On the Poisson-Lie T-plurality of boundary conditions

Conditions for the gluing matrix defining consistent boundary conditions of two-dimensional nonlinear sigma-models are analyzed and reformulated. Transformation properties of the right-invariant fields under Poisson-Lie T-plurality are used to derive a formula for the transformation of the boundary conditions. Examples of transformation of D-branes in two and three dimensions are presented. We investigate obstacles arising in this procedure and propose possible solutions.Comment: 25 pages, LaTeX; major revision, discussion of boundary fields added; author's version of the published pape

N=1 supersymmetric sigma model with boundaries, I

We study an N=1 two-dimensional non-linear sigma model with boundaries representing, e.g., a gauge fixed open string. We describe the full set of boundary conditions compatible with N=1 superconformal symmetry. The problem is analyzed in two different ways: by studying requirements for invariance of the action, and by studying the conserved supercurrent. We present the target space interpretation of these results, and identify the appearance of partially integrable almost product structures.Comment: 24 pages, LaTeX. v2: minor clarification in section 3.2, reference added. v3: section added on N=2 supersymmetry. v4: typos corrected, published versio

E8 Quiver Gauge Theory and Mirror Symmetry

We show that the Higgs branch of a four-dimensional Yang-Mills theory, with gauge and matter content summarised by an E_8 quiver diagram, is identical to the generalised Coulomb branch of a four-dimensional superconformal strongly coupled gauge theory with E_8 global symmetry. This is the final step in showing that there is a Higgs-Coulomb identity of this kind for each of the cases {0}, A_1, A_2, D_4, E_6, E_7 and E_8. This series of equivalences suggests the existence of a mirror symmetry between the quiver theories and the strongly coupled theories. We also discuss how to interpret the parameters of the quiver gauge theory in terms of the Hanany-Witten picture.Comment: 19 pages, 3 figures, references adde

Worldsheet boundary conditions in Poisson-Lie T-duality

We apply canonical Poisson-Lie T-duality transformations to bosonic open string worldsheet boundary conditions, showing that the form of these conditions is invariant at the classical level, and therefore they are compatible with Poisson-Lie T-duality. In particular the conditions for conformal invariance are automatically preserved, rendering also the dual model conformal. The boundary conditions are defined in terms of a gluing matrix which encodes the properties of D-branes, and we derive the duality map for this matrix. We demonstrate explicitly the implications of this map for D-branes in two non-Abelian Drinfel'd doubles.Comment: 20 pages, Latex; v2: typos and wording corrected, references added; v3: three-dimensional example added, reference added, discussion clarified, published versio

D-branes and doubled geometry

We define the open string version of the nonlinear sigma model on doubled geometry introduced by Hull and Reid-Edwards, and derive its boundary conditions. These conditions include the restriction of D-branes to maximally isotropic submanifolds as well as a compatibility condition with the Lie algebra structure on the doubled space. We demonstrate a systematic method to derive and classify D-branes from the boundary conditions, in terms of embeddings both in the doubled geometry and in the physical target space. We apply it to the doubled three-torus with constant H-flux and find D0-, D1-, and D2-branes, which we verify transform consistently under T-dualities mapping the system to f-, Q- and R-flux backgrounds

T-duality for the sigma model with boundaries

We derive the most general local boundary conditions necessary for T-duality to be compatible with superconformal invariance of the two-dimensional N=1 supersymmetric nonlinear sigma model with boundaries. To this end, we construct a consistent gauge invariant parent action by gauging a U(1) isometry, with and without boundary interactions. We investigate the behaviour of the boundary conditions under T-duality, and interpret the results in terms of D-branes.Comment: 48 pages, LaTeX, v2: typos corrected, references adde

A Genome-Wide Pharmacogenetic Study of Growth Hormone Responsiveness

Individual patients vary in their response to growth hormone (GH). No large-scale genome-wide studies have looked for genetic predictors of GH responsiveness. To identify genetic variants associated with GH responsiveness. Genome-wide association study (GWAS). Cohorts from multiple academic centers and a clinical trial. A total of 614 individuals from 5 short stature cohorts receiving GH: 297 with idiopathic short stature, 276 with isolated GH deficiency, and 65 born small for gestational age. Association of more than 2 million variants was tested. Primary analysis: individual single nucleotide polymorphism (SNP) association with first-year change in height standard deviation scores. Secondary analyses: SNP associations in clinical subgroups adjusted for clinical variables; association of polygenic score calculated from 697 genome-wide significant height SNPs with GH responsiveness. No common variant associations reached genome-wide significance in the primary analysis. The strongest suggestive signals were found near the B4GALT4 and TBCE genes. After meta-analysis including replication data, signals at several loci reached or retained genome-wide significance in secondary analyses, including variants near ST3GAL6. There was no significant association with variants previously reported to be associated with GH response nor with a polygenic predicted height score. We performed the largest GWAS of GH responsiveness to date. We identified 2 loci with a suggestive effect on GH responsiveness in our primary analysis and several genome-wide significant associations in secondary analyses that require further replication. Our results are consistent with a polygenic component to GH responsiveness, likely distinct from the genetic regulators of adult height

Double Field Theory for Double D-branes

We consider Hull's doubled formalism for open strings on D-branes in flat space and construct the corresponding effective double field theory. We show that the worldsheet boundary conditions of the doubled formalism describe in a unified way a T-dual pair of D-branes, which we call double D-branes. We evaluate the one-loop beta function for the boundary gauge coupling and then obtain the effective field theory for the double D-branes. The effective field theory is described by a DBI action of double fields. The T-duality covariant form of this DBI action is thus a kind of "master" action, which describes all the double D-brane configurations related by T-duality transformations. We discuss a number of aspects of this effective theory.Comment: Latex, 1+33 pages. v2 with minor corrections, a new reference added. v3 a typo correcte