Green functions and dimensional reduction of quantum fields on product manifolds

We discuss Euclidean Green functions on product manifolds P=NxM. We show that if M is compact then the Euclidean field on P can be approximated by its zero mode which is a Euclidean field on N. We estimate the remainder of this approximation. We show that for large distances on N the remainder is small. If P=R^{D-1}xS^{beta}, where S^{beta} is a circle of radius beta, then the result reduces to the well-known approximation of the D dimensional finite temperature quantum field theory to D-1 dimensional one in the high temperature limit. Analytic continuation of Euclidean fields is discussed briefly.Comment: 17 page

Moduli Stabilization and Cosmology of Type IIB on SU(2)-Structure Orientifolds

We consider type IIB flux compactifications on six-dimensional SU(2)-structure manifolds with O5- and O7-planes. These six-dimensional spaces allow not only for F_3 and H_3 fluxes but also for F_1 and F_5 fluxes. We derive the four-dimensional N=1 scalar potential for such compactifications and present one explicit example of a fully stabilized AdS vacuum with large volume and small string coupling. We then discuss cosmological aspects of these compactifications and derive several no-go theorems that forbid dS vacua and slow-roll inflation under certain conditions. We also study concrete examples of cosets and twisted tori and find that our no-go theorems forbid dS vacua and slow-roll inflation in all but one of them. For the latter we find a dS critical point with \epsilon numerically zero. However, the point has two tachyons and eta-parameter \eta \approx -3.1.Comment: 35 pages + appendices, LaTeX2e; v2: numerical dS extremum added, typos corrected, references adde

The Cosmological Constant Problem and Quintessence

I briefly review the cosmological constant problem and the issue of dark energy (or quintessence). Within the framework of quantum field theory, the vacuum expectation value of the energy momentum tensor formally diverges as $k^4$. A cutoff at the Planck or electroweak scale leads to a cosmological constant which is, respectively, $10^{123}$ or $10^{55}$ times larger than the observed value, \l/8\pi G \simeq 10^{-47} GeV$^4$. The absence of a fundamental symmetry which could set the value of \l to either zero or a very small value leads to {\em the cosmological constant problem}. Most cosmological scenario's favour a large time-dependent \l-term in the past (in order to generate inflation at $z \gg 10^{10}$), and a small \l-term today, to account for the current acceleration of the universe at z \lleq 1. Constraints arising from cosmological nucleosynthesis, CMB and structure formation constrain \l to be sub-dominant during most of the intermediate epoch $10^{10} < z < 1$. This leads to the {\em cosmic coincidence} conundrum which suggests that the acceleration of the universe is a recent phenomenon and that we live during a special epoch when the density in \l and in matter are almost equal. Time varying models of dark energy can, to a certain extent, ameliorate the fine tuning problem (faced by \l), but do not resolve the puzzle of cosmic coincidence. I briefly review tracker models of dark energy, as well as more recent brane inspired ideas and the issue of horizons in an accelerating universe. Model independent methods which reconstruct the cosmic equation of state from supernova observations are also assessed. Finally, a new diagnostic of dark energy -- `Statefinder', is discussed.Comment: Minor typo's corrected, references added and updated. 15 pages, 5 figures. Invited review at ``The Early Universe and Cosmological Observations: a Critical Review'', UCT, Cape Town, July 2001, to appear in "Classical and Quantum Gravity

Light-Front View of The Axial Anomaly

Motivated by an apparent puzzle of the light-front vacua incompatible with the axial anomaly, we have considered the two-dimensional massless Schwinger model for an arbitrary interpolating angle of the quantization surface. By examining spectral deformation of the Dirac sea under an external electric field semiclassically, we have found that the axial anomaly is quantization angle independent. This indicates an intricate nontrivial vacuum structure present even in the light-front limit.Comment: 12 pages, REVTEX, one figure postscript file encode

Role of Matrix Metalloproteinase 13 in Both Endochondral and Intramembranous Ossification during Skeletal Regeneration

Extracellular matrix (ECM) remodeling is important during bone development and repair. Because matrix metalloproteinase 13 (MMP13, collagenase-3) plays a role in long bone development, we have examined its role during adult skeletal repair. In this study we find that MMP13 is expressed by hypertrophic chondrocytes and osteoblasts in the fracture callus. We demonstrate that MMP13 is required for proper resorption of hypertrophic cartilage and for normal bone remodeling during non-stabilized fracture healing, which occurs via endochondral ossification. However, no difference in callus strength was detected in the absence of MMP13. Transplant of wild-type bone marrow, which reconstitutes cells only of the hematopoietic lineage, did not rescue the endochondral repair defect, indicating that impaired healing in Mmp13−/− mice is intrinsic to cartilage and bone. Mmp13−/− mice also exhibited altered bone remodeling during healing of stabilized fractures and cortical defects via intramembranous ossification. This indicates that the bone phenotype occurs independently from the cartilage phenotype. Taken together, our findings demonstrate that MMP13 is involved in normal remodeling of bone and cartilage during adult skeletal repair, and that MMP13 may act directly in the initial stages of ECM degradation in these tissues prior to invasion of blood vessels and osteoclasts

Genetic polymorphisms of the RAS-cytokine pathway and chronic kidney disease

Chronic kidney disease (CKD) in children is irreversible. It is associated with renal failure progression and atherosclerotic cardiovascular (CV) abnormalities. Nearly 60% of children with CKD are affected since birth with congenital or inherited kidney disorders. Preliminary evidence primarily from adult CKD studies indicates common genetic risk factors for CKD and atherosclerotic CV disease. Although multiple physiologic pathways share common genes for CKD and CV disease, substantial evidence supports our attention to the renin angiotensin system (RAS) and the interlinked inflammatory cascade because they modulate the progressions of renal and CV disease. Gene polymorphisms in the RAS-cytokine pathway, through altered gene expression of inflammatory cytokines, are potential factors that modulate the rate of CKD progression and CV abnormalities in patients with CKD. For studying such hypotheses, the cooperative efforts among scientific groups and the availability of robust and affordable technologies to genotype thousands of single nucleotide polymorphisms (SNPs) across the genome make genome-wide association studies an attractive paradigm for studying polygenic diseases such as CKD. Although attractive, such studies should be interpreted carefully, with a fundamental understanding of their potential weaknesses. Nevertheless, whole-genome association studies for diabetic nephropathy and future studies pertaining to other types of CKD will offer further insight for the development of targeted interventions to treat CKD and associated atherosclerotic CV abnormalities in the pediatric CKD population