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

Shape of Deconstruction

We construct a six-dimensional Maxwell theory using a latticized extra space, the continuum limit of which is a shifted torus recently discussed by Dienes. This toy model exhibits the correspondence between continuum theory and discrete theory, and give a geometrical insight to theory-space model building.Comment: 10 pages, 2 figures, RevTeX4. a citation adde

Cosmological Phase Transitions and Radius Stabilization in Higher Dimensions

Recently there has been considerable interest in field theories and string theories with large extra spacetime dimensions. In this paper, we explore the role of such extra dimensions for cosmology, focusing on cosmological phase transitions in field theory and the Hagedorn transition and radius stabilization in string theory. In each case, we find that significant distinctions emerge from the usual case in which such large extra dimensions are absent. For example, for temperatures larger than the scale of the compactification radii, we show that the critical temperature above which symmetry restoration occurs is reduced relative to the usual four-dimensional case, and consequently cosmological phase transitions in extra dimensions are delayed. Furthermore, we argue that if phase transitions do occur at temperatures larger than the compactification scale, then they cannot be of first-order type. Extending our analysis to string theories with large internal dimensions, we focus on the Hagedorn transition and the new features that arise due to the presence of large internal dimensions. We also consider the role of thermal effects in establishing a potential for the radius of the compactified dimension, and we use this to propose a thermal mechanism for generating and stabilizing a large radius of compactification.Comment: 37 pages, LaTeX, 5 figure

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

QCD strings and the thermodynamics of the metastable phase of QCD at large NcN_c

The thermodyanmics of a metastable hadronic phase of QCD at large $N_C$ are related to properties of an effective QCD string. In particular, it is shown that in the large $N_c$ limit and near the maximum hadronic temperature, $T_H$, the energy density and pressure of the metastable phase scale as ${\cal E} \sim (T_H-T)^{-(D_\perp-6)/2}$ (for $D_\perp <6$) and $P \sim (T_H-T)^{-(D_\perp-4)/2}$ (for $D_\perp <4$) where $D_\perp$ is the effective number of transverse dimensions of the string theory. It is shown, however, that for the thermodynamic quantities of interest the limits $T \to T_H$ and $N_c \to \infty$ do not commute. The prospect of extracting $D_\perp$ via lattice simulations of the metastable hadronic phase at moderately large $N_c$ is discussed.Comment: After this paper was published, the author became aware of an important early paper by Charles Thorn on the subject of the QCD phase transition at large N_c and its relation to the Hagedorn spectrum. Given the pioneering nature of Thorn's paper, and the fact that it is not as widely known as it should be, it is important to cite it in the present work. This updated version cites Thorn's wor

Ultraviolet dependence of Kaluza-Klein effects on electroweak observables

In extensions of the standard model (SM) with d extra dimensions at the TeV scale the virtual exchange of Kaluza-Klein (KK) excitations of the gauge bosons gives contributions that change the SM relations between electroweak observables. These corrections are finite only for d=1; for d\ge 2 the infinite tower of KK modes gives a divergent contribution that has to be regularized introducing a cutoff (the string scale). However, the ultraviolet dependence of the KK effects is completely different if the running of the couplings with the scale is taken into account. We find that for larger d the number of excitations at each KK level increases, but their larger number is compensated by the smaller value of the gauge coupling at that scale. As a result, for any number of extra dimensions the exchange of the complete KK tower always gives a finite contribution. We show that (i) for d=1 the running of the gauge coupling decreases an 14% the effect of the KK modes on electroweak observables; (ii) in all cases more than 90% of the total effect comes from the excitations in the seven lowest KK levels and is then independent of ultraviolet physics.Comment: 8 pages, to appear in Phys. Rev.

Ultraviolet sensitivity of rare decays in nonuniversal extra dimensional models

We consider a nonuniversal five dimensional model in which fermions are localised on a four dimensional brane, while gauge bosons and a scalar doublet can travel in the bulk. As a result of KK number non-conservation at the brane-bulk intersection, the ultraviolet divergence does not cancel out in some physical observables. For example, the $B_d \to l^+l^-$ decay amplitude is linearly divergent, while $B$--$\bar{B}$ mixing amplitude is log divergent. We attempt to identify the exact source of this nonrenormalizability. We compare and contrast our results with those obtained in the universal five dimensional model where all particles travel in the extra dimension.Comment: Latex, 11 pages, uses axodraw.st

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

Topology in the Bulk: Gauge Field Solitons in Extra Dimensions

Certain static soliton configurations of gauge fields in 4+1 dimensions correspond to the instanton in 4-Euclidean dimensions ``turned on its side,'' becoming a monopole in 4+1. The periodic instanton solution can be used with the method of images to construct solutions satisfying D-brane boundary conditions. The $\theta$-term on the brane becomes a topological current source, yielding an emission amplitude for monopoles into the bulk. Instantons have a novel reinterpretation in terms of monopole exchange between branes.Comment: 23 pages, 4 figure