Non-simply-laced Lie algebras via F theory strings

In order to describe the appearance in F theory of the non--simply--laced Lie algebras, we use the representation of symmetry enhancements by means of string junctions. After an introduction to the techniques used to describe symmetry enhancement, that is algebraic geometry, BPS states analysis and string junctions, we concentrate on the latter. We give an explicit description of the folding of D_{2n} to B_n of the folding of E_6 to F_4 and that of D_4 to G_2 in terms of junctions and Jordan strings. We also discuss the case of C_n, but we are unable in this case to provide a string interpretation.Comment: 24 pages, 3 figure

Gauge Fluxes in F-theory and Type IIB Orientifolds

We provide a detailed correspondence between G_4 gauge fluxes in F-theory compactifications with SU(n) and SU(n)x(1) gauge symmetry and their Type IIB orientifold limit. Based on the resolution of the relevant F-theory Tate models we classify the factorisable G_4-fluxes and match them with the set of universal D5-tadpole free U(1)-fluxes in Type IIB. Where available, the global version of the universal spectral cover flux corresponds to Type IIB gauge flux associated with a massive diagonal U(1). In U(1)-restricted Tate models extra massless abelian fluxes exist which are associated with specific linear combinations of Type IIB fluxes. Key to a quantitative match between F-theory and Type IIB is a proper treatment of the conifold singularity encountered in the Sen limit of generic F-theory models. We also shed further light on the brane recombination process relating generic and U(1)-restricted Tate models.Comment: 53 pages, 3 figures; v2: Refs added; v3: minor corrections to match version published in JHE

Brane Tilings and Specular Duality

We study a new duality which pairs 4d N=1 supersymmetric quiver gauge theories. They are represented by brane tilings and are worldvolume theories of D3 branes at Calabi-Yau 3-fold singularities. The new duality identifies theories which have the same combined mesonic and baryonic moduli space, otherwise called the master space. We obtain the associated Hilbert series which encodes both the generators and defining relations of the moduli space. We illustrate our findings with a set of brane tilings that have reflexive toric diagrams.Comment: 42 pages, 16 figures, 5 table

Massive Abelian Gauge Symmetries and Fluxes in F-theory

F-theory compactified on a Calabi-Yau fourfold naturally describes non-Abelian gauge symmetries through the singularity structure of the elliptic fibration. In contrast Abelian symmetries are more difficult to study because of their inherently global nature. We argue that in general F-theory compactifications there are massive Abelian symmetries, such as the uplift of the Abelian part of the U(N) gauge group on D7-branes, that arise from non-Kahler resolutions of the dual M-theory setup. The four-dimensional F-theory vacuum with vanishing expectation values for the gauge fields corresponds to the Calabi-Yau limit. We propose that fluxes that are turned on along these U(1)s are uplifted to non-harmonic four-form fluxes. We derive the effective four-dimensional gauged supergravity resulting from F-theory compactifications in the presence of the Abelian gauge factors including the effects of possible fluxes on the gauging, tadpoles and matter spectrum.Comment: 49 page

Towards a Realistic F-theory GUT

We consider semi-local F-theory GUTs arising from a single E_8 point of local enhancement, leading to simple GUT groups based on E_6, SO(10) and SU(5) with SU(3), SU(4) and SU(5) spectral covers, respectively. Assuming the minimal Z_2 monodromy, we determine the homology classes and the associated spectra after flux breaking for each case. Our analysis includes the GUT singlets which have hitherto been ignored but which play a crucial role in phenomenology. Using these results we construct an E_6 based model that demonstrates, for the first time, that it is possible to construct a phenomenologically viable model which leads to the MSSM at low energies. The exotics that result from flux breaking all get a large mass when singlet fields acquire vacuum expectation values driven by D- and F-flatness. Due to the underlying GUT symmetry and the U(1)s descending from E_8, bare baryon- and lepton-number violating terms are forbidden up to and including dimension 5. As a result nucleon decay is naturally suppressed below present bounds. The mu-term is forbidden by the U(1) but is generated at the SUSY breaking scale when a further singlet field acquires a TeV scale vacuum expectation value, driven by the spontaneous breaking of the electroweak symmetry. After including the effect of flux and instanton corrections acceptable quark and charged lepton masses and mixing angles can be obtained. Neutrinos get a mass from the see-saw mechanism through their coupling to singlet neutrinos that acquire large Majorana mass as a result of the monodromy.Comment: This version incorporates an improved discussion of the suppression of nucleon decay and the non-perturbative breaking of the U(1) symmetrie

Computing Brane and Flux Superpotentials in F-theory Compactifications

In four-dimensional F-theory compactifications with N=1 supersymmetry the fields describing the dynamics of space-time filling 7-branes are part of the complex structure moduli space of the internal Calabi-Yau fourfold. We explicitly compute the flux superpotential in F-theory depending on all complex structure moduli, including the 7-brane deformations and the field corresponding to the dilaton-axion. Since fluxes on the 7-branes induce 5-brane charge, a local limit allows to effectively match the F-theory results to a D5-brane in a non-compact Calabi-Yau threefold with threeform fluxes. We analyze the classical and instanton contributions to the F-theory superpotential using mirror symmetry for Calabi-Yau fourfolds. The F-theory compactifications under consideration also admit heterotic dual descriptions and we discuss the identification of the moduli in this non-perturbative duality.Comment: 75 pages, 1 figure; typos corrected, references adde

Abnormality in glutamine-glutamate cycle in the cerebrospinal fluid of cognitively intact elderly individuals with major depressive disorder: a 3-year follow-up study

Major depressive disorder (MDD), common in the elderly, is a risk factor for dementia. Abnormalities in glutamatergic neurotransmission via the N-methyl-D-aspartate receptor (NMDA-R) have a key role in the pathophysiology of depression. This study examined whether depression was associated with cerebrospinal fluid (CSF) levels of NMDA-R neurotransmission-associated amino acids in cognitively intact elderly individuals with MDD and age- and gender-matched healthy controls. CSF was obtained from 47 volunteers (MDD group, N = 28; age- and gender-matched comparison group, N = 19) at baseline and 3-year follow-up (MDD group, N = 19; comparison group, N = 17). CSF levels of glutamine, glutamate, glycine, L-serine and D-serine were measured by highperformance liquid chromatography. CSF levels of amino acids did not differ across MDD and comparison groups. However, the ratio of glutamine to glutamate was significantly higher at baseline in subjects with MDD than in controls. The ratio decreased in individuals with MDD over the 3-year follow-up, and this decrease correlated with a decrease in the severity of depression. No correlations between absolute amino-acid levels and clinical variables were observed, nor were correlations between amino acids and other biomarkers (for example, amyloid-β42, amyloid-β40, and total and phosphorylated tau protein) detected. These results suggest that abnormalities in the glutamine–glutamate cycle in the communication between glia and neurons may have a role in the pathophysiology of depression in the elderly. Furthermore, the glutamine/glutamate ratio in CSF may be a state biomarker for depression