We investigate the role of Casimir energy as a mechanism for brane stability in five-dimensional models with the fifth dimension compactified on an S 1 /Z Z 2 orbifold, which includes the Randall-Sundrum two brane model (RS1). We employ a ζ-function regularization technique utilizing the Schwinger proper time method and the Jacobi theta function identity to calculate the one-loop effective potential. We show that the combination of the Casimir energies of a scalar Higgs field, the three generations of Standard Model fermions and one additional massive non-SM scalar in the bulk produce a non-trivial minimum of the potential. In particular, we consider a scalar field with a coupling in the bulk to a Lorentz violating vector particle localized to the compactified dimension. Such a scalar may provide a natural means of the fine-tuning needed for stabilization of the brane spearation. Lastly, we briefly review the possibility that Casimir energy plays a role in generating the currently observed epoch of cosmological inflation by examining a simple five-dimensional anisotropic metric.
One of the challenges in connecting higher dimensional theories to cosmology is stabilization of the moduli fields. We investigate the role of a Lorentz violating vector field in the context of stabilization. Specifically, we compute the one loop Casimir energy in Randall-Sundrum 5-dimensional (nonsupersymmetric) S 1 /Z 2 orbifolds resulting from the interaction of a real scalar field with periodic boundary conditions with a Lorentz violating vector field. We find that the result is an enhanced attractive Casimir force. Hence, for stability, positive contributions to the Casimir force from branes and additional fields would be required to counter the destabilizing, attractive effect of Lorentz violating fields.
For the weakly coupled heterotic string (WCHS) there is a well-known factor of twenty conflict between the minimum string coupling unification scale, Λ H ∼ 5 × 10 17 GeV, and the projected MSSM gauge coupling unification scale, Λ U ∼ 2.5×10 16 GeV, assuming an intermediate scale desert (ISD). From a bottom-up approach, renormalization effects of intermediate scale MSSM-charged exotics (ISME), which are endemic to quasi-realistic string models, can resolve this issue by pushing the MSSM scale up to the string scale. However, for a generic string model, this implies that the projected Λ U unification under the ISD assumption is accidental. * john perkins@baylor.edu † ben dundee@baylor.edu ‡ richard k obousy@baylor.edu § hattst@wwc.edu ¶ ekasper@physics.tamu.edu m robinson@baylor.edu * * cwsloan@edisto.cofc.edu † † zkrs18@imail.etsu.edu ‡ ‡ gerald cleaver@baylor.edu If the true unification scale is Λ H > ∼5.0 × 10 17 GeV, is it possible that an illusionary unification at Λ U = 2.5 × 10 17 GeV in the ISD scenario is not accidental? This is an issue recently raised again by Binétruy et al. [1]. If it is not accidental, then under what conditions would the assumption of ISME in a WCHS model imply an apparent unification at Λ U < Λ H when an ISD is falsely assumed? J. Geidt's optical unification suggests that Λ U is not accidental and provides sufficient conditions for the appearance of Λ U . In fact, through constrained ISME, optical unification offers a mechanism whereby a generic MSSM scale Λ U < Λ H is guaranteed.A WCHS model was recently constructed that offers the possibility of optical unification [20]. Whether optical unification can be realized depends on the availability of anomaly-cancelling D-and F -flat directions meeting certain phenomenological requirements [21]. This paper reports on the systematic investigation of the optical unification properties of a subset of flat directions of this model that are stringently flat. Stringent flat directions can be guaranteed to be F -flat to all finite order (or to at least a given finite order consistent with electroweak scale supersymmetry breaking) and can be viewed as the likely roots of more general flat directions. Analysis of the phenomenology of stringent flat directions gives an indication of the remaining optical unification phenomenology that must be garnered by flat directions developed from them. This paper is a result of the [2003][2004] NSF REU program at Baylor University. 1 Review of Optical UnificationThe lower limit to string coupling unification in a weakly coupled heterotic string (WCHS) was shown by Kaplunovsky in 1992 to be around Λ H ∼ 5 × 10 17 GeV [2]. In contrast, under the scenario of an intermediate scale desert (ISD), the runnings of the SU(3) C ×SU(2) L ×U(1) Y ([321]) couplings in the Minimal Supersymmetric Standard Model (MSSM) predict a unification scale Λ U ∼ 2.5 × 10 16 GeV [3]. The issue of this factor-of-twenty difference was raised again in the third of the Twenty-Five Questions for String Theorists by Binétruy et al. ...
An algorithm to systematically and efficiently generate free fermionic heterotic string models was recently introduced [1]. This algorithm has been adopted by the Free Fermionic Model Construction (FFMC) program at Baylor University. As its first application, the algorithm is being applied to systematically generate the complete set of free fermionic heterotic string models with untwisted left-moving (worldsheet supersymmetric) sectors, up to continually advancing Layer and Order. Statistical analysis of this study will be reported in the near future. However, in a series of separate notes we will be reporting some of the more interesting models that appear along the way. In this, our first such note, we reveal a different string embedding of E 8 than is standard. That is, rather than realize E 8 via an SO(16) embedding, 248 = 120+128, we realize it via an SU (9) embedding, 248 = 80 + 84 + 84. This is obtained in a Layer 1, Order 6 model for which modular invariance itself dictates a gravitino sector accompany the gauge sector.
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