6D SCFTs and phases of 5D theories

Starting from 6D superconformal field theories (SCFTs) realized via F-theory, we show how reduction on a circle leads to a uniform perspective on the phase structure of the resulting 5D theories, and their possible conformal fixed points. Using the correspon-dence between F-theory reduced on a circle and M-theory on the corresponding elliptically fibered Calabi-Yau threefold, we show that each 6D SCFT with minimal supersymmetry directly reduces to a collection of between one and four 5D SCFTs. Additionally, we find that in most cases, reduction of the tensor branch of a 6D SCFT yields a 5D generalization of a quiver gauge theory. These two reductions of the theory often correspond to different phases in the 5D theory which are in general connected by a sequence of flop transitions in the extended Kähler cone of the Calabi-Yau threefold. We also elaborate on the structure of the resulting conformal fixed points, and emergent flavor symmetries, as realized by M-theory on a canonical singularity

Assessment of Natural Resources Use for Sustainable Development - DPSIR Framework for Case Studies in Portsmouth and Thames Gateway, U.K.

This chapter reports on the uses of the DPSIR framework to assess the sustainability of the intertidal environments within the two UK case study areas, Portsmouth and Thames Gateway. It focuses on statutory conservation areas dominated by intertidal habitats. Two are located in Portsmouth (Portsmouth and Langstone Harbours) and four in the Thames Gateway (Benfleet Marshes, South Thames Estuary, Medway Estuary and the Swale in the Thames Gateway). Based on the reduction of a number of pressures and impacts observed in recent decades and the improvement of overall environmental quality, all six SSSIs are considered to be sustainable in the short and medium term. In the future, it is possible that the impacts of climate change, especially sea-level rise, might result in further reduction in the area and/or quality of intertidal habitats. Further integration between conservation and planning objectives (both for urban development and management of flood risk) at local level is needed to support the long-term sustainability of intertidal habitats

6D SCFTs and gravity

We study how to couple a 6D superconformal field theory (SCFT) to gravity. In F-theory, the models in question are obtained working on the supersymmetric background $\mathbb{R}$ 5,1 × B where B is the base of a compact elliptically fibered Calabi-Yau threefold in which two-cycles have contracted to zero size. When the base has orbifold singularities, we find that the anomaly polynomial of the 6D SCFTs can be understood purely in terms of the intersection theory of fractional divisors: the anomaly coefficient vectors are identified with elements of the orbifold homology. This also explains why in certain cases, the SCFT can appear to contribute a “fraction of a hypermultiplet” to the anomaly polynomial. Quantization of the lattice of string charges also predicts the existence of additional light states beyond those captured by such fractional divisors. This amounts to a refinement to the lattice of divisors in the resolved geometry. We illustrate these general considerations with explicit examples, focusing on the case of F-theory on an elliptic Calabi-Yau threefold with base ${\mathrm{\mathbb{P}}}^2/{\mathbb{Z}}_3$

Migraine mediates the influence of C677T MTHFR genotypes on ischemic stroke risk with a stroke-subtype effect.

BACKGROUND AND PURPOSE: The objective was to investigate the role of C677T MTHFR polymorphism in migraine pathogenesis and in the migraine-ischemic stroke pathway. METHODS: A first genotype-migraine association study was conducted on 100 patients with migraine with aura (MA), 106 with migraine without aura (MO), and 105 subjects without migraine, which provided evidence in favor of association of the TT677 MTHFR genotype with increased risk of MA compared with both control subjects (OR, 2.48; 95% CI, 1.11 to 5.58) and patients with MO (OR, 2.21; 95% CI, 1.01 to 4.82). Based on these findings, mediational models of the genotype-migraine-stroke pathway were fitted on a group of 106 patients with spontaneous cervical artery dissection, 227 young patients whose ischemic stroke was unrelated to a spontaneous cervical artery dissection (noncervical artery dissection), and 187 control subjects, and a genotype-migraine partial mediation model was selected. RESULTS: Both migraine and the TT genotype were more strongly associated to the subgroup of patients with spontaneous cervical artery dissection (OR, 4.06; 95% CI, 1.63 to 10.02 for MA; OR, 5.45; 95% CI, 3.03 to 9.79 for MO; OR, 2.87; 95% CI, 1.45 to 5.68 for TT genotype) than to the subgroup of patients with noncervical artery dissection ischemic stroke (OR, 2.22; 95% CI, 1.00 to 4.96 for MA; OR, 1.81; 95% CI, 1.02 to 3.22 for TT genotype) as compared with controls. CONCLUSIONS: Migraine may act as mediator in the methylenetetrahydrofolate reductase-ischemic stroke pathway with a more prominent effect in the subgroup of patients with spontaneous artery dissection

Higher S-dualities and Shephard-Todd groups

Abstract: Seiberg and Witten have shown that in N=2$$\mathcal{N}=2$$ SQCD with Nf = 2Nc = 4 the S-duality group PSL2\u2124$$\mathrm{P}\mathrm{S}\mathrm{L}\left(2,\mathrm{\mathbb{Z}}\right)$$ acts on the flavor charges, which are weights of Spin(8), by triality. There are other N=2$$\mathcal{N}=2$$ SCFTs in which SU(2) SYM is coupled to strongly-interacting non-Lagrangian matter: their matter charges are weights of E6, E7 and E8 instead of Spin(8). The S-duality group PSL2\u2124$$\mathrm{P}\mathrm{S}\mathrm{L}\left(2,\mathrm{\mathbb{Z}}\right)$$ acts on these weights: what replaces Spin(8) triality for the E6, E7, E8root lattices? In this paper we answer the question. The action on the matter charges of (a finite central extension of) PSL2\u2124$$\mathrm{P}\mathrm{S}\mathrm{L}\left(2,\mathrm{\mathbb{Z}}\right)$$ factorizes trough the action of the exceptional Shephard-Todd groups G4 and G8 which should be seen as complex analogs of the usual triality group S3 43WeylA2$${\mathfrak{S}}_3\simeq \mathrm{Weyl}\left({A}_2\right)$$. Our analysis is based on the identification of S-duality for SU(2) gauge SCFTs with the group of automorphisms of the cluster category of weighted projective lines of tubular type. \ua9 2015, The Author(s)

On Arnold's 14 `exceptional' N=2 superconformal gauge theories

We study the four-dimensional superconformal N=2 gauge theories engineered by the Type IIB superstring on Arnold's 14 exceptional unimodal singularities (a.k.a. Arnold's strange duality list), thus extending the methods of 1006.3435 to singularities which are not the direct sum of minimal ones. In particular, we compute their BPS spectra in several `strongly coupled' chambers. From the TBA side, we construct ten new periodic Y-systems, providing additional evidence for the existence of a periodic Y-system for each isolated quasi-homogeneous singularity with $\hat c<2$ (more generally, for each N=2 superconformal theory with a finite BPS chamber whose chiral primaries have dimensions of the form N/l).Comment: 73 pages, 7 figure

Interaction between proatherosclerotic factors and right-to-left shunt on the risk of cryptogenic stroke: the Italian Project on Stroke in Young Adults.

Objective: To explore the interaction effects between cardiac interatrial right-to-left shunt (RLS) and proatherosclerotic factors on the risk of brain ischaemia. Design: Multicentre Italian caseecontrol study. Setting: University hospitals. Participants: 588 patients with cryptogenic stroke (CS) aged ≤45 years and 585 control subjects consecutively enrolled as part of the Italian Project on Stroke in Young Adults. Methods: Interaction effects between RLS and an individual proatherosclerotic score computed from the number of conventional vascular risk factors for the risk of CS were investigated. Data were examined by logistic regression models and expressed as interaction OR or interaction risk difference (RD). Results: CS risk increased with increasing number of proatherosclerotic factors in subjects without RLS (OR 2.73; 95% CI 1.98 to 3.76; RD +0.246; 95% CI +0.17 to +0.32; for subjects with one or more factors), but was higher in subjects with RLS and no additional proatherosclerotic factors (OR 5.14; 95% CI 3.49 to 7.58; RD +0.388; 95% CI +0.31 to +0.47) compared with subjects without RLS and no risk factors. Negative interaction and antagonistic effects between RLS and proatherosclerotic factors were observed (interaction OR 0.52; 95% CI 0.31 to 0.91; interaction RD -0.17; 95% CI -0.29 to -0.05). Conclusions: The influence of RLS on the risk of CS decreases with increasing number of atherosclerotic factors, and is highest when such factors are absent. Individual proatherosclerotic profiles may help to identify patients with CS whose patent foramen ovale is probably pathogenic

6D RG flows and nilpotent hierarchies

With the eventual aim of classifying renormalization group flows between 6D superconformal field theories (SCFTs), we study flows generated by the vevs of "conformal matter," a generalization of conventional hypermultiplets which naturally appear in the F-theory classification of 6D SCFTs. We consider flows in which the parent UV theory is (on its partial tensor branch) a linear chain of gauge groups connected by conformal matter, with one flavor group G at each end of the chain, and in which the symmetry breaking of the conformal matter at each end is parameterized by the orbit of a nilpotent element, i.e. T-brane data, of one of these flavor symmetries. Such nilpotent orbits admit a partial ordering, which is reflected in a hierarchy of IR fixed points. For each such nilpotent orbit, we determine the corresponding tensor branch for the resulting SCFT. An important feature of this algebraic approach is that it also allows us to systematically compute the unbroken flavor symmetries inherited from the parent UV theory.Comment: v2: 53 pages, 12 figures, clarifications added, typos correcte