Solving the hierarchy problem with noncompact extra dimensions

We show that gravitational effects of global cosmic 3-branes can be responsible for compactification from six to four space-time dimensions, naturally producing the observed hierarchy between electroweak and gravitational forces. The finite radius of the transverse dimensions follows from Einstein's equation, and is exponentially large compared with the scales associated with the 3-brane. The space-time ends on a mild naked singularity at the boundary of the transverse dimensions; nevertheless unitary boundary conditions render the singularity harmless.     

The Benney hierarchy and the Dirichlet boundary problem in two dimensions

A theoretical connection between reductions of the Benney hierarchy and the Dirichlet problem for Laplace's equation in the plane is made. The connection is used to deduce general formulas for the uniformizations of two spectral functions associated with N-parameter reductions of the hierarchy. Two types of reduction are considered: one type has been considered by previous authors using alternative arguments, the second type is new. The formulas are general and are expressed in terms of the modified Green's function (for Laplace's equation) in arbitrary N-connected, reflectionally-symmetric, planar domains. The Benney moments are found to be purely geometrical quantities associated with these domains.     

The evaluation map in field theory,sigma-models and strings I

The rôle of the evaluation map in anomaly calculations for field theory, sigma-models and strings is investigated. In this paper, anomalies in field theory (with and without a backgrounds connection), are obtained as pull-backs of suitable forms via evaluation maps. The cohomology of the group of gauge transformations is computed in terms of the cohomology of the base manifold and of the cohomology of the structure group. This allows us to clarify the different topological significance of gauge and gravitational anomalies. The relation between locality and universality is discussed and local cohomology is linked to the cohomology of classifying spaces. The problem of combining the locality requirement and the index theorem approach to anomalies is also examined. Anomaly cancellation in field theories derived from superstrings is analyzed and the relevant geometrical constraints are discussed.On leave of absence from Dipartimento di Fisica dell'Universitá di Padova and Istituto Nazionale di Fisica Nucleare, Sezione di PadovaWork supported in part by: Ministero Pubblica Istruzione (research project on Geometry and Physics)On leave of absence from Department of Mathematics, University of North Carolina, Chapel Hill, N.C. 27514. Work supported in part by N.S.F.     

Minimal supersymmetric Higgs bosons with extra dimensions as the source of reheating and all matter

We consider the possibility that the dark energy responsible for inflation is deposited into extra dimensions outside of our observable Universe. Reheating and all matter can then be obtained from the minimal supersymmetric standard model flat direction condensate involving the Higgs bosons Hu and Hd, which acquires large amplitude by virtue of quantum fluctuations during inflation. The reheat temperature is TRH < or = 10(9) GeV so that there is no gravitino problem. We find a spectral index ns 1 with a very weak dependence on the Higgs potential.     

Compact hyperbolic extra dimensions: branes, kaluza-klein modes, and cosmology

We reconsider theories with low gravitational (or string) scale M(*) where Newton's constant is generated via new large-volume spatial dimensions, while standard model states are localized to a 3-brane. Utilizing compact hyperbolic manifolds we show that the spectrum of Kaluza-Klein modes is radically altered. This allows the early Universe to evolve normally up to substantial temperatures, and completely negates the astrophysical constraints on M(*). Furthermore, an exponential hierarchy between the usual Planck scale and the true fundamental scale of physics can emerge with only O(1) coefficients. The linear size of the internal space remains small. The proposal has striking testable signatures.     

A discrete velocity model of a gas: Global in time solutions of the BBGKY hierarchy

In the present paper we study the evolution of a system of hard disks moving in the plane with a finite number of velocities as in the framework of a discrete velocity model of the Enskog equation, proposed in previous papers. Starting from the BBGKY hierarchy of such a system we give existence and uniqueness results for the initial value problem in suitable Banach spaces. In particular, the main result presented is the global in time weak solution to the BBGKY hierarchy for local equilibrium initial data, in the thermodynamic limit.     

A system of strings and springs in three dimensions

A three-dimensional array of classical strings and springs oscillating in three dimensions is investigated with combined analytical-numerical tools. The strings are continuous and linear. The long time behavior of the system changes dramatically when the springs are changed from linear to non-linear. The equipartition of energy, even among the particles, is badly violated. The power spectrum is consistent with chaotic motion. The maximal Lyapunov exponent is vanishing within our approximation. The most remarkable finding is a certain pairing of time averages for the particles, which occurs for many initial conditions in the non-linear case.     

The hierarchy problem in the scalar triplet model

We investigate the possibility of maintaining the hierarchy of the gauge and lepton number symmetry breakdown in the context of the Gelmini-Roncadelli model of electroweak interactions. Calculating the effective potential in the one-loop approximation, we find the additional constraints one must impose on the scalar self-couplings to protect the tree level hierarchy from dangerous radiative corrections.     

Supersymmetric large extra dimensions and the cosmological constant: an update

This article critically reviews the proposal for addressing the cosmological constant problem within the framework of supersymmetric large extra dimensions (SLED), as recently proposed in hep-th/0304256. After a brief restatement of the cosmological constant problem, a short summary of the proposed mechanism is given. The emphasis is on the perspective of the low-energy effective theory in order to see how it addresses the problem of why low-energy particles like the electron do not contribute too large a vacuum energy. This is followed by a discussion of the main objections, which are grouped into the following five topics: (1) Weinberg’s No-Go Theorem. (2) Are hidden tunings of the theory required, and are these stable under renormalization? (3) Why should the mechanism apply only now and not rule out possible earlier epochs of inflationary dynamics? (4) How big are quantum effects, and which are the most dangerous? and (5) Even if successful, can the mechanism be consistent with cosmological or current observational constraints? It is argued that there are plausible reasons why the mechanism can thread the potential objections, but that a definitive proof that it does depends on addressing well-defined technical points. These points include identifying what fixes the size of the extra dimensions, checking how topological obstructions renormalize and performing specific calculations of quantum corrections. More detailed studies of these issues, which are well within reach of our present understanding of extra-dimensional theories, are currently underway. As such, the jury remains out concerning the proposal, although the prospects for acquittal still seem good. (An abridged version of this article appears in the proceedings of SUSY 2003.)     

Gravitating global monopoles in extra dimensions and the braneworld concept

Multidimensional configurations with a Minkowski external spacetime and a spherically symmetric global monopole in extra dimensions are discussed in the context of the braneworld concept. The monopole is formed with a hedgehoglike set of scalar fields φⁱ with a symmetry-breaking potential V depending on the magnitude φ² = φⁱφⁱ. All possible kinds of globally regular configurations are singled out without specifying the shape of V(φ). These variants are governed by the maximum value φ_m of the scalar field, characterizing the energy scale of symmetry breaking. If φ_m < φ_cr (where φ_cr is a critical value of φ related to the multidimensional Planck scale), the monopole reaches infinite radii, whereas in the “strong field regime,” when φ_m ≥ φ_cr, the monopole may end with a finite-radius cylinder or have two regular centers. The warp factors of monopoles with both infinite and finite radii may either exponentially grow or tend to finite constant values far from the center. All such configurations are shown to be able to trap test scalar matter, in striking contrast to RS2 type five-dimensional models. The monopole structures obtained analytically are also found numerically for the Mexican hat potential with an additional parameter acting as a cosmological constant.     

Superluminal neutrinos and extra dimensions: Constraints from the null energy condition

In light of the recent results from the OPERA Collaboration, indicating that neutrinos can travel superluminally, I review a simple extra-dimensional strategy for accommodating such behavior; and I also explain why it is hard in this strategy to avoid violating the null energy condition somewhere in the extra dimensions.     

Stabilization of extra dimensions and the dimensionality of the observed space

We present a simple model for the late time stabilization of extra dimensions. The basic idea is that brane solutions wrapped around extra dimensions, which is allowed by string theory, will resist expansion due to their winding mode. The momentum modes in principle work in the opposite way. It is this interplay that leads to dynamical stabilization. We use the idea of democratic wrapping, where in a given decimation of extra dimensions, all possible winding cases are considered. To further simplify the study we assumed a symmetric decimation in which the total number of extra dimensions is taken to be Np where N can be called the order of the decimation. We also assumed that extra dimensions all have the topology of tori. We show that with these rather conservative assumptions, there exist solutions to the field equations in which the extra dimensions are stabilized and that the conditions do not depend on p. This fact means that there exists at least one solution to the asymmetric decimation case. If we denote the number of observed space dimensions (excluding time) by m, the condition for stabilization is m≥3 for pure Einstein gravity and m≤3 for dilaton gravity massaged by a string theory parameter, namely the dilaton coupling to branes. PACS 98.80.-k; 11.25.Uv     

The asymptotic behavior of Casimir force in the presence of compactified universal extra dimensions

The Casimir effect for parallel plates in the presence of compactified universal extra dimensions within the frame of Kaluza–Klein theory is analyzed. Having regularized and discussed the expressions of Casimir force in the limit, we show that the nature of Casimir force is repulsive if the distance between the plates is large enough and the higher-dimensional spacetime is, the greater the value of repulsive Casimir force between plates is. The repulsive nature of the force is not consistent with the experimental phenomena.     

The Casimir force on a piston in the spacetime with extra compactified dimensions

A Casimir piston for massless scalar fields obeying Dirichlet boundary conditions in high-dimensional spacetimes within the frame of Kaluza–Klein theory is analyzed. We derive and calculate the exact expression for the Casimir force on the piston. We also compute the Casimir force in the limit that one outer plate is moved to the extremely distant place to show that the reduced force is associated with the properties of additional spatial dimensions. The more dimensionality the spacetime has, the stronger the extra-dimension influence is. The Casimir force for the piston in the model including a third plate under the background with extra compactified dimensions always keeps attractive. Further we find that when the limit is taken the Casimir force between one plate and the piston will change to be the same form as the corresponding force for the standard system consisting of two parallel plates in the four-dimensional spacetimes if the ratio of the plate-piston distance and extra dimensions size is large enough.     

Model-independent Veltman condition,naturalness and the little hierarchy problem

We adopt a bottom-up Effective Field Theory(EFT)approach to derive a model-independent Veltman condition to cancel out the quadratic divergences in the Higgs mass.We show using the equivalence theorem that all the deviations in the Higgs couplings to the W and Z from the SM predictions should vanish.We argue based on tree-level unitarity that any new physics that naturally cancels out the quadratic divergences should be ≤19 TeV.We show that the level of fine-tuning required is unless the O(0:1%-1%) UV sector has a symmetry that forces the satisfaction of the model-independent Veltman condition,in which case all fine-tuning is eliminated.We also conjecture that,if no new physics that couples to the Higgs is observed up to~19 TeV,or if the Higgs couplings to the SM particles conform to the SM predictions,then the Higgs either does not couple to any UV sector or is fine-tuned.     

SuperB production,matter stability and gauge hierarchy in SUSY GUTs

We analyze the connections between the problems of the cosmological baryon asymmetry (CBA), matter stability and mass hierarchy in supersymmetric Grand Unified models. We show that the typical delay of the phase transition in supersymmetric theories as well as a natural solution to the triplet-doublet Higgs hierarchy problem imply baryon production after the Grand Unification phase transition which in a wide class of SUSY GUTs takes place atT～10⁹–10¹⁰ GeV. Light Higgs colour triplets as a means of producing the CBA are discussed in detail. An alternative mechanism involving a singlet superfield is proposed leading to striking consequences in proton decay with the appearance of (B+L) conserving modes with a muon and a kaon in the final state:n→μ^? K ⁺,p μ ^2212;π⁺ K ⁺ and a lifetime of 10³¹ years.     

The almost periodic solutions to the equations of the KdV hierarchy

The Milne equation is used as the auxiliary equation instead of the usual Schrödinger equation, when the almost periodic solutions of the KdV hierarchy are looked for. Its almost periodic solution is found for the finite band (gap) potential and its time dependence is determined in the general case, provided the potential satisfies the KdV equations. Further investigated problems are: trace formulas and their applications, the Bloch functions, conserved quantities, the Poisson brackets and the Hamiltonian system.