Logical Dreams

We discuss the past and future of set theory, axiom systems and independence results. We deal in particular with cardinal arithmetic

Analysis of MERCATOR data Part I: variable B stars

We re-classified 31 variable B stars which were observed more than 50 times in the Geneva photometric system with the P7 photometer attached to the MERCATOR telescope (La Palma) during its first 3 years of scientific observations. HD89688 is a possible beta Cephei/slowly pulsating B star hybrid and the main mode of the COROT target HD180642 shows non-linear effects. The Maia candidates are re-classified as either ellipsoidal variables or spotted stars. Although the mode identification is still ongoing, all the well-identified modes so far have a degree l = 0, 1 or 2.Comment: 4 pages, 3 figures. To appear in: Proceedings of JENAM 2005 'Distant worlds', Communications in Asteroseismolog

Paraoxonase 2 protein is spatially expressed in the human placenta and selectively reduced in labour

Humans parturition involves interaction of hormonal, neurological, mechanical stretch and inflammatory pathways and the placenta plays a crucial role. The paraoxonases (PONs 1–3) protect against oxidative damage and lipid peroxidation, modulation of endoplasmic reticulum stress and regulation of apoptosis. Nothing is known about the role of PON2 in the placenta and labour. Since PON2 plays a role in oxidative stress and inflammation, both features of labour, we hypothesised that placental PON2 expression would alter during labour. PON2 was examined in placentas obtained from women who delivered by cesarean section and were not in labour and compared to the equivalent zone of placentas obtained from women who delivered vaginally following an uncomplicated labour. Samples were obtained from 12 sites within each placenta: 4 equally spaced apart pieces were sampled from the inner, middle and outer placental regions. PON2 expression was investigated by Western blotting and real time PCR. Two PON2 forms, one at 62 kDa and one at 43 kDa were found in all samples. No difference in protein expression of either isoform was found between the three sites in either the labour or non-labour group. At the middle site there was a highly significant decrease in PON2 expression in the labour group when compared to the non-labour group for both the 62 kDa form (p = 0.02) and the 43 kDa form (p = 0.006). No spatial differences were found within placentas at the mRNA level in either labour or non-labour. There was, paradoxically, an increase in PON2 mRNA in the labour group at the middle site only. This is the first report to describe changes in PON2 in the placenta in labour. The physiological and pathological significance of these remains to be elucidated but since PON2 is anti-inflammatory further studies are warranted to understand its role

Lorentz Violation in Extra Dimensions

In theories with extra dimensions it is well known that the Lorentz invariance of the $D=4+n$-dimensional spacetime is lost due to the compactified nature of the $n$ dimensions leaving invariance only in 4d. In such theories other sources of Lorentz violation may exist associated with the physics that initiated the compactification process at high scales. Here we consider the possibility of capturing some of this physics by analyzing the higher dimensional analog of the model of Colladay and Kostelecky. In that scenario a complete set of Lorentz violating operators arising from spontaneous Lorentz violation, that are not obviously Planck-scale suppressed, are added to the Standard Model action. Here we consider the influence of the analogous set of operators which break Lorentz invariance in 5d within the Universal Extra Dimensions picture. We show that such operators can greatly alter the anticipated Kaluza-Klein(KK) spectra, induce electroweak symmetry breaking at a scale related to the inverse compactification radius, yield sources of parity violation in, e.g., 4d QED/QCD and result in significant violations of KK-parity conservation produced by fermion Yukawa couplings, thus destabilizing the lightest KK particle. LV in 6d is briefly discussed.Comment: 26 pages, 2 figures; additional references and discussio

A Class of Topological Actions

We review definitions of generalized parallel transports in terms of Cheeger-Simons differential characters. Integration formulae are given in terms of Deligne-Beilinson cohomology classes. These representations of parallel transport can be extended to situations involving distributions as is appropriate in the context of quantized fields.Comment: 41 pages, no figure

Realistic D-Brane Models on Warped Throats: Fluxes, Hierarchies and Moduli Stabilization

We describe the construction of string theory models with semirealistic spectrum in a sector of (anti) D3-branes located at an orbifold singularity at the bottom of a highly warped throat geometry, which is a generalisation of the Klebanov-Strassler deformed conifold. These models realise the Randall-Sundrum proposal to naturally generate the Planck/electroweak hierarchy in a concrete string theory embedding, and yielding interesting chiral open string spectra. We describe examples with Standard Model gauge group (or left-right symmetric extensions) and three families of SM fermions, with correct quantum numbers including hypercharge. The dilaton and complex structure moduli of the geometry are stabilised by the 3-form fluxes required to build the throat. We describe diverse issues concerning the stabilisation of geometric Kahler moduli, like blow-up modes of the orbifold singularities, via D term potentials and gauge theory non-perturbative effects, like gaugino condensation. This local geometry, once embedded in a full compactification, could give rise to models with all moduli stabilised, and with the potential to lead to de Sitter vacua. Issues of gauge unification, proton stability, supersymmetry breaking and Yukawa couplings are also discussed.Comment: 46 pages, 13 figures (figures 3 and 13 corrected

BGWM as Second Constituent of Complex Matrix Model

Earlier we explained that partition functions of various matrix models can be constructed from that of the cubic Kontsevich model, which, therefore, becomes a basic elementary building block in "M-theory" of matrix models. However, the less topical complex matrix model appeared to be an exception: its decomposition involved not only the Kontsevich tau-function but also another constituent, which we now identify as the Brezin-Gross-Witten (BGW) partition function. The BGW tau-function can be represented either as a generating function of all unitary-matrix integrals or as a Kontsevich-Penner model with potential 1/X (instead of X^3 in the cubic Kontsevich model).Comment: 42 page

Chiral bosonization for non-commutative fields

A model of chiral bosons on a non-commutative field space is constructed and new generalized bosonization (fermionization) rules for these fields are given. The conformal structure of the theory is characterized by a level of the Kac-Moody algebra equal to $(1+ \theta^2)$ where $\theta$ is the non-commutativity parameter and chiral bosons living in a non-commutative fields space are described by a rational conformal field theory with the central charge of the Virasoro algebra equal to 1. The non-commutative chiral bosons are shown to correspond to a free fermion moving with a speed equal to $c^{\prime} = c \sqrt{1+\theta^2}$ where $c$ is the speed of light. Lorentz invariance remains intact if $c$ is rescaled by $c \to c^{\prime}$. The dispersion relation for bosons and fermions, in this case, is given by $\omega = c^{\prime} | k|$.Comment: 16 pages, JHEP style, version published in JHE

R Symmetries in the Landscape

In the landscape, states with $R$ symmetries at the classical level form a distinct branch, with a potentially interesting phenomenology. Some preliminary analyses suggested that the population of these states would be significantly suppressed. We survey orientifolds of IIB theories compactified on Calabi-Yau spaces based on vanishing polynomials in weighted projective spaces, and find that the suppression is quite substantial. On the other hand, we find that a $Z_2$ R-parity is a common feature in the landscape. We discuss whether the cosmological constant and proton decay or cosmology might select the low energy branch. We include also some remarks on split supersymmetry.Comment: 13 page