The phase diagram of the lattice Calogero-Sutherland model

We introduce a {\it lattice} version of the Calogero Sutherland model adapted to describe $1/d^2$ pairwise interacting steps with discrete positions on a vicinal surface. The configurational free energy is obtained within a transfer matrix method. The full phase diagram for attractive and for repulsive interaction is deduced. For attraction, critical temperatures of faceting transitions are found to depend on step density.Comment: latex PRBCalogSuth.tex, 6 files, 4 pages [SPEC-S00/900

Hints of R-parity violation in B decays into τν\tau \nu

In this article we show that the recently observed enhanced semi-leptonic and leptonic decay rates of the B meson into \tau \nu modes can be explained within the frame work of R-parity violating (RPV) MSSM. In particular, RPV contributions involving the exchange of right-handed down-type squarks give a universal contribution to the B+ --> \tau \nu, B --> D \tau \nu and the B --> D* \tau \nu decays. We find that the masses and couplings that explain the enhanced B decay rates are phenomelogically viable and the squarks can possibly be observed at the LHC.Comment: 8 pages and 3 figures; Updated section 2 and 3, but results are unmodifie

On hypercharge flux and exotics in F-theory GUTs

We study SU(5) Grand Unified Theories within a local framework in F-theory with multiple extra U(1) symmetries arising from a small monodromy group. The use of hypercharge flux for doublet-triplet splitting implies massless exotics in the spectrum that are protected from obtaining a mass by the U(1) symmetries. We find that lifting the exotics by giving vacuum expectation values to some GUT singlets spontaneously breaks all the U(1) symmetries which implies that proton decay operators are induced. If we impose an additional R-parity symmetry by hand we find all the exotics can be lifted while proton decay operators are still forbidden. These models can retain the gauge coupling unification accuracy of the MSSM at 1-loop. For models where the generations are distributed across multiple curves we also present a motivation for the quark-lepton mass splittings at the GUT scale based on a Froggatt-Nielsen approach to flavour.Comment: 38 pages; v2: emphasised possibility of avoiding exotics in models without a global E8 structure, added ref, journal versio

Un-oriented Quiver Theories for Majorana Neutrons

In the context of un-oriented open string theories, we identify quivers whereby a Majorana mass for the neutron is indirectly generated by exotic instantons. We discuss two classes of (Susy) Standard Model like quivers, depending on the embedding of SU(2)_W in the Chan-Paton group. In both cases, the main mechanism involves a vector-like pair mixing through a non-perturbative mass term. We also discuss possible relations between the phenomenology of Neutron-Antineutron oscillations and LHC physics in these models. In particular, a vector-like pair of color-triplet scalars or color-triplet fermions could be directly detected at LHC, compatibly with n-\bar{n} limits. Finally we briefly comment on Pati-Salam extensions of our models.Comment: More comments on phenomenology and fluxes, Re-discussion of SM-quivers compatible with n-cycles conditions Version accepted by JHE

MSSM in view of PAMELA and Fermi-LAT

We take the MSSM as a complete theory of low energy phenomena, including neutrino masses and mixings. This immediately implies that the gravitino is the only possible dark matter candidate. We study the implications of the astrophysical experiments such as PAMELA and Fermi-LAT, on this scenario. The theory can account for both the realistic neutrino masses and mixings, and the PAMELA data as long as the slepton masses lie in the $500-10^6$TeV range. The squarks can be either light or heavy, depending on their contribution to radiative neutrino masses. On the other hand, the Fermi-LAT data imply heavy superpartners, all out of LHC reach, simply on the grounds of the energy scale involved, for the gravitino must weigh more than 2 TeV. The perturbativity of the theory also implies an upper bound on its mass, approximately $6-7$TeV.Comment: Published version, figures update

Rational F-Theory GUTs without exotics

We construct F-theory GUT models without exotic matter, leading to the MSSM matter spectrum with potential singlet extensions. The interplay of engineering explicit geometric setups, absence of four-dimensional anomalies, and realistic phenomenology of the couplings places severe constraints on the allowed local models in a given geometry. In constructions based on the spectral cover we find no model satisfying all these requirements. We then provide a survey of models with additional U(1) symmetries arising from rational sections of the elliptic fibration in toric constructions and obtain phenomenologically appealing models based on SU(5) tops. Furthermore we perform a bottom-up exploration beyond the toric section constructions discussed in the literature so far and identify benchmark models passing all our criteria, which can serve as a guideline for future geometric engineering.Comment: 27 Pages, 1 Figur

Flavour in supersymmetry: horizontal symmetries or wave function renormalisation

We compare theoretical and experimental predictions of two main classes of models addressing fermion mass hierarchies and flavour changing neutral currents (FCNC) effects in supersymmetry: Froggatt-Nielsen (FN) U(1) gauged flavour models and Nelson-Strassler/extra dimensional models with hierarchical wave functions for the families. We show that whereas the two lead to identical predictions in the fermion mass matrices, the second class generates a stronger suppression of FCNC effects. We prove that, whereas at first sight the FN setup is more constrained due to anomaly cancelation conditions, imposing unification of gauge couplings in the second setup generates conditions which precisely match the mixed anomaly constraints in the FN setup. Finally, we provide an economical extra dimensional realisation of the hierarchical wave functions scenario in which the leptonic FCNC can be efficiently suppressed due to the strong coupling (CFT) origin of the electron mass.Comment: 23 page

R-parity violation in SU(5)

We show that judiciously chosen R-parity violating terms in the minimal renormalizable supersymmetric SU(5) are able to correct all the phenomenologically wrong mass relations between down quarks and charged leptons. The model can accommodate neutrino masses as well. One of the most striking consequences is a large mixing between the electron and the Higgsino. We show that this can still be in accord with data in some regions of the parameter space and possibly falsified in future experiments.Comment: 30 pages, 1 figure. Revised version. To appear in JHE

Random Convex Hulls and Extreme Value Statistics

In this paper we study the statistical properties of convex hulls of $N$ random points in a plane chosen according to a given distribution. The points may be chosen independently or they may be correlated. After a non-exhaustive survey of the somewhat sporadic literature and diverse methods used in the random convex hull problem, we present a unifying approach, based on the notion of support function of a closed curve and the associated Cauchy's formulae, that allows us to compute exactly the mean perimeter and the mean area enclosed by the convex polygon both in case of independent as well as correlated points. Our method demonstrates a beautiful link between the random convex hull problem and the subject of extreme value statistics. As an example of correlated points, we study here in detail the case when the points represent the vertices of $n$ independent random walks. In the continuum time limit this reduces to $n$ independent planar Brownian trajectories for which we compute exactly, for all $n$, the mean perimeter and the mean area of their global convex hull. Our results have relevant applications in ecology in estimating the home range of a herd of animals. Some of these results were announced recently in a short communication [Phys. Rev. Lett. {\bf 103}, 140602 (2009)].Comment: 61 pages (pedagogical review); invited contribution to the special issue of J. Stat. Phys. celebrating the 50 years of Yeshiba/Rutgers meeting

SLITRK2, an X-linked modifier of the age at onset in C9orf72 frontotemporal lobar degeneration

The G4C2-repeat expansion in C9orf72 is the most common cause of frontotemporal dementia and of amyotrophic lateral sclerosis. The variability of age at onset and phenotypic presentations is a hallmark of C9orf72 disease. In this study, we aimed to identify modifying factors of disease onset in C9orf72 carriers using a family-based approach, in pairs of C9orf72 carrier relatives with concordant or discordant age at onset. Linkage and association analyses provided converging evidence for a locus on chromosome Xq27.3. The minor allele A of rs1009776 was associated with an earlier onset (P = 1 × 10-5). The association with onset of dementia was replicated in an independent cohort of unrelated C9orf72 patients (P = 0.009). The protective major allele delayed the onset of dementia from 5 to 13 years on average depending on the cohort considered. The same trend was observed in an independent cohort of C9orf72 patients with extreme deviation of the age at onset (P = 0.055). No association of rs1009776 was detected in GRN patients, suggesting that the effect of rs1009776 was restricted to the onset of dementia due to C9orf72. The minor allele A is associated with a higher SLITRK2 expression based on both expression quantitative trait loci (eQTL) databases and in-house expression studies performed on C9orf72 brain tissues. SLITRK2 encodes for a post-synaptic adhesion protein. We further show that synaptic vesicle glycoprotein 2 and synaptophysin, two synaptic vesicle proteins, were decreased in frontal cortex of C9orf72 patients carrying the minor allele. Upregulation of SLITRK2 might be associated with synaptic dysfunctions and drives adverse effects in C9orf72 patients that could be modulated in those carrying the protective allele. How the modulation of SLITRK2 expression affects synaptic functions and influences the disease onset of dementia in C9orf72 carriers will require further investigations. In summary, this study describes an original approach to detect modifier genes in rare diseases and reinforces rising links between C9orf72 and synaptic dysfunctions that might directly influence the occurrence of first symptoms