Kaluza-Klein States versus Winding States: Can Both Be Above the String Scale?

When closed strings propagate in extra compactified dimensions, a rich spectrum of Kaluza-Klein states and winding states emerges. Since the masses of Kaluza-Klein states and winding states play a reciprocal role, it is often believed that either the lightest Kaluza-Klein states or the lightest winding states must be at or below the string scale. In this paper, we demonstrate that this conclusion is no longer true for compactifications with non-trivial shape moduli. Specifically, we demonstrate that toroidal compactifications exist for which all Kaluza-Klein states as well as all winding states are heavier than the string scale. This observation could have important phenomenological implications for theories with reduced string scales, suggesting that it is possible to cross the string scale without detecting any states associated with spacetime compactification.Comment: 8 pages, LaTeX, no figure

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

Adventures in Thermal Duality (II): Towards a Duality-Covariant String Thermodynamics

In a recent companion paper, we observed that the rules of ordinary thermodynamics generally fail to respect thermal duality, a symmetry of string theory under which the physics at temperature T is related to the physics at the inverse temperature 1/T. Even when the free energy and internal energy exhibit the thermal duality symmetry, the entropy and specific heat are defined in such a way that this symmetry is destroyed. In this paper, we propose a modification of the traditional definitions of these quantities, yielding a manifestly duality-covariant thermodynamics. At low temperatures, these modifications produce "corrections" to the standard definitions of entropy and specific heat which are suppressed by powers of the string scale. These corrections may nevertheless be important for the full development of a consistent string thermodynamics. We find, for example, that the string-corrected entropy can be smaller than the usual entropy at high temperatures, suggesting a possible connection with the holographic principle. We also discuss some outstanding theoretical issues prompted by our approach.Comment: 31 pages, 6 figures, 1 conversatio

Comment on ``Inflation and flat directions in modular invariant superstring effective theories''

The inflation model of Gaillard, Lyth and Murayama is revisited, with a systematic scan of the parameter space for dilaton stabilization during inflation.Comment: 7 pages, 2 figure

Inference of crack statistics from observations on an outcropping

It is difficult to examine the cracks in a three-dimensional body; one is usually limited to observations on an outcropping, a cut, or a plane obtained by sectioning a sample. This paper considers two problems. The direct problem is to find the distribution of line segments in a plane section when the three-dimensional distribution of cracks is homogeneous, isotropic, and exponential. This distribution can be expressed in closed form by means of Hankel functions. It is shown that the distribution in a plane section is qualitatively different from the three-dimensional distribution in having a peak for a finite value of segment length, i.e., there is a most probable (non-zero) segment length. It is also concluded that the mean segment size in the plane is ..pi../2 times the mean crack diameter in three dimensions. This result is consistent with the well-known observation that small cracks have a lower probability of being intercepted by a plane than larger cracks. The number density of line segments is finally expressed in terms of the Hankel function of order zero. The indirect problem is to infer the three-dimensional distribution of cracks from the distribution on a section, which could be, for example, an outcropping. This problem is solved by deriving an integral equation relating the three-dimensional distribution of cracks and the distribution of line segments in a plane, and showing that it can be solved for an arbitrary distribution of segments on the out-cropping. The special case of the Hankel distribution leads to the exponential distribution in three dimensions; thus, thesolution method is verified. 3 figures

Effect of finite rotation on a problem in plastic deformation

The development of constitutive laws for large-strain plastic flow requires both an appropriate kinematic framework to characterize the deformation and a suitable set of physical relations between the selected measures of stress and strain rate. In this paper it is argued that deformation is best characterized by taking, as the measure of strain rate, the stretching (the symmetric part of the velocity gradient) and assuming that it can be represented as the sum of an elastic and plastic part. Though this is a natural extension (or perhaps only a restatement) of the 1930 hypothesis of Reuss, its consequences differ from some more recent hypotheses based on modern theories of deformation. Since plastic flow laws are expressed in rate form it is necessary to have a suitable definition of stress rate. Though this has has been a subject of much analysis and numerous hypotheses, Dienes has shown that a unique stress rate follows from the necessity of formulating the constitutive law in material axes, and that such a stress rate is frame invariant. The same paper shows the relation of rate of angular velocity (material rotation rate), deformation and spin (vorticity). In this paper this formulation is used in expressing constitutive relations for plastic flow, including both ideal plasticity and kinematic hardening, and the results are compared with those obtained using the Zaremba-Jaumann-Noll approximation. 24 references

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.

Effects of Extra Space-time Dimensions on the Fermi Constant

Effects of Kaluza-Klein excitations associated with extra dimensions with large radius compactifications on the Fermi constant are explored. It is shown that the current precision determinations of the Fermi constant, of the fine structure constant, and of the W and Z mass put stringent constraints on the compactification radius. The analysis excludes one extra space time dimension below $\sim 1.6$ TeV, and excludes 2, 3 and 4 extra space dimensions opening simultaneously below $\sim$ 3.5 TeV, 5.7 TeV and 7.8 TeV at the $90$. Implications of these results for future collider experiments are discussed.Comment: 12 pages including one figur

Multiple-shock initiation via statistical crack mechanics

Statistical Crack Mechanics (SCRAM) is a theoretical approach to the behavior of brittle materials that accounts for the behavior of an ensemble of microcracks, including their opening, shear, growth, and coalescence. Mechanical parameters are based on measured strain-softening behavior. In applications to explosive and propellant sensitivity it is assumed that closed cracks act as hot spots, and that the heating due to interfacial friction initiates reactions which are modeled as one-dimensional heat flow with an Arrhenius source term, and computed in a subscale grid. Post-ignition behavior of hot spots is treated with the burn model of Ward, Son and Brewster. Numerical calculations using SCRAM-HYDROX are compared with the multiple-shock experiments of Mulford et al. in which the particle velocity in PBX 9501 is measured with embedded wires, and reactions are initiated and quenched

Phenomenology of Noncommutative Field Theories

Experimental limits on the violation of four-dimensional Lorentz invariance imply that noncommutativity among ordinary spacetime dimensions must be small. In this talk, I review the most stringent bounds on noncommutative field theories and suggest a possible means of evading them: noncommutativity may be restricted to extra, compactified spatial dimensions. Such theories have a number of interesting features, including Abelian gauge fields whose Kaluza-Klein excitations have self couplings. We consider six-dimensional QED in a noncommutative bulk, and discuss the collider signatures of the model.Comment: 7 pages RevTeX, 4 eps figures, Invited plenary talk, IX Mexican Workshop on Particles and Fields, November 17-22, 2003, Universidad de Colima, Mexic