Supersymmetric Gauge Theories from Branes and Orientifold Six-planes

We study brane configurations in the presence of orientifold six-planes. After deriving the curves for N=2 supersymmetric SU(Nc) gauge theories with one flavor in the symmetric or antisymmetric representation and Nf fundamental flavors, we rotate the brane configuration, reducing the supersymmetry to N=1. For the case of an antisymmetric flavor and less than two fundamental flavors, nonperturbative effects lead to a brane configuration that is topologically a torus. Using the description of the orientifold six-planes as Dn singularities we discuss the Higgs branches for N=2 brane configurations with Sp/SO gauge groups and the related N=1 theories with tensor representations.Comment: 30 pages (harvmac b-mode), 5 figures, (v2 minor corrections), (v3 sign error corrected

Duality of Chiral N=1 Supersymmetric Gauge Theories via Branes

Using a six-orientifold on top of a NS-fivebrane we construct a chiral N=1 supersymmetric gauge theory in four dimensions with gauge group SU(N_c) and matter in the symmetric, antisymmetric and (anti)fundamental representations. Anomaly cancellation is fulfilled by the requirement of a smooth RR 7-form charge distribution and leads us to the introduction of 8 half D-sixbranes ending on the NS-fivebrane. We obtain the dual model from branes by a linking number argument. We check explicitly the 't Hooft anomaly matching conditions and the map between deformations in the original and the dual model.Comment: 16 pages, 2 figures, TeX, harvmac, table

Higgs-Yukawa model on the lattice

We present results from two projects on lattice calculations for the Higgs-Yukawa model. First we report progress on the search of first-order thermal phase transitions in the presence of a dimension-six operator, with the choices of bare couplings that lead to viable phenomenological predictions. In this project the simulations are performed using overlap fermions to implement the required chiral symmetry. Secondly, our study for applying finite-size scaling techniques near the Gaussian fixed point of the Higgs-Yukawa model is presented. We discuss the analytical formulae for the Higgs Yukawa model and show results for a first numerical study in the pure $O(4)$ scalar sector of the theory.Comment: 8 pages, 4 figures; Contribution to the proceedings of the 35th International Symposium on Lattice Field Theory, 18 - 24 June 2017, Granada, Spai

The MacLane class and the Eremenko-Lyubich class

In 1970 G. R. MacLane asked if it is possible for a locally univalent function in the class A to have an arc tract. This question remains open, but several results about it have been given. We significantly strengthen these results, in particular replacing the condition of local univalence by the more general condition that the set of critical values is bounded. Also, we adapt a recent powerful technique of C. J. Bishop in order to show that there is a function in the Eremenko-Lyubich class for the disc that is not in the class A

454 screening of individual MHC variation in an endemic island passerine

Genes of the major histocompatibility complex (MHC) code for receptors that are central to the adaptive immune response of vertebrates. These genes are therefore important genetic markers with which to study adaptive genetic variation in the wild. Next-generation sequencing (NGS) has increasingly been used in the last decade to genotype the MHC. However, NGS methods are highly prone to sequencing errors, and although several methodologies have been proposed to deal with this, until recently there have been no standard guidelines for the validation of putative MHC alleles. In this study, we used the 454 NGS platform to screen MHC class I exon 3 variation in a population of the island endemic Berthelot’s pipit (Anthus berthelotii). We were able to characterise MHC genotypes across 309 individuals with high levels of repeatability. We were also able to determine alleles that had low amplification efficiencies, whose identification within individuals may thus be less reliable. At the population level we found lower levels of MHC diversity in Berthelot’s pipit than in its widespread continental sister species the tawny pipit (Anthus campestris), and observed trans-species polymorphism. Using the sequence data, we identified signatures of gene conversion and evidence of maintenance of functionally divergent alleles in Berthelot’s pipit. We also detected positive selection at 10 codons. The present study therefore shows that we have an efficient method for screening individual MHC variation across large datasets in Berthelot’s pipit, and provides data that can be used in future studies investigating spatio-temporal patterns and scales of selection on the MHC