Supersymmetric non-linear sigma-models with boundaries revisited

We study two-dimensional supersymmetric non-linear sigma-models with boundaries. We derive the most general family of boundary conditions in the non-supersymmetric case. Next we show that no further conditions arise when passing to the N=1 model. We present a manifest N=1 off-shell formulation. The analysis is greatly simplified compared to previous studies and there is no need to introduce non-local superspaces nor to go (partially) on-shell. Whether or not torsion is present does not modify the discussion. Subsequently, we determine under which conditions a second supersymmetry exists. As for the case without boundaries, two covariantly constant complex structures are needed. However, because of the presence of the boundary, one gets expressed in terms of the other one and the remainder of the geometric data. Finally we recast some of our results in N=2 superspace and discuss applications.Comment: LaTeX, 23 page

Koebe 1/4-Theorem and Inequalities in N=2 Super-QCD

The critical curve ${\cal C}$ on which ${\rm Im}\,\hat\tau =0$, $\hat\tau=a_D/a$, determines hyperbolic domains whose Poincar\'e metric is constructed in terms of $a_D$ and $a$. We describe ${\cal C}$ in a parametric form related to a Schwarzian equation and prove new relations for $N=2$ Super $SU(2)$ Yang-Mills. In particular, using the Koebe 1/4-theorem and Schwarz's lemma, we obtain inequalities involving $u$, $a_D$ and $a$, which seem related to the Renormalization Group. Furthermore, we obtain a closed form for the prepotential as function of $a$. Finally, we show that $\partial_{\hat\tau} \langle {\rm tr}\,\phi^2\rangle_{\hat \tau}={1\over 8\pi i b_1}\langle \phi\rangle_{\hat\tau}^2$, where $b_1$ is the one-loop coefficient of the beta function.Comment: 11 pages, LaTex file, Expanded version: new results, technical details explained, misprints corrected and references adde

On the covariant quantization of tensionless bosonic strings in AdS spacetime

The covariant quantization of the tensionless free bosonic (open and closed) strings in AdS spaces is obtained. This is done by representing the AdS space as an hyperboloid in a flat auxiliary space and by studying the resulting string constrained hamiltonian system in the tensionless limit. It turns out that the constraint algebra simplifies in the tensionless case in such a way that the closed BRST quantization can be formulated and the theory admits then an explicit covariant quantization scheme. This holds for any value of the dimension of the AdS space.Comment: 1+16 pages; v4 two clarifications adde

Decay of Unstable D-branes with Electric Field

Using the techniques of two dimensional conformal field theory we construct time dependent classical solutions in open string theory describing the decay of an unstable D-brane in the presence of background electric field, and explicitly evaluate the time dependence of the energy momentum tensor and the fundamental string charge density associated with this solution. The final decay product can be interpreted as a combination of stretched fundamental strings and tachyon matter.Comment: 35 pages, LaTe

New insights into the genetic etiology of Alzheimer's disease and related dementias

Characterization of the genetic landscape of Alzheimer's disease (AD) and related dementias (ADD) provides a unique opportunity for a better understanding of the associated pathophysiological processes. We performed a two-stage genome-wide association study totaling 111,326 clinically diagnosed/'proxy' AD cases and 677,663 controls. We found 75 risk loci, of which 42 were new at the time of analysis. Pathway enrichment analyses confirmed the involvement of amyloid/tau pathways and highlighted microglia implication. Gene prioritization in the new loci identified 31 genes that were suggestive of new genetically associated processes, including the tumor necrosis factor alpha pathway through the linear ubiquitin chain assembly complex. We also built a new genetic risk score associated with the risk of future AD/dementia or progression from mild cognitive impairment to AD/dementia. The improvement in prediction led to a 1.6- to 1.9-fold increase in AD risk from the lowest to the highest decile, in addition to effects of age and the APOE ε4 allele

A genome-wide gene-environment interaction study of breast cancer risk for women of European ancestry

Background Genome-wide studies of gene–environment interactions (G×E) may identify variants associated with disease risk in conjunction with lifestyle/environmental exposures. We conducted a genome-wide G×E analysis of ~ 7.6 million common variants and seven lifestyle/environmental risk factors for breast cancer risk overall and for estrogen receptor positive (ER +) breast cancer. Methods Analyses were conducted using 72,285 breast cancer cases and 80,354 controls of European ancestry from the Breast Cancer Association Consortium. Gene–environment interactions were evaluated using standard unconditional logistic regression models and likelihood ratio tests for breast cancer risk overall and for ER + breast cancer. Bayesian False Discovery Probability was employed to assess the noteworthiness of each SNP-risk factor pairs. Results Assuming a 1 × 10–5 prior probability of a true association for each SNP-risk factor pairs and a Bayesian False Discovery Probability < 15%, we identified two independent SNP-risk factor pairs: rs80018847(9p13)-LINGO2 and adult height in association with overall breast cancer risk (ORint = 0.94, 95% CI 0.92–0.96), and rs4770552(13q12)-SPATA13 and age at menarche for ER + breast cancer risk (ORint = 0.91, 95% CI 0.88–0.94). Conclusions Overall, the contribution of G×E interactions to the heritability of breast cancer is very small. At the population level, multiplicative G×E interactions do not make an important contribution to risk prediction in breast cancer