Gerald B. Cleaver

FREE FERMIONIC HETEROTIC MODEL BUILDING AND ROOT SYSTEMS

We consider an alternative derivation of the GSO Projection in the free fermionic construction of the weakly coupled heterotic string in terms of root systems, as well as the interpretation of the GSO Projection in this picture. We then present an algorithm to systematically and efficiently generate input sets (i.e. basic vectors) in order to study landscape statistics with minimal computational cost. For example, the improvement at order 6 is ≈10-13 over a traditional brute force approach, and improvement increases with order. We then consider an example of statistics on a relatively simple class of models.

Casimir energy and brane stability

Abstract 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 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 produces 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 fine tuning needed for stabilization of the brane separation. Finally, 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.

RADIUS DESTABILIZATION IN FIVE-DIMENSIONAL ORBIFOLDS DUE TO AN ENHANCED CASIMIR EFFECT

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 five-dimensional (non-supersymmetric) S1/ Z2 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.

On a NAHE variation

Abstract We present a variation of the NAHE-basis for free fermionic heterotic string models. By rotating some of the boundary conditions of the NAHE periodic/anti-periodic fermions { y m , y ¯ m , w m , w ¯ m } , for m = 1 to 6, associated with the six compact dimensions of a bosonic lattice/orbifold model, we show an additional method for enhancing the standard NAHE gauge group of SO ( 10 ) back to E 6 . This rotation transforms ( SO ( 10 ) ⊗ SO ( 6 ) 3 ) obs ⊗ ( E 8 ) hid into ( E 6 ⊗ U ( 1 ) 5 ) obs ⊗ SO ( 22 ) hid . When SO ( 10 ) is enhanced to E 6 in this manner, the i th MSSM matter generation in the SO ( 10 ) 16 i rep, originating in the twisted basis vector b i , recombines with both its associated untwisted MSSM Higgs in a 10 i rep and an untwisted non-Abelian singlet ϕ i , to form a 27 i rep of E 6 . Beginning instead with the E 6 model, the inverse transformation of the fermion boundary conditions corresponds to partial GUT breaking via boundary rotation. Correspondence between free fermionic models with Z 2 ⊗ Z 2 twist (especially of the NAHE class) and orbifold models with a similar twist has received further attention recently. Our NAHE variation also involves a Z 2 ⊗ Z 2 twist and offers additional understanding regarding the free fermion/orbifold correspondence. Further, models based on this NAHE variation offer some different phenomenological features compared to NAHE-based models. In particular, the more compact Z 2 ⊗ Z 2 twist of the NAHE variation offers a range of mirror models not possible from NAHE-based models. Examples of such models are presented.

A NON-STANDARD STRING EMBEDDING OF E8

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 E8 than is standard. That is, rather than realize E8 via an SO(16) embedding, 248 = 120 + 128, we realize it via an SU(9) embedding, . This is obtained in a Layer 1, Order 6 model for which modular invariance itself dictates a gravitino sector accompany the gauge sector.