Twenty-five questions for string theorists

Abstract

In an effort to promote communication between the formal and phenomenological branches of the high-energy theory community, we provide a description of some important issues in supersymmetric and string phenomenology. We describe each within the context of string constructions, illustrating them with specific examples where applicable. Each topic culminates in a set of questions that we believe are amenable to direct consideration by string theorists, and whose answers we think could help connect string theory and phenomenology.

Kähler Stabilized, Modular Invariant Heterotic String Models

“…The precise form of the bilinear B-terms depends on how the supersymmetric µ-parameter of the Higgs potential is generated. This remains an open problem in superstring phenomenology, 10 as fundamental mass parameters are generally zero for fields in the massless spectrum. For the purposes of this section we merely give the general result.…”

Stringent phenomenological investigation into heterotic string optical unification

“…In the minimal case, two VEV fields must be 3's and one VEV field must be a3 (or vice versa). In this case, if triplets 3 i , i = 1, 2 receive respective VEVs 1) where R i and G i are respective magnitudes (up to a sign) of hidden red and green charges, and exp{iπθ i } are respective overall phases, then SU(3) D-flatness is maintained by a3 with VEV…”

“…* 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?…”

“…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 [1].One resolution to the factor-of-twenty difference between these two scales. is a grand unified theory (GUT) between the MSSM and string scales.…”

“…That is, a shift of the intermediate scale Λ I simply produces a shift in Λ U , rather than the disappearance of Λ U . Thus, a string model with optical unification offers a resolution to question three of [1].Successful optical unification requires three things [17]. First, the effective level of the hypercharge generator must be the standard…”