Weakly-coupled Heterotic String Research Articles

KÄHLER STABILIZED, MODULAR INVARIANT HETEROTIC STRING MODELS

We review the theory and phenomenology of effective supergravity theories based on orbifold compactifications of the weakly-coupled heterotic string. In particular, we consider theories in which the four-dimensional theory displays target space modular invariance and where the dilatonic mode undergoes Kähler stabilization. A self-contained exposition of effective Lagrangian approaches to gaugino condensation and heterotic string theory is presented, leading to the development of the models of Binétruy, Gaillard and Wu. Various aspects of the phenomenology of this class of models are considered. These include issues of supersymmetry breaking and superpartner spectra, the role of anomalous U(1) factors, issues of flavor and R-parity conservation, collider signatures, axion physics, and early universe cosmology. For the vast majority of phenomenological considerations the theories reviewed here compare quite favorably to other string-derived models in the literature. Theoretical objections to the framework and directions for further research are identified and discussed.

Stringent phenomenological investigation into heterotic string optical unification

For the weakly coupled heterotic string (WCHS) there is a well-known factor of 20 conflict between the minimum string coupling unification scale, ${\ensuremath{\Lambda}}_{H}\ensuremath{\sim}5\ifmmode\times\else\texttimes\fi{}{10}^{17}\text{ }\text{ }\mathrm{GeV}$, and the projected minimal supersymmetric standard model (MSSM) gauge coupling unification scale, ${\ensuremath{\Lambda}}_{U}\ensuremath{\sim}2.5\ifmmode\times\else\texttimes\fi{}{10}^{16}\text{ }\text{ }\mathrm{GeV}$, assuming an intermediate scale desert (ISD). From a bottom-up approach, renormalization effects of intermediate scale MSSM-charged exotics (ISME), which are endemic to quasirealistic 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 ${\ensuremath{\Lambda}}_{U}$ unification under the ISD assumption is accidental. If the true unification scale is ${\ensuremath{\Lambda}}_{H}\ensuremath{\gtrsim}5.0\ifmmode\times\else\texttimes\fi{}{10}^{17}\text{ }\text{ }\mathrm{GeV}$, is it possible that an illusionary unification at ${\ensuremath{\Lambda}}_{U}=2.5\ifmmode\times\else\texttimes\fi{}{10}^{17}\text{ }\text{ }\mathrm{GeV}$ in the ISD scenario is not accidental? (This is an issue recently raised again by Bin\'etruy et al..) Optical unification suggests that ${\ensuremath{\Lambda}}_{U}$ might not be accidental. Through its ISME constraints, optical unification offers a mechanism whereby a generic MSSM scale ${\ensuremath{\Lambda}}_{U}<{\ensuremath{\Lambda}}_{H}$ is guaranteed. A WCHS model was recently constructed that could yield optical unification, depending on the availability of anomaly-cancelling $D$- and $F$-flat directions that meet optical unification ISME requirements. We report the results of a systematic investigation of the optical unification properties of a subset of flat directions of this model that are stringently flat. Stringent flat directions do not require significant fine-tuning and can be easily guaranteed to be $F$-flat to all finite order (or to at least a given finite order consistent with electroweak scale supersymmetry breaking). They are the likely roots of more complicated (and arguably, more finely tuned) flat directions. To realize optical unification, a flat direction must keep all exotic triplets and doublets massless down to an intermediate mass scale, except for three extra pairs of Higgs which must acquire MSSM (or higher) scale mass. Additionally, six out of seven pairs of exotic hypercharged non-Abelian singlets must acquire MSSM (or higher) scale mass, while the remaining pair remains massless down to the intermediate scale. Our investigation revealed that the best stringent directions could induce MSSM scale or higher mass to at most three of the six pairs of exotic singlets, and to only two out of three pairs of exotic Higgs. Each of these stringent flat directions keeps all of the exotic triplets and remaining exotic doublets massless down to an intermediate scale. Thus, some fine-tuning away from stringent flat directions is necessary, if it is possible for an additional three pairs of exotic hypercharged singlets and one more pair of extra Higgs to become MSSM scale massive. Future research may indicate if such flat directions exist. This paper is a product of the 2003-2004 NSF REU program at Baylor University.

Direct and indirect detection of dark matter in heterotic orbifold models

We study the neutralino dark matter phenomenology in the context of effective field theories derived from the weakly-coupled heterotic string. We consider in particular direct detection and indirect detection with neutrino telescopes rates. The two cases of moduli dominated and dilaton dominated SUSY breaking lead to completely different phenomenologies. Even if in both cases relic density constraints can be fulfilled, moduli domination generically leads to detection rates which are much below the present and future experimental sensitivities, whereas dilaton domination gives high detection rates accessible to the next generation of experiments. This could make dark matter searches an alternative way to constrain high energy fundamental parameters.

Inflation and Kähler stabilization of the dilaton

The problems of attempting inflationary model-building in a theory containing a dilaton are explained. In particular, I study the shape of the dilaton potential today and during inflation, based on a weakly-coupled heterotic string model where corrections to the Kahler potential are assumed to be responsible for dilaton stabilization. Although no specific model-building is attempted, if the inflationary energy density is related to the scale of gaugino condensation, then the dilaton may be stabilized close enough to today's value that there is no significant change in the GUT scale coupling. This can occur in a very wide range of models, and helps to provide some justification for the standard predictions of the spectral index. I explain how this result can ultimately be traced to the supersymmetry structure of the theory.

Phenomenology of nonstandard embedding and five-branes in M theory

We study the phenomenology of the strong-coupling limit of $E_8\times E_8$ heterotic string obtained from M-theory, using a Calabi-Yau compactification. After summarizing the standard embedding results, we concentrate on non-standard embedding vacua as well as vacua where non-perturbative objects as five-branes are present. We analyze in detail the different scales of the theory, eleven-dimensional Planck mass, compactification scale, orbifold scale, and how they are related taking into account higher order corrections. To obtain the phenomenologically favored GUT scale is easier than in standard embedding vacua. To lower this scale to intermediate ($\approx 10^{11}$ GeV) or 1 TeV values or to obtain the radius of the orbifold as large as a millimetre is possible. However, we point out that these special limits are unnatural. Finally, we perform a systematic analysis of the soft supersymmetry-breaking terms. We point out that scalar masses larger than gaugino masses can easily be obtained unlike the standard embedding case and the weakly-coupled heterotic string.

Gaugino mass in the heterotic string with Scherk-Schwarz compactification

The generic observable sector gaugino mass in the weakly-coupled heterotic string compactified to four dimensions by the Scherk-Schwarz scheme (together with hidden sector gaugino condensation inducing the super-Higgs effect with a vanishing cosmological constant) is shown to be nonzero at tree level, being of the order of the gravitino mass, modulo reasonable assumptions regarding the magnitude of the condensate and the Scherk-Schwarz mass parameters.

Recent progress in weakly-coupled heterotic string phenomenology

Some recent developments in the weakly-coupled heterotic string phenomenology are reviewed. We discuss several important issues such as dilaton/moduli stabilization, supersymmetry breaking (by hidden-sector gaugino condensation), gauge coupling unification (or the Newton's constant), the QCD axion, as well as cosmological problems involving the dilaton/moduli and the axion.

M-theory model-building and proton stability

We study the problem of baryon stability in M theory, starting from realistic four-dimensional string models constructed using the free-fermion formulation of the weakly-coupled heterotic string. Suitable variants of these models manifest an enhanced custodial gauge symmetry that forbids to all orders the appearance of dangerous dimension-five baryon-decay operators. We exhibit the underlying geometric (bosonic) interpretation of these models, which have a $Z_2 \times Z_2$ orbifold structure similar, but not identical, to the class of Calabi-Yau threefold compactifications of M and F theory investigated by Voisin and Borcea. A related generalization of their work may provide a solution to the problem of proton stability in M theory.