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

U(N|M) quantum mechanics on Kaehler manifolds

We study the extended supersymmetric quantum mechanics, with supercharges transforming in the fundamental representation of U(N|M), as realized in certain one-dimensional nonlinear sigma models with Kaehler manifolds as target space. We discuss the symmetry algebra characterizing these models and, using operatorial methods, compute the heat kernel in the limit of short propagation time. These models are relevant for studying the quantum properties of a certain class of higher spin field equations in first quantization.Comment: 21 pages, a reference adde

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

Quantum theory of massless (p,0)-forms

We describe the quantum theory of massless (p,0)-forms that satisfy a suitable holomorphic generalization of the free Maxwell equations on Kaehler spaces. These equations arise by first-quantizing a spinning particle with a U(1)-extended local supersymmetry on the worldline. Dirac quantization of the spinning particle produces a physical Hilbert space made up of (p,0)-forms that satisfy holomorphic Maxwell equations coupled to the background Kaehler geometry, containing in particular a charge that measures the amount of coupling to the U(1) part of the U(d) holonomy group of the d-dimensional Kaehler space. The relevant differential operators appearing in these equations are a twisted exterior holomorphic derivative and its hermitian conjugate (twisted Dolbeault operators with charge q). The particle model is used to obtain a worldline representation of the one-loop effective action of the (p,0)-forms. This representation allows to compute the first few heat kernel coefficients contained in the local expansion of the effective action and to derive duality relations between (p,0) and (d-p-2,0)-forms that include a topological mismatch appearing at one-loop.Comment: 32 pages, 3 figure

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

Pharmacologically directed strategies in academic anticancer drug discovery based on the European NCI compounds initiative

Background: The European NCI compounds programme, a joint initiative of the EORTC Research Branch, Cancer Research Campaign and the US National Cancer Institute, was initiated in 1993. The objective was to help the NCI in reducing the backlog of in vivo testing of potential anticancer compounds, synthesised in Europe that emerged from the NCI in vitro 60-cell screen. Methods: Over a period of more than twenty years the EORTC—Cancer Research Campaign panel reviewed ~2000 compounds of which 95 were selected for further evaluation. Selected compounds were stepwise developed with clear go/no go decision points using a pharmacologically directed programme. Results: This approach eliminated quickly compounds with unsuitable pharmacological properties. A few compounds went into Phase I clinical evaluation. The lessons learned and many of the principles outlined in the paper can easily be applied to current and future drug discovery and development programmes. Conclusions: Changes in the review panel, restrictions regarding numbers and types of compounds tested in the NCI in vitro screen and the appearance of targeted agents led to the discontinuation of the European NCI programme in 2017 and its transformation into an academic platform of excellence for anticancer drug discovery and development within the EORTC-PAMM group. This group remains open for advice and collaboration with interested parties in the field of cancer pharmacology

Sequence dependent antitumour efficacy of the vascular disrupting agent ZD6126 in combination with paclitaxel

The clinical success of small-molecule vascular disrupting agents (VDAs) depends on their combination with conventional therapies. Scheduling and sequencing remain key issues in the design of VDA–chemotherapy combination treatments. This study examined the antitumour activity of ZD6126, a microtubule destabilising VDA, in combination with paclitaxel (PTX), a microtubule-stabilising cytotoxic drug, and the influence of schedule and sequence on the efficacy of the combination. Nude mice bearing MDA-MB-435 xenografts received weekly cycles of ZD6126 (200 mg kg−1 i.p.) administered at different times before or after PTX (10, 20, and 40 mg kg−1 i.v.). ZD6126 given 2 or 24 h after PTX showed no significant benefit, a result that was attributed to a protective effect of PTX against ZD6126-induced vascular damage and tumour necrosis, a hallmark of VDA activity. Paclitaxel counteracting activity was reduced by distancing drug administrations, and ZD6126 given 72 h after PTX potentiated the VDA's antitumour activity. Schedules with ZD6126 given before PTX improved therapeutic activity, which was paralleled by a VDA-induced increase in cell proliferation in the viable tumour tissue. Paclitaxel given 72 h after ZD6126 yielded the best response (50% tumours regressing). A single treatment with ZD6126 followed by weekly administration of PTX was sufficient to achieve a similar response (57% remissions). These findings show that schedule, sequence and timing are crucial in determining the antitumour efficacy of PTX in combination with ZD6126. Induction of tumour necrosis and increased proliferation in the remaining viable tumour tissue could be exploited as readouts to optimise schedules and maximise therapeutic efficacy

For which side the bell tolls: The laterality of approach-avoidance associative networks

The two hemispheres of the brain appear to play different roles in emotion and/or motivation. A great deal of previous research has examined the valence hypothesis (left hemisphere = positive; right = negative), but an increasing body of work has supported the motivational hypothesis (left hemisphere = approach; right = avoidance) as an alternative. The present investigation (N = 117) sought to provide novel support for the latter perspective. Left versus right hemispheres were briefly activated by neutral lateralized auditory primes. Subsequently, participants categorized approach versus avoidance words as quickly and accurately as possible. Performance in the task revealed that approach-related thoughts were more accessible following left-hemispheric activation, whereas avoidance-related thoughts were more accessible following right-hemispheric activation. The present results are the first to examine such lateralized differences in accessible motivational thoughts, which may underlie more “downstream” manifestations of approach and avoidance motivation such as judgments, decision making, and behavior