Supersymmetric Extension of Hopf Maps: N=4 sigma-models and the S^3 -> S^2 Fibration

We discuss four off-shell N=4 D=1 supersymmetry transformations, their associated one-dimensional sigma-models and their mutual relations. They are given by I) the (4,4)_{lin} linear supermultiplet (supersymmetric extension of R^4), II) the (3,4,1)_{lin} linear supermultiplet (supersymmetric extension of R^3), III) the (3,4,1)_{nl} non-linear supermultiplet living on S^3 and IV) the (2,4,2)_{nl} non-linear supermultiplet living on S^2. The I -> II map is the supersymmetric extension of the R^4 -> R^3 bilinear map, while the II -> IV map is the supersymmetric extension of the S^3 -> S^2 first Hopf fibration. The restrictions on the S^3, S^2 spheres are expressed in terms of the stereographic projections. The non-linear supermultiplets, whose supertransformations are local differential polynomials, are not equivalent to the linear supermultiplets with the same field content. The sigma-models are determined in terms of an unconstrained prepotential of the target coordinates. The Uniformization Problem requires solving an inverse problem for the prepotential. The basic features of the supersymmetric extension of the second and third Hopf maps are briefly sketched. Finally, the Schur's lemma (i.e. the real, complex or quaternionic property) is extended to all minimal linear supermultiplets up to N<=8.Comment: 24 page

On the Construction and the Structure of Off-Shell Supermultiplet Quotients

Recent efforts to classify representations of supersymmetry with no central charge have focused on supermultiplets that are aptly depicted by Adinkras, wherein every supersymmetry generator transforms each component field into precisely one other component field or its derivative. Herein, we study gauge-quotients of direct sums of Adinkras by a supersymmetric image of another Adinkra and thus solve a puzzle from Ref.[2]: The so-defined supermultiplets do not produce Adinkras but more general types of supermultiplets, each depicted as a connected network of Adinkras. Iterating this gauge-quotient construction then yields an indefinite sequence of ever larger supermultiplets, reminiscent of Weyl's construction that is known to produce all finite-dimensional unitary representations in Lie algebras.Comment: 20 pages, revised to clarify the problem addressed and solve

On Graph-Theoretic Identifications of Adinkras, Supersymmetry Representations and Superfields

In this paper we discuss off-shell representations of N-extended supersymmetry in one dimension, ie, N-extended supersymmetric quantum mechanics, and following earlier work on the subject codify them in terms of certain graphs, called Adinkras. This framework provides a method of generating all Adinkras with the same topology, and so also all the corresponding irreducible supersymmetric multiplets. We develop some graph theoretic techniques to understand these diagrams in terms of a relatively small amount of information, namely, at what heights various vertices of the graph should be "hung". We then show how Adinkras that are the graphs of N-dimensional cubes can be obtained as the Adinkra for superfields satisfying constraints that involve superderivatives. This dramatically widens the range of supermultiplets that can be described using the superspace formalism and organizes them. Other topologies for Adinkras are possible, and we show that it is reasonable that these are also the result of constraining superfields using superderivatives. The family of Adinkras with an N-cubical topology, and so also the sequence of corresponding irreducible supersymmetric multiplets, are arranged in a cyclical sequence called the main sequence. We produce the N=1 and N=2 main sequences in detail, and indicate some aspects of the situation for higher N.Comment: LaTeX, 58 pages, 52 illustrations in color; minor typos correcte

The Real Anatomy of Complex Linear Superfields

Recent work on classicication of off-shell representations of N-extended worldline supersymmetry without central charges has uncovered an unexpectedly vast number--trillions of even just (chromo)topology types--of so called adinkraic supermultiplets. Herein, we show by explicit analysis that a long-known but rarely used representation, the complex linear supermultiplet, is not adinkraic, cannot be decomposed locally, but may be reduced by means of a Wess-Zumino type gauge. This then indicates that the already unexpectedly vast number of adinkraic off-shell supersymmetry representations is but the proverbial tip of the iceberg.Comment: 21 pages, 4 figure

The Birmingham Boron Neutron Capture Therapy (BNCT) project : developments towards selective internal particle therapy

This paper will review progress on two aspects of the Birmingham BNCT project. Firstly on evaluation of the effects of high and low LET radiations when delivered simultaneously, and secondly on attempts to optimise delivery of the boron carrier compound BPA through pharmacokinetic studies. Simultaneous or non-simultaneous irradiations of V79 cells with alpha-particle and X-ray irradiations were performed. Alpha doses of 2 and 2.5 Gy were chosen and the impact on survival when delivered separately or simultaneously with variable doses of X-rays was evaluated. The pharmacokinetics of the delivery of a new formulation of BPA (BPA-mannitol) are being investigated in brain tumour patients through a study with 2 × 2 design featuring intravenous and intracarotid artery infusion of BPA, with or without a mannitol bolus. On the combined effect of low and high LET radiations, a synergistic effect was observed when alpha and X-ray doses are delivered simultaneously. The effect is only present at the 2.5 Gy alpha dose and is a very substantial effect on both the shape of the survival curve and the level of cell killing. This indicates that the alpha component may have the effect of inhibiting the repair of damage from the low LET radiation dose delivered simultaneously. On the pharmacokinetics of BPA, data on the first three cohorts indicate that bioavailability of BPA in brain ECF is increased substantially through the addition of a mannitol bolus, as well as by the use of intracarotid artery route of infusion. In both cases, for some patients the levels after infusion approach those seen in blood, whereas the ECF levels for intravenous infusion without mannitol are typically less than 10% of the blood values

Perampanel in the general population and in people with intellectual disability: Differing responses

This is the author accepted manuscript. The final version is available under a Creative Commons Licence (https://creativecommons.org/licenses/by-nc-nd/4.0/) from the publisher via the DOI in this record.PURPOSE: There is a shortfall of suitably powered studies to provide evidence for safe prescribing of AEDs to people with Intellectual Disability (ID). We report clinically useful information on differences in response to Perampanel (PER) adjunctive treatment for refractory epilepsy between ID sub-groups and general population from the UK Ep-ID Research Register. METHOD: Pooled retrospective case notes data of consented people with epilepsy (PWE) prescribed PER from 6 UK centres was classified as per WHO guidance into groups of moderate -profound ID, mild ID and General population. Demographics, concomitant AEDs, starting and maximum dosage, exposure length, adverse effects, dropout rates, seizure type and frequency were collected. Group differences were reported as odds ratios estimated from univariable logistic regression models. RESULTS: Of the 144 PWE (General population 71, Mild ID 48, Moderate to profound ID 48) examined the association between withdrawal and ID type was marginally statistically significant (p=0.07). Moderate to profound ID PWE were less likely to come off PER compared to mild ID (OR=0.19, CI=0.04-0.92, p=0.04). Differences in mental health side effects by groups was marginally statistically significant (p=0.06). Over 50% seizure improvement was seen in 11% of General population, 24% mild ID and 26% Moderate to profound ID. CONCLUSIONS: PER seems safe in PWE with ID. It is better tolerated by PWE with Moderate to profound ID than PWE with higher functioning. Caution is advised when history of mental health problems is present. The standardised approach of the Ep-ID register UK used confirms that responses to AEDs by different ID groups vary between themselves and General population

On the Decomposition of Clifford Algebras of Arbitrary Bilinear Form

Clifford algebras are naturally associated with quadratic forms. These algebras are Z_2-graded by construction. However, only a Z_n-gradation induced by a choice of a basis, or even better, by a Chevalley vector space isomorphism Cl(V) \bigwedge V and an ordering, guarantees a multi-vector decomposition into scalars, vectors, tensors, and so on, mandatory in physics. We show that the Chevalley isomorphism theorem cannot be generalized to algebras if the Z_n-grading or other structures are added, e.g., a linear form. We work with pairs consisting of a Clifford algebra and a linear form or a Z_n-grading which we now call 'Clifford algebras of multi-vectors' or 'quantum Clifford algebras'. It turns out, that in this sense, all multi-vector Clifford algebras of the same quadratic but different bilinear forms are non-isomorphic. The usefulness of such algebras in quantum field theory and superconductivity was shown elsewhere. Allowing for arbitrary bilinear forms however spoils their diagonalizability which has a considerable effect on the tensor decomposition of the Clifford algebras governed by the periodicity theorems, including the Atiyah-Bott-Shapiro mod 8 periodicity. We consider real algebras Cl_{p,q} which can be decomposed in the symmetric case into a tensor product Cl_{p-1,q-1} \otimes Cl_{1,1}. The general case used in quantum field theory lacks this feature. Theories with non-symmetric bilinear forms are however needed in the analysis of multi-particle states in interacting theories. A connection to q-deformed structures through nontrivial vacuum states in quantum theories is outlined.Comment: 25 pages, 1 figure, LaTeX, {Paper presented at the 5th International Conference on Clifford Algebras and their Applications in Mathematical Physics, Ixtapa, Mexico, June 27 - July 4, 199

The VLT-FLAMES Tarantula Survey III: A very massive star in apparent isolation from the massive cluster R136

VFTS 682 is located in an active star-forming region, at a projected distance of 29 pc from the young massive cluster R136 in the Tarantula Nebula of the Large Magellanic Cloud. It was previously reported as a candidate young stellar object, and more recently spectroscopically revealed as a hydrogen-rich Wolf-Rayet (WN5h) star. Our aim is to obtain the stellar properties, such as its intrinsic luminosity, and to investigate the origin of VFTS 682. To this purpose, we model optical spectra from the VLT-FLAMES Tarantula Survey with the non-LTE stellar atmosphere code CMFGEN, as well as the spectral energy distribution from complementary optical and infrared photometry. We find the extinction properties to be highly peculiar (RV ~4.7), and obtain a surprisingly high luminosity log(L/Lsun) = 6.5 \pm 0.2, corresponding to a present-day mass of ~150Msun. The high effective temperature of 52.2 \pm 2.5kK might be explained by chemically homogeneous evolution - suggested to be the key process in the path towards long gamma-ray bursts. Lightcurves of the object show variability at the 10% level on a timescale of years. Such changes are unprecedented for classical Wolf-Rayet stars, and are more reminiscent of Luminous Blue Variables. Finally, we discuss two possibilities for the origin of VFTS 682: (i) the star either formed in situ, which would have profound implications for the formation mechanism of massive stars, or (ii) VFTS 682 is a slow runaway star that originated from the dense cluster R136, which would make it the most massive runaway known to date.Comment: 5 pages, 5 figures, accepted by A&A Letter

Ni spin switching induced by magnetic frustration in FeMn/Ni/Cu(001)

Abstract Epitaxially grown FeMn/Ni/Cu(001) films are investigated by Photoemission Electron Microscopy and Magneto-Optic Kerr Effect. We find that as the FeMn overlayer changes from paramagnetic to antiferromagnetic state, it could switch the ferromagnetic Ni spin direction from out-of-plane to in-plane direction of the film. This phenomenon reveals a new mechanism of creating magnetic anisotropy and is attributed to the out-of-plane spin frustration at the FeMn-Ni interface