Gravity, Two Times, Tractors, Weyl Invariance and Six Dimensional Quantum Mechanics

Fefferman and Graham showed some time ago that four dimensional conformal geometries could be analyzed in terms of six dimensional, ambient, Riemannian geometries admitting a closed homothety. Recently it was shown how conformal geometry provides a description of physics manifestly invariant under local choices of unit systems. Strikingly, Einstein's equations are then equivalent to the existence of a parallel scale tractor (a six component vector subject to a certain first order covariant constancy condition at every point in four dimensional spacetime). These results suggest a six dimensional description of four dimensional physics, a viewpoint promulgated by the two times physics program of Bars. The Fefferman--Graham construction relies on a triplet of operators corresponding, respectively to a curved six dimensional light cone, the dilation generator and the Laplacian. These form an sp(2) algebra which Bars employs as a first class algebra of constraints in a six-dimensional gauge theory. In this article four dimensional gravity is recast in terms of six dimensional quantum mechanics by melding the two times and tractor approaches. This "parent" formulation of gravity is built from an infinite set of six dimensional fields. Successively integrating out these fields yields various novel descriptions of gravity including a new four dimensional one built from a scalar doublet, a tractor vector multiplet and a conformal class of metrics.Comment: 27 pages, LaTe

Capsaicin 8% dermal patch in clinical practice: an expert opinion

Introduction: Neuropathic pain (NP) is caused by a lesion or disease of the somatosensory system, which can severely impact patients’ quality of life. The current-approved treatments for NP comprise of both centrally acting agents and topical drugs, including capsaicin 8% dermal patches, which is approved for the treatment of peripheral NP. / Areas covered: The authors summarize literature data regarding capsaicin use in patients who suffer from NP and discuss the clinical applications of this topical approach. / Expert opinion: Overall, the capsaicin 8% dermal patch is as effective in reducing pain intensity as other centrally active agents (i.e. pregabalin). Some studies have also reported fewer systemic side effects, a faster onset of action and superior treatment satisfaction compared with systemic agents. In our opinion, capsaicin 8% dermal patches also present additional advantages, such as a good systemic tolerability, the scarcity of adverse events, the possibility to combine it with other agents, and a good cost-effective profile. It is important to note that, as the mechanism of action of capsaicin 8% is the ‘defunctionalization’ of small afferent fibers through interaction with TRPV1 receptors, the peripheral expression of this receptor on nociceptor fibers, is crucial to predict patient’s response to treatment

Worldline approach to noncommutative field theory

The study of the heat-trace expansion in noncommutative field theory has shown the existence of Moyal nonlocal Seeley-DeWitt coefficients which are related to the UV/IR mixing and manifest, in some cases, the non-renormalizability of the theory. We show that these models can be studied in a worldline approach implemented in phase space and arrive to a master formula for the $n$-point contribution to the heat-trace expansion. This formulation could be useful in understanding some open problems in this area, as the heat-trace expansion for the noncommutative torus or the introduction of renormalizing terms in the action, as well as for generalizations to other nonlocal operators.Comment: 19 pages, version

Quantum theories of (p,q)-forms

We describe quantum theories for massless (p,q)-forms living on Kaehler spaces. In particular we consider four different types of quantum theories: two types involve gauge symmetries and two types are simpler theories without gauge invariances. The latter can be seen as building blocks of the former. Their equations of motion can be obtained in a natural way by first-quantizing a spinning particle with a U(2)-extended supersymmetry on the worldline. The particle system contains four supersymmetric charges, represented quantum mechanically by the Dolbeault operators and their hermitian conjugates. After studying how the (p,q)-form field theories emerge from the particle system, we investigate their one loop effective actions, identify corresponding heat kernel coefficients, and derive exact duality relations. The dualities are seen to include mismatches related to topological indices and analytic torsions, which are computed as Tr(-1)^F and Tr[(-1)^F F] in the first quantized supersymmetric nonlinear sigma model for a suitable fermion number operator F.Comment: 44 pages, 2 figures, a reference adde

Sphingolipid synthesis inhibition by myriocin administration enhances lipid consumption and ameliorates lipid response to myocardial ischemia reperfusion injury

Myocardial infarct requires prompt thrombolytic therapy or primary percutaneous coronary intervention to limit the extent of necrosis, but reperfusion creates additional damage. Along with reperfusion, a maladaptive remodeling phase might occur and it is often associated with inflammation, oxidative stress, as well as a reduced ability to recover metabolism homeostasis. Infarcted individuals can exhibit reduced lipid turnover and their accumulation in cardiomyocytes, which is linked to a deregulation of peroxisome proliferator activated receptors (PPARs), controlling fatty acids metabolism, energy production, and the anti-inflammatory response. We previously demonstrated that Myriocin can be effectively used as post-conditioning therapeutic to limit ischemia/reperfusion-induced inflammation, oxidative stress, and infarct size, in a murine model. In this follow-up study, we demonstrate that Myriocin has a critical regulatory role in cardiac remodeling and energy production, by up-regulating the transcriptional factor EB, PPARs nuclear receptors and genes involved in fatty acids metabolism, such as VLDL receptor, Fatp1, CD36, Fabp3, Cpts, and mitochondrial FA dehydrogenases. The overall effects are represented by an increased \u3b2-oxidation, together with an improved electron transport chain and energy production. The potent immunomodulatory and metabolism regulatory effects of Myriocin elicit the molecule as a promising pharmacological tool for post-conditioning therapy of myocardial ischemia/reperfusion injury

Galileons as Wess-Zumino Terms

We show that the galileons can be thought of as Wess-Zumino terms for the spontaneous breaking of space-time symmetries. Wess-Zumino terms are terms which are not captured by the coset construction for phenomenological Lagrangians with broken symmetries. Rather they are, in d space-time dimensions, d-form potentials for (d+1)-forms which are non-trivial co-cycles in Lie algebra cohomology of the full symmetry group relative to the unbroken symmetry group. We introduce the galileon algebras and construct the non-trivial (d+1)-form co-cycles, showing that the presence of galileons and multi-galileons in all dimensions is counted by the dimensions of particular Lie algebra cohomology groups. We also discuss the DBI and conformal galileons from this point of view, showing that they are not Wess-Zumino terms, with one exception in each case.Comment: 49 pages. v2 minor changes, version appearing in JHE

Local Unit Invariance, Back-Reacting Tractors and the Cosmological Constant Problem

When physics is expressed in a way that is independent of local choices of unit systems, Riemannian geometry is replaced by conformal geometry. Moreover masses become geometric, appearing as Weyl weights of tractors (conformal multiplets of fields necessary to keep local unit invariance manifest). The relationship between these weights and masses is through the scalar curvature. As a consequence mass terms are spacetime dependent for off-shell gravitational backgrounds, but happily constant for physical, Einstein manifolds. Unfortunately this introduces a naturalness problem because the scalar curvature is proportional to the cosmological constant. By writing down tractor stress tensors (multiplets built from the standard stress tensor and its first and second derivatives), we show how back-reaction solves this naturalness problem. We also show that classical back-reaction generates an interesting potential for scalar fields. We speculate that a proper description of how physical systems couple to scale, could improve our understanding of naturalness problems caused by the disparity between the particle physics and observed, cosmological constants. We further give some ideas how an ambient description of tractor calculus could lead to a Ricci-flat/CFT correspondence which generalizes the AdS side of Maldacena's duality to a Ricci-flat space of one higher dimension.Comment: 20 pages, 2 figure

First order parent formulation for generic gauge field theories

We show how a generic gauge field theory described by a BRST differential can systematically be reformulated as a first order parent system whose spacetime part is determined by the de Rham differential. In the spirit of Vasiliev's unfolded approach, this is done by extending the original space of fields so as to include their derivatives as new independent fields together with associated form fields. Through the inclusion of the antifield dependent part of the BRST differential, the parent formulation can be used both for on and off-shell formulations. For diffeomorphism invariant models, the parent formulation can be reformulated as an AKSZ-type sigma model. Several examples, such as the relativistic particle, parametrized theories, Yang-Mills theory, general relativity and the two dimensional sigma model are worked out in details.Comment: 36 pages, additional sections and minor correction

Clinical characteristics and patterns of healthcare utilization in patients with painful neuropathic disorders in UK general practice: a retrospective cohort study

<p>Abstract</p> <p>Background</p> <p>Clinical characteristics and patterns of healthcare utilization in patients with painful neuropathic disorders (PNDs) who are under the care of general practitioners (GPs) in the UK are not well understood.</p> <p>Methods</p> <p>Using a large electronic UK database, we identified all adults (age ≥ 18 years) with any GP encounters between 1 January 2006 - 31 December 2006 at which a diagnosis of PND was noted ("PND patients"). An age-and gender-matched comparison group also was constituted consisting of randomly selected patients with one or more GP encounters-but no mention of PNDs-during this period. Characteristics and patterns of healthcare utilization of patients in the two groups were then examined over the one-year study period.</p> <p>Results</p> <p>The study sample consisted of 31,688 patients with mention of PNDs and an equal number of matched comparators; mean age was 56 years, and 62% were women. The prevalence of various comorbidities was higher among patients in the PND group, including digestive disorders (31% vs. 17% for comparison group), circulatory disorders (29% vs. 22%), and depression (4% vs. 3%) (all <it>p </it>< 0.01). Receipt of prescriptions for pain-related pharmacotherapy also was higher among PND patients, including nonsteroidal anti-inflammatory drugs (56% of PND patients had one or more such prescriptions vs. only 22% in the comparison group), opioids (49% vs. 12%), tricyclic antidepressants (20% vs. 1%), and antiepileptics (12% vs. 1%) (all <it>p </it>< 0.01). PND patients also averaged significantly more GP visits (22.8 vs. 14.2) and referrals to specialists (2.8 vs. 1.4) over one year (both comparisons <it>p </it>< 0.01).</p> <p>Conclusions</p> <p>Patients with PNDs under the care of GPs in the UK have relatively high levels of use of healthcare services and pain-related pharmacotherapy.</p