N = 3 chiral supergravity compatible with the reality condition and higher N chiral Lagrangian density

We obtain N = 3 chiral supergravity (SUGRA) compatible with the reality condition by applying the prescription of constructing the chiral Lagrangian density from the usual SUGRA. The $N = 3$ chiral Lagrangian density in first-order form, which leads to the Ashtekar's canonical formulation, is determined so that it reproduces the second-order Lagrangian density of the usual SUGRA especially by adding appropriate four-fermion contact terms. We show that the four-fermion contact terms added in the first-order chiral Lagrangian density are the non-minimal terms required from the invariance under first-order supersymmetry transformations. We also discuss the case of higher N theories, especially for N = 4 and N = 8.Comment: 20 pages, Latex, some more discussions and new references added, some typos corrected, accepted for publication in Physical Review

Minimal Off-Shell Version of N = 1 Chiral Supergravity

We construct the minimal off-shell formulation of N = 1 chiral supergravity (SUGRA) introducing a complex antisymmetric tensor field $B_{\mu \nu}$ and a complex axial-vector field $A_{\mu}$ as auxiliary fields. The resulting algebra of the right- and left-handed supersymmetry (SUSY) transformations closes off shell and generates chiral gauge transforamtions and vector gauge transformations in addition to the transformations which appear in the case without auxiliary fields.Comment: 9 pages, late

Local time and the pricing of time-dependent barrier options

A time-dependent double-barrier option is a derivative security that delivers the terminal value $\phi(S_T)$ at expiry $T$ if neither of the continuous time-dependent barriers b_\pm:[0,T]\to \RR_+ have been hit during the time interval $[0,T]$. Using a probabilistic approach we obtain a decomposition of the barrier option price into the corresponding European option price minus the barrier premium for a wide class of payoff functions $\phi$, barrier functions $b_\pm$ and linear diffusions $(S_t)_{t\in[0,T]}$. We show that the barrier premium can be expressed as a sum of integrals along the barriers $b_\pm$ of the option's deltas \Delta_\pm:[0,T]\to\RR at the barriers and that the pair of functions $(\Delta_+,\Delta_-)$ solves a system of Volterra integral equations of the first kind. We find a semi-analytic solution for this system in the case of constant double barriers and briefly discus a numerical algorithm for the time-dependent case.Comment: 32 pages, to appear in Finance and Stochastic

A candidate for a background independent formulation of M theory

A class of background independent membrane field theories are studied, and several properties are discovered which suggest that they may play a role in a background independent form of M theory. The bulk kinematics of these theories are described in terms of the conformal blocks of an algebra G on all oriented, finite genus, two-surfaces. The bulk dynamics is described in terms of causal histories in which time evolution is specified by giving amplitudes to certain local changes of the states. Holographic observables are defined which live in finite dimensional states spaces associated with boundaries in spacetime. We show here that the natural observables in these boundary state spaces are, when G is chosen to be Spin(D) or a supersymmetric extension of it, generalizations of matrix model coordinates in D dimensions. In certain cases the bulk dynamics can be chosen so the matrix model dynamics is recoverd for the boundary observables. The bosonic and supersymmetric cases in D=3 and D=9 are studied, and it is shown that the latter is, in a certain limit, related to the matrix model formulation of M theory. This correspondence gives rise to a conjecture concerning a background independent form of M theory in terms of which excitations of the background independent membrane field theory that correspond to strings and D0 branes are identified.Comment: Latex 46 pages, 21 figures, new results included which lead to a modification of the statement of the basic conjecture. Presentation improve

Quantum geometry with intrinsic local causality

The space of states and operators for a large class of background independent theories of quantum spacetime dynamics is defined. The SU(2) spin networks of quantum general relativity are replaced by labelled compact two-dimensional surfaces. The space of states of the theory is the direct sum of the spaces of invariant tensors of a quantum group G_q over all compact (finite genus) oriented 2-surfaces. The dynamics is background independent and locally causal. The dynamics constructs histories with discrete features of spacetime geometry such as causal structure and multifingered time. For SU(2) the theory satisfies the Bekenstein bound and the holographic hypothesis is recast in this formalism.Comment: Latex 33 pages, 7 Figure, epsfi

Gravitational Instantons and Moduli Spaces of Topological 2-form Gravity

A topological version of four-dimensional (Euclidean) Einstein gravity which we propose regards anti-self-dual 2-forms and an anti-self-dual part of the frame connections as fundamental fields. The theory describes the moduli spaces of conformally self-dual Einstein manifolds for the non-zero cosmological constant case and Einstein-Kahlerian manifold with the vanishing real first Chern class for the zero cosmological constant. In the non-zero cosmological constant case, we evaluate the index of the elliptic complex associated with the moduli space and calculate the partition function. We also clarify the moduli space and its dimension for the zero cosmological constant case which are related to the Plebansky's heavenly equations.Comment: 36pages, LaTex, TIT/HEP-247/COSMO-4

Towards a tensionless string field theory for the N=(2,0) CFT in d=6

We describe progress in using the field theory of tensionless strings to arrive at a Lagrangian for the six-dimensional $\mathcal N=(2,0)$ conformal theory. We construct the free part of the theory and propose an ansatz for the cubic vertex in light-cone superspace. By requiring closure of the $(2,0)$ supersymmetry algebra, we fix the cubic vertex up to two parameters.Comment: 46 pages, 2 figures. V2: references added; minor changes and improvement

Oxidative Stress Correlates with Headache Symptoms in Fibromyalgia: Coenzyme Q10 Effect on Clinical Improvement

This is an open-access article distributed under the terms of the Creative Commons Attribution License.[Background]: Fibromyalgia (FM) is a chronic pain syndrome with unknown etiology and a wide spectrum of symptoms such as allodynia, debilitating fatigue, joint stiffness and migraine. Recent studies have shown some evidences demonstrating that oxidative stress is associated to clinical symptoms in FM of fibromyalgia. We examined oxidative stress and bioenergetic status in blood mononuclear cells (BMCs) and its association to headache symptoms in FM patients. The effects of oral coenzyme Q 10 (CoQ 10) supplementation on biochemical markers and clinical improvement were also evaluated. [Methods]: We studied 20 FM patients and 15 healthy controls. Clinical parameters were evaluated using the Fibromyalgia Impact Questionnaire (FIQ), visual analogues scales (VAS), and the Headache Impact Test (HIT-6). Oxidative stress was determined by measuring CoQ 10, catalase and lipid peroxidation (LPO) levels in BMCs. Bioenergetic status was assessed by measuring ATP levels in BMCs. [Results]: We found decreased CoQ 10, catalase and ATP levels in BMCs from FM patients as compared to normal control (P<0.05 and P<0.001, respectively) We also found increased level of LPO in BMCs from FM patients as compared to normal control (P<0.001). Significant negative correlations between CoQ 10 or catalase levels in BMCs and headache parameters were observed (r = -0.59, P<0.05; r = -0.68, P<0.05, respectively). Furthermore, LPO levels showed a significant positive correlation with HIT-6 (r = 0.33, P<.05). Oral CoQ 10 supplementation restored biochemical parameters and induced a significant improvement in clinical and headache symptoms (P<0.001). [Discussion]: The results of this study suggest a role for mitochondrial dysfunction and oxidative stress in the headache symptoms associated with FM. CoQ10 supplementation should be examined in a larger placebo controlled trial as a possible treatment in FM.This work has been supported by IV Plan Propio de Investigación (University of Seville, ref. 2010/00000453), FIS PI10/00543 grant, FIS EC08/00076 grant, Ministerio de Sanidad, Spain and Fondo Europeo de Desarrollo Regional (FEDER-Unión Europea), SAS 111242 grant, Servicio Andaluz de Salud-Junta de Andalucía, Proyecto de Investigación de Excelencia de la Junta de Andalucía CTS-5725 and Federación Andaluza de Fibromialgia y Fatiga Crónica (ALBA Andalucía).Peer Reviewe

The Fission Yeast Stress-Responsive MAPK Pathway Promotes Meiosis via the Phosphorylation of Pol II CTD in Response to Environmental and Feedback Cues

The RRM-type RNA-binding protein Mei2 is a master regulator of meiosis in fission yeast, in which it stabilizes meiosis-specific mRNAs by blocking their destruction. Artificial activation of Mei2 can provoke the entire meiotic process, and it is suspected that Mei2 may do more than the stabilization of meiosis-specific mRNAs. In our current study using a new screening system, we show that Mei2 genetically interacts with subunits of CTDK-I, which phosphorylates serine-2 residues on the C-terminal domain of RNA polymerase II (Pol II CTD). Phosphorylation of CTD Ser-2 is essential to enable the robust transcription of ste11, which encodes an HMG-type transcription factor that regulates the expression of mei2 and other genes necessary for sexual development. CTD Ser-2 phosphorylation increases under nitrogen starvation, and the stress-responsive MAP kinase pathway, mediated by Wis1 MAPKK and Sty1 MAPK, is critical for this stress response. Sty1 phosphorylates Lsk1, the catalytic subunit of CTDK-I. Furthermore, a feedback loop stemming from activated Mei2 to Win1 and Wis4 MAPKKKs operates in this pathway and eventually enhances CTD Ser-2 phosphorylation and ste11 transcription. Hence, in addition to starting meiosis, Mei2 functions to reinforce the commitment to it, once cells have entered this process. This study also demonstrates clearly that the stress-responsive MAP kinase pathway can modulates gene expression through phosphorylation of Pol II CTD