Constraints for the existence of flat and stable non-supersymmetric vacua in supergravity

We further develop on the study of the conditions for the existence of locally stable non-supersymmetric vacua with vanishing cosmological constant in supergravity models involving only chiral superfields. Starting from the two necessary conditions for flatness and stability derived in a previous paper (which involve the Kahler metric and its Riemann tensor contracted with the supersymmetry breaking auxiliary fields) we show that the implications of these constraints can be worked out exactly not only for factorizable scalar manifolds, but also for symmetric coset manifolds. In both cases, the conditions imply a strong restriction on the Kahler geometry and constrain the vector of auxiliary fields defining the Goldstino direction to lie in a certain cone. We then apply these results to the various homogeneous coset manifolds spanned by the moduli and untwisted matter fields arising in string compactifications, and discuss their implications. Finally, we also discuss what can be said for completely arbitrary scalar manifolds, and derive in this more general case some explicit but weaker restrictions on the Kahler geometry.Comment: 22 pages, Latex, no figure

A New Method for Finding Vacua in String Phenomenology

One of the central problems of string-phenomenology is to find stable vacua in the four dimensional effective theories which result from compactification. We present an algorithmic method to find all of the vacua of any given string-phenomenological system in a huge class. In particular, this paper reviews and then extends hep-th/0606122 to include various non-perturbative effects. These include gaugino condensation and instantonic contributions to the superpotential.Comment: 27 pages, 5 .eps figures. V2: Minor corrections, reference adde

Minimal Stability in Maximal Supergravity

Recently, it has been shown that maximal supergravity allows for non-supersymmetric AdS critical points that are perturbatively stable. We investigate this phenomenon of stability without supersymmetry from the sGoldstino point of view. In particular, we calculate the projection of the mass matrix onto the sGoldstino directions, and derive the necessary conditions for stability. Indeed we find a narrow window allowing for stable SUSY breaking points. As a by-product of our analysis, we find that it seems impossible to perturb supersymmetric critical points into non-supersymmetric ones: there is a minimal amount of SUSY breaking in maximal supergravity.Comment: 27 pages, 1 figure. v2: two typos corrected, published versio

Regulatory polymorphisms in extracellular matrix protease genes and susceptibility to rheumatoid arthritis: a case-control study

Many extracellular matrix (ECM) proteases seem to be important in rheumatoid arthritis (RA) and regulation of their transcription levels is a critical mechanism for controlling their activity. We have investigated, therefore, whether the best-characterized single nucleotide polymorphisms (SNPs) affecting transcription of the ECM proteases that have been related with joint pathology are associated with RA susceptibility. Nine SNPs in eight genes were selected by bibliographic search, including SNPs in the genes encoding matrix metalloproteinase (MMP)1, MMP2, MMP3, MMP7, MMP9, MMP13, plasminogen activator, tissue type (PLAT) and PAI-1. They were studied in a case-control setting that included 550 RA patients and 652 controls of Spanish ancestry from a single center. Genotyping was performed by single-base extension. Only two of the nine SNPs showed significant association with RA susceptibility. RA patients showed increased frequencies of the -7351 T allele of the gene encoding PLAT (36.4% versus 32.1% in controls, p = 0.026) and the -1306 T allele of the gene encoding MMP2 (24.5% versus 20.3% in controls, p = 0.013). These two alleles seemed to cooperate according to an additive model with respect to increased RA susceptibility (p = 0.004), and they were the low-expression alleles of the respective SNPs in a PLAT enhancer and the MMP2 promoter. These findings are in agreement with previous data suggesting that these two ECM proteases have a protective role in RA pathology. Confirmation of these associations will be needed to support these hypotheses. The remaining SNPs did not show association, either individually or collectively. Therefore, although regulatory SNPs in ECM proteases did not show any major effect on RA susceptibility, it was possible to find modest associations that, if replicated, will have interesting implications in the understanding of RA pathology

Metastable supergravity vacua with F and D supersymmetry breaking

We study the conditions under which a generic supergravity model involving chiral and vector multiplets can admit viable metastable vacua with spontaneously broken supersymmetry and realistic cosmological constant. To do so, we impose that on the vacuum the scalar potential and all its first derivatives vanish, and derive a necessary condition for the matrix of its second derivatives to be positive definite. We study then the constraints set by the combination of the flatness condition needed for the tuning of the cosmological constant and the stability condition that is necessary to avoid unstable modes. We find that the existence of such a viable vacuum implies a condition involving the curvature tensor for the scalar geometry and the charge and mass matrices for the vector fields. Moreover, for given curvature, charges and masses satisfying this constraint, the vector of F and D auxiliary fields defining the Goldstino direction is constrained to lie within a certain domain. The effect of vector multiplets relative to chiral multiplets is maximal when the masses of the vector fields are comparable to the gravitino mass. When the masses are instead much larger or much smaller than the gravitino mass, the effect becomes small and translates into a correction to the effective curvature. We finally apply our results to some simple classes of examples, to illustrate their relevance.Comment: 40 pages; v2 some clarifications added in the introduction; v3 some typos correcte

No metastable de Sitter vacua in N=2 supergravity with only hypermultiplets

We study the stability of vacua with spontaneously broken supersymmetry in N = 2 supergravity theories with only hypermultiplets. Focusing on the projection of the scalar mass matrix along the sGoldstino directions, we are able to derive a universal upper bound on the lowest mass eigenvalue. This bound only depends on the gravitino mass and the cosmological constant, but not on the details of the quaternionic manifold spanned by the scalar fields. Comparing with the Breitenlohner-Freedman bound shows that metastability requires the cosmological constant to be smaller than a certain negative critical value. Therefore, only AdS vacua with a sufficiently negative cosmological constant can be stable, while Minkowski and dS vacua necessarily have a tachyonic direction

Lack of association of a variable number of aspartic acid residues in the asporin gene with osteoarthritis susceptibility: case-control studies in Spanish Caucasians

A recent genetic association study has identified a microsatellite in the coding sequence of the asporin gene as a susceptibility factor for osteoarthritis (OA). Alleles of this microsatellite determine the variable number of aspartic acid residues in the amino-terminal end of the asporin protein. Asporin binds directly to the growth factor transforming growth factor beta and inhibits its anabolic effects in cartilage, which include stimulation of collagen and aggrecan synthesis. The OA-associated allele, with 14 aspartic acid residues, inhibits the anabolic effects of transforming growth factor beta more strongly than other asporin alleles, leading to increased OA liability. We have explored whether the association found in several cohorts of Japanese hip OA and knee OA patients was also present in Spanish Caucasians. We studied patients that had undergone total joint replacement for primary OA in the hip (n = 303) or the knee (n = 188) and patients with hand OA (n = 233), and we compared their results with controls (n = 294) lacking overt OA clinical symptoms. No significant differences were observed in any of the multiple comparisons performed, which included global tests of allele frequency distributions and specific comparisons as well as stratification by affected joint and by sex. Our results, together with reports from the United Kingdom and Greece, indicate that the stretch of aspartic acid residues in asporin is not an important factor in OA susceptibility among European Caucasians. It remains possible that lifestyle, environmental or genetic differences allow for an important effect of asporin variants in other ethnic groups as has been reported in the Japanese, but this should be supported by additional studies

A geometric bound on F-term inflation

We discuss a general bound on the possibility to realise inflation in any minimal supergravity with F-terms. The derivation crucially depends on the sGoldstini, the scalar field directions that are singled out by spontaneous supersymmetry breaking. The resulting bound involves both slow-roll parameters and the geometry of the K\"ahler manifold of the chiral scalars. We analyse the inflationary implications of this bound, and in particular discuss to what extent the requirements of single field and slow-roll can both be met in F-term inflation.Comment: 14 pages, improved analysis, references added, matches published versio

Models of Modular Inflation and Their Phenomenological Consequences

We study models of modular inflation of the form expected to arise from low energy effective actions of superstring theories. We argue on general grounds that the most likely models of modular slow-roll inflation are small field models in which the inflaton moves about a Planck distance from an extremum of the potential. We then focus on models in which the inflaton is the bosonic component of a single (complex) chiral superfield and explain the generic difficulties in designing small field models of modular inflation. We then show that if the Kaehler potential (KP) of the inflaton is logarithmic as in perturbative string theories, then it is not possible to satisfy the slow-roll conditions for any superpotential. We find that if the corrections to the KP are large enough so it can be approximated by a canonical KP in the vicinity of the extremum, then viable slow-roll inflation is possible. In this case, several parameters have to be tuned to a fraction of a percent. We give a prescription for designing successful small field supergravity models of inflation when the KP is canonical and calculate the slow-roll parameters from the superpotential parameters. Our results strengthen the case for models in which the moduli slowly roll about a Planck distance from a relatively high scale extremum that is located in the vicinity of the central region of moduli space units. Generic models of this class predict a red spectrum of scalar perturbations and negligible spectral index running. They also predict a characteristic suppression of tensor perturbations despite the high scale of inflation. Consequently, a detection of primordial tensor anisotropies or spectral index running in cosmic microwave background observations in the foreseeable future will rule out this entire class of modular inflation models.Comment: 35 pages, 1 figur