Global aspects of the space of 6D N = 1 supergravities

We perform a global analysis of the space of consistent 6D quantum gravity theories with N = 1 supersymmetry, including models with multiple tensor multiplets. We prove that for theories with fewer than T = 9 tensor multiplets, a finite number of distinct gauge groups and matter content are possible. We find infinite families of field combinations satisfying anomaly cancellation and admitting physical gauge kinetic terms for T > 8. We find an integral lattice associated with each apparently-consistent supergravity theory; this lattice is determined by the form of the anomaly polynomial. For models which can be realized in F-theory, this anomaly lattice is related to the intersection form on the base of the F-theory elliptic fibration. The condition that a supergravity model have an F-theory realization imposes constraints which can be expressed in terms of this lattice. The analysis of models which satisfy known low-energy consistency conditions and yet violate F-theory constraints suggests possible novel constraints on low-energy supergravity theories.Comment: 41 pages, 1 figur

6D supergravity without tensor multiplets

We systematically investigate the finite set of possible gauge groups and matter content for N = 1 supergravity theories in six dimensions with no tensor multiplets, focusing on nonabelian gauge groups which are a product of SU(N) factors. We identify a number of models which obey all known low-energy consistency conditions, but which have no known string theory realization. Many of these models contain novel matter representations, suggesting possible new string theory constructions. Many of the most exotic matter structures arise in models which precisely saturate the gravitational anomaly bound on the number of hypermultiplets. Such models have a rigid symmetry structure, in the sense that there are no moduli which leave the full gauge group unbroken.Comment: 31 pages, latex; v2, v3: minor corrections, references adde

Two-Centered Magical Charge Orbits

We determine the two-centered generic charge orbits of magical N = 2 and maximal N = 8 supergravity theories in four dimensions. These orbits are classified by seven U-duality invariant polynomials, which group together into four invariants under the horizontal symmetry group SL(2,R). These latter are expected to disentangle different physical properties of the two-centered black-hole system. The invariant with the lowest degree in charges is the symplectic product (Q1,Q2), known to control the mutual non-locality of the two centers.Comment: 1+17 pages, 1 Table; v2: Eq. (3.23) corrected; v3: various refinements in text and formulae, caption of Table 1 expanded, Footnote and Refs. added. To appear on JHE

Spin-2 spectrum of defect theories

We study spin-2 excitations in the background of the recently-discovered type-IIB solutions of D'Hoker et al. These are holographically-dual to defect conformal field theories, and they are also of interest in the context of the Karch-Randall proposal for a string-theory embedding of localized gravity. We first generalize an argument by Csaki et al to show that for any solution with four-dimensional anti-de Sitter, Poincare or de Sitter invariance the spin-2 excitations obey the massless scalar wave equation in ten dimensions. For the interface solutions at hand this reduces to a Laplace-Beltrami equation on a Riemann surface with disk topology, and in the simplest case of the supersymmetric Janus solution it further reduces to an ordinary differential equation known as Heun's equation. We solve this equation numerically, and exhibit the spectrum as a function of the dilaton-jump parameter $\Delta\phi$. In the limit of large $\Delta\phi$ a nearly-flat linear-dilaton dimension grows large, and the Janus geometry becomes effectively five-dimensional. We also discuss the difficulties of localizing four-dimensional gravity in the more general backgrounds with NS5-brane or D5-brane charge, which will be analyzed in detail in a companion paper.Comment: 41 pages, 6 figure

Matrix Norms, BPS Bounds and Marginal Stability in N=8 Supergravity

We study the conditions of marginal stability for two-center extremal black holes in N-extended supergravity in four dimensions, with particular emphasis on the N=8 case. This is achieved by exploiting triangle inequalities satisfied by matrix norms. Using different norms and relative bounds among them, we establish the existence of marginal stability and split attractor flows both for BPS and some non-BPS solutions. Our results are in agreement with previous analysis based on explicit construction of multi-center solutions.Comment: 1+15 pages; v2: some new formulas added and misprints corrected; v3: typos fixed, various refinements, Sec. 2.4 rewritten; to appear on JHE

Citizenship:Contrasting Dynamics at the Interface of Integration and Constitutionalism

EUDO Citizenship ObservatoryThis paper explores the different ways in which citizenship has played a role in polity formation in the context of the European Union. It focuses on both the ‘integration’ and the ‘constitution’ dimensions. The paper thus has two substantive sections. The first addresses the role of citizenship of the Union, examining the dynamic relationship between this concept, the role of the Court of Justice, and the free movement dynamic of EU law. The second turns to citizenship in the Union, looking at some recent political developments under which concepts of citizenship, and democratic membership as a key dimension of citizenship, have been given greater prominence. One key finding of the paper is that there is a tension between citizenship of the Union, as part of the EU's ‘old’ incremental constitutionalism based on the constitutionalisation of the existing Treaties, and citizenship in the Union, where the possibilities of a ‘new’ constitutionalism based on renewed constitutional documents have yet to be fully realise

Constraints on 6D Supergravity Theories with Abelian Gauge Symmetry

We study six-dimensional N=(1,0) supergravity theories with abelian, as well as non-abelian, gauge group factors. We show that for theories with fewer than nine tensor multiplets, the number of possible combinations of gauge groups - including abelian factors - and non-abelian matter representations is finite. We also identify infinite families of theories with distinct U(1) charges that cannot be ruled out using known quantum consistency conditions, though only a finite subset of these can arise from known string constructions.Comment: 49 pages, latex; v2: minor corrections, references added; v3: minor correction

Mapping Differentiation under Mixed Culture Conditions Reveals a Tunable Continuum of T Cell Fates

Cell differentiation is typically directed by external signals that drive opposing regulatory pathways. Studying differentiation under polarizing conditions, with only one input signal provided, is limited in its ability to resolve the logic of interactions between opposing pathways. Dissection of this logic can be facilitated by mapping the system's response to mixtures of input signals, which are expected to occur in vivo, where cells are simultaneously exposed to various signals with potentially opposing effects. Here, we systematically map the response of naïve T cells to mixtures of signals driving differentiation into the Th1 and Th2 lineages. We characterize cell state at the single cell level by measuring levels of the two lineage-specific transcription factors (T-bet and GATA3) and two lineage characteristic cytokines (IFN-γ and IL-4) that are driven by these transcription regulators. We find a continuum of mixed phenotypes in which individual cells co-express the two lineage-specific master regulators at levels that gradually depend on levels of the two input signals. Using mathematical modeling we show that such tunable mixed phenotype arises if autoregulatory positive feedback loops in the gene network regulating this process are gradual and dominant over cross-pathway inhibition. We also find that expression of the lineage-specific cytokines follows two independent stochastic processes that are biased by expression levels of the master regulators. Thus, cytokine expression is highly heterogeneous under mixed conditions, with subpopulations of cells expressing only IFN-γ, only IL-4, both cytokines, or neither. The fraction of cells in each of these subpopulations changes gradually with input conditions, reproducing the continuous internal state at the cell population level. These results suggest a differentiation scheme in which cells reflect uncertainty through a continuously tuneable mixed phenotype combined with a biased stochastic decision rather than a binary phenotype with a deterministic decision

Altered Resting State in Diabetic Neuropathic Pain

BACKGROUND: The spontaneous component of neuropathic pain (NP) has not been explored sufficiently with neuroimaging techniques, given the difficulty to coax out the brain components that sustain background ongoing pain. Here, we address for the first time the correlates of this component in an fMRI study of a group of eight patients suffering from diabetic neuropathic pain and eight healthy control subjects. Specifically, we studied the functional connectivity that is associated with spontaneous neuropathic pain with spatial independent component analysis (sICA). PRINCIPAL FINDINGS: Functional connectivity analyses revealed a cortical network consisting of two anti-correlated patterns: one includes the left fusiform gyrus, the left lingual gyrus, the left inferior temporal gyrus, the right inferior occipital gyrus, the dorsal anterior cingulate cortex bilaterally, the pre and postcentral gyrus bilaterally, in which its activity is correlated negatively with pain and positively with the controls; the other includes the left precuneus, dorsolateral prefrontal, frontopolar cortex (both bilaterally), right superior frontal gyrus, left inferior frontal gyrus, thalami, both insulae, inferior parietal lobuli, right mammillary body, and a small area in the left brainstem, in which its activity is correlated positively with pain and negatively with the controls. Furthermore, a power spectra analyses revealed group differences in the frequency bands wherein the sICA signal was decomposed: patients' spectra are shifted towards higher frequencies. CONCLUSION: In conclusion, we have characterized here for the first time a functional network of brain areas that mark the spontaneous component of NP. Pain is the result of aberrant default mode functional connectivity