The Signature Triality of Majorana-Weyl Spacetimes

Higher dimensional Majorana-Weyl spacetimes present space-time dualities which are induced by the Spin(8) triality automorphisms. Different signature versions of theories such as 10-dimensional SYM's, superstrings, five-branes, F-theory, are shown to be interconnected via the S_3 permutation group. Bilinear and trilinear invariants under space-time triality are introduced and their possible relevance in building models possessing a space-versus-time exchange symmetry is discussed. Moreover the Cartan's ``vector/chiral spinor/antichiral spinor" triality of SO(8) and SO(4,4) is analyzed in detail and explicit formulas are produced in a Majorana-Weyl basis. This paper is the extended version of hep-th/9907148.Comment: 28 pages, LaTex. Extended version of hep-th/990714

Option Pricing Formulas based on a non-Gaussian Stock Price Model

Options are financial instruments that depend on the underlying stock. We explain their non-Gaussian fluctuations using the nonextensive thermodynamics parameter $q$. A generalized form of the Black-Scholes (B-S) partial differential equation, and some closed-form solutions are obtained. The standard B-S equation ($q=1$) which is used by economists to calculate option prices requires multiple values of the stock volatility (known as the volatility smile). Using $q=1.5$ which well models the empirical distribution of returns, we get a good description of option prices using a single volatility.Comment: final version (published

From p-branes to Cosmology

We study the relationship between static p-brane solitons and cosmological solutions of string theory or M-theory. We discuss two different ways in which extremal p-branes can be generalised to non-extremal ones, and show how wide classes of recently discussed cosmological models can be mapped into non-extremal p-brane solutions of one of these two kinds. We also extend previous discussions of cosmological solutions to include some that make use of cosmological-type terms in the effective action that can arise from the generalised dimensional reduction of string theory or M-theory.Comment: Latex, 24 pages, no figur

Time-like T-duality algebra

When compactifying M- or type II string-theories on tori of indefinite space-time signature, their low energy theories involve sigma models on E_{n(n)}/H_n, where H_n is a not necessarily compact subgroup of E_{n(n)} whose complexification is identical to the complexification of the maximal compact subgroup of E_{n(n)}. We discuss how to compute the group H_n. For finite dimensional E_{n(n)}, a formula derived from the theory of real forms of E_n algebra's gives the possible groups immediately. A few groups that have not appeared in the literature are found. For n=9,10,11 we compute and describe the relevant real forms of E_n and H_n. A given H_n can correspond to multiple signatures for the compact torus. We compute the groups H_n for all compactifications of M-, M*-, and M'-theories, and type II-, II*- and II'-theories on tori of arbitrary signature, and collect them in tables that outline the dualities between them. In an appendix we list cosets G/H, with G split and H a subgroup of G, that are relevant to timelike toroidal compactifications and oxidation of theories with enhanced symmetries.Comment: LaTeX, 37 pages, 1 eps-figure, uses JHEP.cls; v2. corrected typo's in tables 16 and 17, minor changes to tex

A Survey of Local Optical Committees (LOCs) involved in Cataract Pathways within the London Region

Purpose: Cataract enhanced service (direct referral) schemes have been in existence for over 12 years. Such schemes make better use of the primary care practitioner's professional expertise and have the potential to reduce costs and provide an improved patient pathway. Surprisingly little has been published about these schemes, hence there is a lack of evidence to inform local decision making about existing and future services. The aim of this study was to provide more evidence by surveying the Local Optical Committees (LOCs) to obtain their views on their involvement or lack of involvement in cataract enhanced service schemes in the London region. Secondary aims were to compare how schemes operate and determine why schemes do not exist in some areas. Method: A structured survey of London’s 14 LOCs was carried out on two occasions (2007 and 2012). LOCs were contacted via e-mail, telephone or written letter. Some supporting information was obtained from PCTs. All data were analysed qualitatively. Results: In 2007, only two out of the 10 LOCs that had participated in the 2005 Cataract Choose and Book scheme were involved in running a full direct referral scheme. This had risen to six by 2012 with a total of 11 LOCs having participated in a trial/pilot scheme by that date. The remaining three LOCs have never participated in a scheme. Although there are similarities across schemes (e.g. requirement for accreditation, a referral fee etc), marked differences were found in patient booking arrangements, requirements during initial assessment and post-operative assessment. The percentage of LOCs involved in full schemes in the London region (43%) is lower than for the rest of England (69%). Where trial/pilot schemes had run but no full scheme had been implemented the major reasons reported were: lack of central funding; the schemes were only feasibility studies; and the requirement for a Unique Booking Reference Number (UBRN) for the Choose and Book process. Conclusions: Enhanced cataract service schemes do not always develop into full schemes even if the trial/pilot scheme has been deemed successful. Schemes may have a more prominent role in future with requirements on Clinical Commissioning Groups to provide an improved patient experience within tighter financial constraints. The co-ordinating activity across England of the Local Optical Committee Support Unit (LOCSU) and the newly formed Local Professional Networks for Eyecare should help increase uniformity of approach. All established cataract schemes will need to be re-procured during 2013/14 if they are to continue without interruption

Superspace formulation of general massive gauge theories and geometric interpretation of mass-dependent BRST symmetries

A superspace formulation is proposed for the osp(1,2)-covariant Lagrangian quantization of general massive gauge theories. The superalgebra os0(1,2) is considered as subalgebra of sl(1,2); the latter may be considered as the algebra of generators of the conformal group in a superspace with two anticommuting coordinates. The mass-dependent (anti)BRST symmetries of proper solutions of the quantum master equations in the osp(1,2)-covariant formalism are realized in that superspace as invariance under translations combined with mass-dependent special conformal transformations. The Sp(2) symmetry - in particular the ghost number conservation - and the "new ghost number" conservation are realized as invariance under symplectic rotations and dilatations, respectively. The transformations of the gauge fields - and of the full set of necessarily required (anti)ghost and auxiliary fields - under the superalgebra sl(1,2) are determined both for irreducible and first-stage reducible theories with closed gauge algebra.Comment: 35 pages, AMSTEX, precision of reference

Duality Invariant M-theory: Gauged supergravities and Scherk-Schwarz reductions

We consider the reduction of the duality invariant approach to M-theory by a U-duality group valued Scherk-Schwarz twist. The result is to produce potentials for gauged supergravities that are normally associated with non-geometric compactifications. The local symmetry reduces to gauge transformations with the gaugings exactly matching those of the embedding tensor approach to gauged supergravity. Importantly, this approach now includes a nontrivial dependence of the fields on the extra coordinates of the extended space.Comment: 22 pages Latex; v2: typos corrected and references adde

Asymmetric Orbifolds, Non-Geometric Fluxes and Non-Commutativity in Closed String Theory

In this paper we consider a class of exactly solvable closed string flux backgrounds that exhibit non-commutativity in the closed string coordinates. They are realized in terms of freely-acting asymmetric Z_N-orbifolds, which are themselves close relatives of twisted torus fibrations with elliptic Z_N-monodromy (elliptic T-folds). We explicitly construct the modular invariant partition function of the models and derive the non-commutative algebra in the string coordinates, which is exact to all orders in {\alpha}'. Finally, we relate these asymmetric orbifold spaces to inherently stringy Scherk-Schwarz backgrounds and non-geometric fluxes.Comment: 30 page

Millimeter polarisation of the protoplanetary nebula OH 231.8+4.2: A follow-up study with CARMA

In order to investigate the characteristics and influence of the magnetic field in evolved stars, we performed a follow-up investigation of our previous submillimeter analysis of the proto-planetary nebula (PPN) OH 231.8+4.2 (Sabin et al. 2014), this time at 1.3mm with the CARMA facility in polarisation mode for the purpose of a multi-scale analysis. OH 231.8+4.2 was observed at ~2.5" resolution and we detected polarised emission above the 3-sigma threshold (with a mean polarisation fraction of 3.5 %). The polarisation map indicates an overall organised magnetic field within the nebula. The main finding in this paper is the presence of a structure mostly compatible with an ordered toroidal component that is aligned with the PPN's dark lane. We also present some alternative magnetic field configuration to explain the structure observed. These data complete our previous SMA submillimeter data for a better investigation and understanding of the magnetic field structure in OH 231.8+4.2.Comment: 7 pages, 5 figures, 2 tables. Accepted for publication in MNRA

Stiffness and energy losses in cylindrically symmetric superconductor levitating systems

Stiffness and hysteretic energy losses are calculated for a magnetically levitating system composed of a type-II superconductor and a permanent magnet when a small vibration is produced in the system. We consider a cylindrically symmetric configuration with only vertical movements and calculate the current profiles under the assumption of the critical state model. The calculations, based on magnetic energy minimization, take into account the demagnetization fields inside the superconductor and the actual shape of the applied field. The dependence of stiffness and hysteretic energy losses upon the different important parameters of the system such as the superconductor aspect ratio, the relative size of the superconductor-permanent magnet, and the critical current of the superconductor are all systematically studied. Finally, in view of the results, we provide some trends on how a system such as the one studied here could be designed in order to optimize both the stiffness and the hysteretic losses.Comment: 8 pages; 8 figure