 10^{-13}$ GeV$^{-1}$) in theories with 3 extra dimensions and $M_{\rm F}=1$ TeV. For comparison, based on recent data obtained from lowest level underground experiments, we derive the experimental limits: $g_{a \gamma \gamma} \stackrel{<}{{}_\sim} 2.5\times 10^{-11}$ GeV$^{-1}$ and $g_{a \gamma \gamma} \stackrel{<}{{}_\sim} 1.2\times 10^{-11}$ GeV$^{-1}$ in the aforementioned theories with 2 and 3 large compact dimensions, respectively.Comment: 19 pages, extended version, as to appear in Physical Review

Neutrino Masses from Large Extra Dimensions

Recently it was proposed that the standard model (SM) degrees of freedom reside on a $(3+1)$-dimensional wall or ``3-brane'' embedded in a higher-dimensional spacetime. Furthermore, in this picture it is possible for the fundamental Planck mass \mst to be as small as the weak scale \mst\simeq O(\tev) and the observed weakness of gravity at long distances is due the existence of new sub-millimeter spatial dimensions. We show that in this picture it is natural to expect neutrino masses to occur in the 10^{-1} - 10^{-4}\ev range, despite the lack of any fundamental scale higher than \mst. Such suppressed neutrino masses are not the result of a see-saw, but have intrinsically higher-dimensional explanations. We explore two possibilities. The first mechanism identifies any massless bulk fermions as right-handed neutrinos. These give naturally small Dirac masses for the same reason that gravity is weak at long distances in this framework. The second mechanism takes advantage of the large {\it infrared} desert: the space in the extra dimensions. Here, small Majorana neutrino masses are generated by breaking lepton number on distant branes.Comment: 17 pages, late

Invisible Axions and Large-Radius Compactifications

We study some of the novel effects that arise when the QCD axion is placed in the ``bulk'' of large extra spacetime dimensions. First, we find that the mass of the axion can become independent of the energy scale associated with the breaking of the Peccei-Quinn symmetry. This implies that the mass of the axion can be adjusted independently of its couplings to ordinary matter, thereby providing a new method of rendering the axion invisible. Second, we discuss the new phenomenon of laboratory axion oscillations (analogous to neutrino oscillations), and show that these oscillations cause laboratory axions to ``decohere'' extremely rapidly as a result of Kaluza-Klein mixing. This decoherence may also be a contributing factor to axion invisibility. Third, we discuss the role of Kaluza-Klein axions in axion-mediated processes and decays, and propose several experimental tests of the higher-dimensional nature of the axion. Finally, we show that under certain circumstances, the presence of an infinite tower of Kaluza-Klein axion modes can significantly accelerate the dissipation of the energy associated with cosmological relic axion oscillations, thereby enabling the Peccei-Quinn symmetry-breaking scale to exceed the usual four-dimensional relic oscillation bounds. Together, these ideas therefore provide new ways of obtaining an ``invisible'' axion within the context of higher-dimensional theories with large-radius compactifications.Comment: 43 pages, LaTeX, 6 figure

Large Mixing Induced by the Strong Coupling with a Single Bulk Neutrinos

Neutrino is a good probe of extra dimensions. Large mixing and the apparent lack of very complicated oscillation patterns may be an indication of large couplings between the brane and a single bulk neutrino. A simple and realistic five-dimensional model of this kind is discussed. It requires a sterile in addition to three active neutrinos on the brane, all coupled strongly to one common bulk neutrino, but not directly among themselves. Mindful that sterile neutrinos are disfavored in the atmospheric and solar data, we demand induced mixing to occur among the active neutrinos, but not between the active and the sterile. The size $R$ of the extra dimension is arbitrary in this model, otherwise it contains six parameters which can be used to fit the three neutrino masses and the three mixing angles. However, in the model those six parameters must be suitably ordered, so a successful fit is not guaranteed. It turns out that not only the data can be fitted, but as a result of the ordering, a natural connection between the smallness of the reactor angle $\theta_{13}$ and the smallness of the mass-gap ratio $\Delta M^2_{solar}/\Delta M^2_{atmospheric}$ can be derived.Comment: Misprints above eq. (22) corrected. To appear in PR

Fractal Theory Space: Spacetime of Noninteger Dimensionality

We construct matter field theories in ``theory space'' that are fractal, and invariant under geometrical renormalization group (RG) transformations. We treat in detail complex scalars, and discuss issues related to fermions, chirality, and Yang-Mills gauge fields. In the continuum limit these models describe physics in a noninteger spatial dimension which appears above a RG invariant ``compactification scale,'' M. The energy distribution of KK modes above M is controlled by an exponent in a scaling relation of the vacuum energy (Coleman-Weinberg potential), and corresponds to the dimensionality. For truncated-s-simplex lattices with coordination number s the spacetime dimensionality is 1+(3+2ln(s)/ln(s+2)). The computations in theory space involve subtleties, owing to the 1+3 kinetic terms, yet the resulting dimensionalites are equivalent to thermal spin systems. Physical implications are discussed.Comment: 28 pages, 6 figures; Paper has been amplified with a more detailed discussion of a number of technical issue

Gauge coupling flux thresholds, exotic matter and the unification scale in F-SU(5) GUT

We explore the gauge coupling relations and the unification scale in F-theory SU(5) GUT broken down to the Standard Model by an internal U(1)Y gauge flux. We consider variants with exotic matter representations which may appear in these constructions and investigate their role in the effective field theory model. We make a detailed investigation on the conditions imposed on the extraneous matter to raise the unification scale and make the color triplets heavy in order to avoid fast proton decay. We also discuss in brief the implications on the gaugino masses.Comment: 20 pages, 3 figures, references and extended comments on KK thresholds effects adde

4D-2D equivalence for large- N Yang-Mills theory

General string-theoretic considerations suggest that four-dimensional large-N gauge theories should have dual descriptions in terms of two-dimensional conformal field theories. However, for nonsupersymmetric confining theories such as pure Yang-Mills theory, a long-standing challenge has been to explicitly show that any such dual descriptions actually exist. In this paper, we consider the large-N limit of four-dimensional pure Yang-Mills theory compactified on a three-sphere in the solvable limit where the sphere radius is small compared to the strong length scale, and demonstrate that the confined-phase spectrum of this gauge theory coincides with the spectrum of an irrational two-dimensional conformal field theory