Quantum gauge theories on noncommutative 3-d space

We consider a class of gauge invariant models on the noncommutative space $\mathbb{R}^3_\lambda$, a deformation of $\mathbb{R}^3$. Focusing on massless models with no linear $A_i$ dependence, we obtain noncommutative gauge models for which the computation of the propagator can be done in a convenient gauge. We find that the infrared singularity of the massless propagator disappears in the computation of the correlation functions. We show that massless gauge invariant models on $\mathbb{R}^3_\lambda$ have quantum instabilities of the vacuum, signaled by the occurrence of non vanishing 1-point functions for some but not all of the components of the gauge potential. The tadpole contribution to the effective action cannot be interpreted as a standard $\sigma$-term. Its global symmetry does not fit with the one of the classical action, reminiscent to an explicit global symmetry breaking term.Comment: 31 pages. Section 2 modified with two new subsections about derivations of the algebra and the integration measure. References adde

High-quality SNPs from genic regions highlight introgression patterns among European white oaks (Quercus petraea and Q. robur)

International audienceIn the post-genomics era, non-model species like most Fagaceae still lack operational diversity resources for population genomics studies. Sequence data were produced from over 800 gene fragments covering ~530 kb across the genic partition of European oaks, in a discovery panel of 25 individuals from western and central Europe (11 Quercus petraea, 13 Q. robur, one Q. ilex as an outgroup). Regions targeted represented broad functional categories potentially involved in species ecological preferences, and a random set of genes. Using a high-quality dedicated pipeline, we provide a detailed characterization of these genic regions, which included over 14500 polymorphisms, with ~12500 SNPs −218 being triallelic-, over 1500 insertion-deletions, and ~200 novel di- and tri-nucleotide SSR loci. This catalog also provides various summary statistics within and among species, gene ontology information, and standard formats to assist loci choice for genotyping projects. The distribution of nucleotide diversity (θπ) and differentiation (FST) across genic regions are also described for the first time in those species, with a mean n θπ close to ~0.0049 in Q. petraea and to ~0.0045 in Q. robur across random regions, and a mean FST ~0.13 across SNPs. The magnitude of diversity across genes is within the range estimated for long-term perennial outcrossers, and can be considered relatively high in the plant kingdom, with an estimate across the genome of 41 to 51 million SNPs expected in both species. Individuals with typical species morphology were more easily assigned to their corresponding genetic cluster for Q. robur than for Q. petraea, revealing higher or more recent introgression in Q. petraea and a stronger species integration in Q. robur in this particular discovery panel. We also observed robust patterns of a slightly but significantly higher diversity in Q. petraea, across a random gene set and in the abiotic stress functional category, and a heterogeneous landscape of both diversity and differentiation. To explain these patterns, we discuss an alternative and non-exclusive hypothesis of stronger selective constraints in Q. robur, the most pioneering species in oak forest stand dynamics, additionally to the recognized and documented introgression history in both species despite their strong reproductive barriers. The quality of the data provided here and their representativity in terms of species genomic diversity make them useful for possible applications in medium-scale landscape and molecular ecology projects. Moreover, they can serve as reference resources for validation purposes in larger-scale resequencing projects. This type of project is preferentially recommended in oaks in contrast to SNP array development, given the large nucleotide variation and the low levels of linkage disequilibrium revealed

Development and implementation of a highly-multiplexed SNP array for genetic mapping in maritime pine and comparative mapping with loblolly pine

<p>Abstract</p> <p>Background</p> <p>Single nucleotide polymorphisms (SNPs) are the most abundant source of genetic variation among individuals of a species. New genotyping technologies allow examining hundreds to thousands of SNPs in a single reaction for a wide range of applications such as genetic diversity analysis, linkage mapping, fine QTL mapping, association studies, marker-assisted or genome-wide selection. In this paper, we evaluated the potential of highly-multiplexed SNP genotyping for genetic mapping in maritime pine (<it>Pinus pinaster </it>Ait.), the main conifer used for commercial plantation in southwestern Europe.</p> <p>Results</p> <p>We designed a custom GoldenGate assay for 1,536 SNPs detected through the resequencing of gene fragments (707 <it>in vitro </it>SNPs/Indels) and from Sanger-derived Expressed Sequenced Tags assembled into a unigene set (829 <it>in silico </it>SNPs/Indels). Offspring from three-generation outbred (G2) and inbred (F2) pedigrees were genotyped. The success rate of the assay was 63.6% and 74.8% for <it>in silico </it>and <it>in vitro </it>SNPs, respectively. A genotyping error rate of 0.4% was further estimated from segregating data of SNPs belonging to the same gene. Overall, 394 SNPs were available for mapping. A total of 287 SNPs were integrated with previously mapped markers in the G2 parental maps, while 179 SNPs were localized on the map generated from the analysis of the F2 progeny. Based on 98 markers segregating in both pedigrees, we were able to generate a consensus map comprising 357 SNPs from 292 different loci. Finally, the analysis of sequence homology between mapped markers and their orthologs in a <it>Pinus taeda </it>linkage map, made it possible to align the 12 linkage groups of both species.</p> <p>Conclusions</p> <p>Our results show that the GoldenGate assay can be used successfully for high-throughput SNP genotyping in maritime pine, a conifer species that has a genome seven times the size of the human genome. This SNP-array will be extended thanks to recent sequencing effort using new generation sequencing technologies and will include SNPs from comparative orthologous sequences that were identified in the present study, providing a wider collection of anchor points for comparative genomics among the conifers.</p

An analytic regularisation scheme on curved space-times with applications to cosmological space-times

reserved3noWe develop a renormalisation scheme for time-ordered products in interacting field theories on curved space-times that consists of an analytic regularisation of Feynman amplitudes and a minimal subtraction of the resulting pole parts. This scheme is directly applicable to space-times with Lorentzian signature, manifestly generally covariant, invariant under any space-time isometries present, and constructed to all orders in perturbation theory. Moreover, the scheme correctly captures the nongeometric state-dependent contribution of Feynman amplitudes, and it is well suited for practical computations. To illustrate this last point, we compute explicit examples on a generic curved space-time and demonstrate how momentum space computations in cosmological space-times can be performed in our scheme. In this work, we discuss only scalar fields in four space-time dimensions, but we argue that the renormalisation scheme can be directly generalised to other space-time dimensions and field theories with higher spin as well as to theories with local gauge invariance.mixedGéré, Antoine; Hack, Thomas-Paul; Pinamonti, NicolaGere, ANTOINE NICOLAS ODILON; Hack, THOMAS PAUL; Pinamonti, Nicol