Supersymmetry, Ricci Flat Manifolds and the String Landscape

A longstanding question in superstring/$M$ theory is does it predict supersymmetry below the string scale? We formulate and discuss a necessary condition for this to be true; this is the mathematical conjecture that all stable, compact Ricci flat manifolds have special holonomy in dimensions below eleven. Almost equivalent is the proposal that the landscape of all geometric, stable, string/$M$ theory compactifications to Minkowski spacetime (at leading order) are supersymmetric. For simply connected manifolds, we collect together a number of physically relevant mathematical results, emphasising some key outstanding problems and perhaps less well known results. For non-simply connected, non-supersymmetric Ricci flat manifolds we demonstrate that many cases suffer from generalised Witten bubble of nothing instabilities.Comment: 15 pages. V2: corrected some typos. V3: Sign corrected in table and additional comments on 9 and 10 dimensions adde

Compactified String Theories -- Generic Predictions for Particle Physics

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 and dark matter: a non-thermal cosmological history before primordial nucleosynthesis, a scale of supersymmetry breaking which is "high" as in gravity mediation, scalar superpartners too heavy to be produced at the LHC (although gluino production is expected in many cases), and a significant fraction of dark matter in the form of axions. 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, predictions for various aspects of dark matter physics, as well as predictions for future precision measurements, can be made. As a prototypical example, $M$ theory compactified on a manifold of $G_2$ 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 were derived, from the key theoretical ideas to the final phenomenological predictions.Comment: 30 pages, 1 figure. Invited Review for International Journal of Modern Physics

Hidden Sectors in String Theory: Kinetic Mixings, Fifth Forces and Quintessence

Light moduli fields in string compactifications can have interesting implications for particle physics and cosmology. Fifth force bounds impose stringent constraints on the interactions of such moduli with the visible sector. To be consistent with the bounds, they need to be part of hidden sectors which interact with the Standard Model with weaker-than-Planck suppressed interactions. We consider scenarios in which the visible sector degrees of freedom are localised in the compactification and light moduli arise as closed string degrees of freedom associated with hidden sectors which are geometrically separated (in the extra-dimensions) from the Standard Model. Kinetic mixings lead to interactions between the moduli and the visible sector - we compute these using Kaehler potentials of string/M-theory compactifications. We argue that in general these interactions provide a lower bound on the strength of the interactions between the moduli and the visible sector. The interactions scale with inverse powers of the volume of the compactification, thus fifth force bounds can be translated to lower bounds on the volume of the extra-dimensions. We find that compactification volumes have to be large to evade the bounds. This imposes interesting constraints on quintessence model building in string theory. Our results for the strength of the interactions can also be used to quantify the fine-tuning necessary for the stability of the potential of a light modulus against quantum corrections involving visible sector loops

Bounds on Scalar Masses in Theories of Moduli Stabilization

In recent years it has been realised that pre-BBN decays of moduli can be a significant source of dark matter production, giving a `non-thermal WIMP miracle' and substantially reduced fine-tuning in cosmological axion physics. We study moduli masses and sharpen the claim that moduli dominated the pre-BBN Universe. We conjecture that in any string theory with stabilized moduli there will be at least one modulus field whose mass is of order (or less than) the gravitino mass. Cosmology then generically requires the gravitino mass not be less than about 30 TeV and the cosmological history of the Universe is non-thermal prior to BBN. Stable LSP's produced in these decays can account for the observed dark matter if they are `wino-like.' We briefly consider implications for the LHC, rare decays, and dark matter direct detection and point out that these results could prove challenging for models attempting to realize gauge mediation in string theory.Comment: 7 pages. v3: published versio

A Non-thermal WIMP Miracle

Light scalar fields with only gravitational strength couplings are typically present in UV complete theories of physics beyond the Standard Model. In the early universe it is natural for these fields to dominate the energy density, and their subsequent decay, if prior to BBN, will typically yield some dark matter particles in their decay products. In this paper we make the observation that a Non-thermal WIMP `Miracle' may result: that is, in the simplest solution to the cosmological moduli problem, non-thermally produced WIMPs can naturally account for the observed dark matter relic density. Such a solution may be generic in string theory compactifications.Comment: 6 pages, no figures, References added, minor errors correcte

Ricci Flat Metrics, Flat Connections and G2G_{2}-Manifolds

Inspired by considerations in $M$-theory, we prove the equivalence between the moduli spaces of (suitably complexified) torsion free $G_{2}$-structures on 7-manifolds which are families of hyperK\"ahler ALE 4-manifolds fibered over compact flat 3-manifolds $T^{3}/K$ and certain moduli spaces of flat $G^{\mathbb{C}}_{ADE}$ connections on $T^{3}/K$

Coulomb and Higgs Phases of G2G_2-manifolds

Ricci flat manifolds of special holonomy are a rich framework as models of the extra dimensions in string/$M$-theory. At special points in vacuum moduli space, special kinds of singularities occur and demand a physical interpretation. In this paper we show that the topologically distinct $G_2$-holonomy manifolds arising from desingularisations of codimension four orbifold singularities due to Joyce and Karigiannis correspond physically to Coulomb and Higgs phases of four dimensional gauge theories. The results suggest generalisations of the Joyce-Karigiannis construction to arbitrary ADE-singularities and higher order twists which we explore in detail in explicitly solvable local models. These models allow us to derive an isomorphism between moduli spaces of Ricci flat metrics on these non-compact $G_2$-manifolds and flat ADE-connections on compact flat 3-manifolds which we establish explicitly for $\operatorname{SU}(n)$.Comment: 22 page