Perspectives on String Phenomenology

The following sections are included:

• Contents
• Preface
• Acknowledgments

Can we try to say what an electron (or a quark, gluon or photon) is, as opposed to just describing its properties. String theory can address that question.

I discuss moduli: what they are, and what they are not, where they come from and where they are useful, where they are physically irrelevant and where they are crucial.

Since the first “string revolution” of 1984, the weakly coupled E₈ ⊗ E₈ heterotic string theory has been a promising candidate for the underlying theory of the Standard Model. The particle spectrum and the issue of dilaton stabilization are reviewed. Specific models for hidden sector condensation and supersymmetry breaking are described and their phenomenological and cosmological implications are discussed. The importance of T-duality is emphasized. Theoretical challenges to finding a satisfactory vacuum, as well as constraints from LHC data are addressed.

String theoretical ideas might be relevant for particle physics model building. Ideally one would hope to find a unified theory of all fundamental interactions. There are only few consistent string theories in D = 10 or 11 space-time dimensions, but a huge landscape in D = 4. We have to explore this landscape to identify models that describe the known phenomena of particle physics. Properties of compactified six spatial dimensions are crucial in that respect. We postulate some useful rules to investigate this landscape and construct realistic models. We identify common properties of the successful models and formulate lessons for further model building.

In keeping with the “Perspectives” theme of this volume, this Chapter provides a personal perspective on the string landscape. Along the way, the perspectives of many other physicists are discussed as well. No attempt is made to provide a thorough and balanced review of the field, and indeed there is a slight emphasis on my own contributions to this field, as these contributions have been critical to forming my perspective. This Chapter is adapted from a Colloquium which I have delivered at a number of institutions worldwide, and I have attempted to retain the informal and non-technical spirit and style of this Colloquium presentation as much as possible.

We survey some of the basic mathematical ideas and techniques which are used in string phenomenology, such as constructions of Calabi-Yau manifolds, singularities and orbifolds, toric geometry, variation of complex structure, and mirror symmetry.

Perhaps the most important way string theory has affected the perspective of particle physics phenomenology is through the “string theory landscape”. We discuss the evidence supporting its existence, describe the regions of the landscape that have been explored, and examine what the string theory landscape might imply for most Standard Model problems.

A brief overview is presented of the progress made during the past few years on the general structure of local models of particle physics from string theory including: moduli stabilisation, supersymmetry breaking, global embedding in compact Calabi-Yau compactifications and potential cosmological implications. Type IIB D-brane constructions and the Large Volume Scenario (LVS) are discussed in some detail emphasising the recent achievements and the main open questions.

We give a lightning overview of recent progress in F-theory model building. After a review of the basic paradigm of geometric engineering of grand unified theories by elliptically fibered Calabi-Yau fourfolds, we explain the connection to local models, construction of fluxes, phenomenological implications as well as the recent advances in building global models with U(1) symmetries.

In recent years it has been realized that in string/M theories compactified to four dimensions which satisfy cosmological constraints, it is possible to make some generic predictions for particle physics: a non-thermal cosmological history before primordial nucleosynthesis, a scale of supersymmetry breaking which is “high” as in gravity mediation, and scalar superpartners too heavy to be produced at the LHC (although gluino production is predicted in many cases). When the matter and gauge spectrum below the compactification scale is that of the MSSM, a robust prediction of about 125 GeV for the Higgs boson mass, as well as predictions for future precision measurements, can be made. As a prototypical example, M theory compactified on a manifold of G₂ holonomy leads to a good candidate for our “string vacuum”, with the TeV scale emerging from the Planck scale, a de Sitter vacuum, robust electroweak symmetry breaking, and solutions of the weak and strong CP problems. In this article we review how these and other results are derived, from the key theoretical ideas to the final phenomenological predictions.

String/M theory is an exciting framework within which to try to understand our universe and its properties.Compactified string/M theories address and offer solutions to almost every important question and issue in particle physics and particle cosmology. Earlier goals of finding a top-down “vacuum selection” principle and deriving the 4D theory have not yet been realized.Does that mean we should stop trying, as nearly all string theorists have…

This is a short review of string cosmology. We wish to connect string-scale physics as closely as possible to observables accessible to current or near-future experiments. Our possible best hope to do so is a description of inflation in string theory. The energy scale of inflation can be as high as that of Grand Unification (GUT). If this is the case, this is the closest we can possibly get in energy scales to string-scale physics. Hence, GUT-scale inflation may be our best candidate phenomenon to preserve traces of string-scale dynamics. Our chance to look for such traces is the primordial gravitational wave, or tensor mode signal produced during inflation. For GUT-scale inflation this is strong enough to be potentially visible as a B-mode polarization of the cosmic microwave background (CMB). Moreover, a GUT-scale inflation model has a trans-Planckian excursion of the inflaton scalar field during the observable amount of inflation. Such large-field models of inflation have a clear need for symmetry protection against quantum corrections. This makes them ideal candidates for a description in a candidate fundamental theory like string theory. At the same time the need of large-field inflation models for UV completion makes them particularly susceptible to preserve imprints of their string-scale dynamics in the inflationary observables, the spectral index n_s and the fractional tensor mode power r. Hence, we will focus this review on axion monodromy inflation as a mechanism of large-field inflation in string theory.

We review the tension between the observational evidence for dark energy and various theoretical considerations. This tension has motivated a reconsideration of the issue of naturalness, and spawned various exotic approaches toward an acceptable solution. We discuss attempts to realize dark energy in string theory, and the perspective on the string landscape that these results have suggested.

I review the ideas of holographic space-time (HST), Cosmological SUSY breaking (CSB), and the Pyramid Schemes, which are the only known models of Tera-scale physics consistent with CSB, current particle data, and gauge coupling unification. There is considerable uncertainty in the estimate of the masses of supersymmetric partners of the standard model particles, but the model predicts that the gluino is probably out of reach of the LHC, squarks may be in reach, and the NLSP is a right handed slepton, which should be discovered soon.