The Conformal Anomaly in General Rank 1 Symmetric Spaces and Associated Operator Product

We compute the one-loop effective action and the conformal anomaly associated with the product $\bigotimes_p{\cal L}_p$ of the Laplace type operators ${\cal L}_p, p=1,2$, acting in irreducible rank 1 symmetric spaces of non-compact type. The explicit form of the zeta functions and the conformal anomaly of the stress-energy momentum tensor is derived.Comment: 10 pages, LaTe

An approach for the calculation of one-loop effective actions, vacuum energies, and spectral counting functions

In this paper, we provide an approach for the calculation of one-loop effective actions, vacuum energies, and spectral counting functions and discuss the application of this approach in some physical problems. Concretely, we construct the equations for these three quantities; this allows us to achieve them by directly solving equations. In order to construct the equations, we introduce shifted local one-loop effective actions, shifted local vacuum energies, and local spectral counting functions. We solve the equations of one-loop effective actions, vacuum energies, and spectral counting functions for free massive scalar fields in $\mathbb{R}^{n}$, scalar fields in three-dimensional hyperbolic space $H_{3}$ (the Euclidean Anti-de Sitter space $AdS_{3}$), in $H_{3}/Z$ (the geometry of the Euclidean BTZ black hole), and in $S^{1}$, and the Higgs model in a $(1+1)$-dimensional finite interval. Moreover, in the above cases, we also calculate the spectra from the counting functions. Besides exact solutions, we give a general discussion on approximate solutions and construct the general series expansion for one-loop effective actions, vacuum energies, and spectral counting functions. In doing this, we encounter divergences. In order to remove the divergences, renormalization procedures are used. In this approach, these three physical quantities are regarded as spectral functions in the spectral problem.Comment: 37 pages, no figure. This is an enlarged and improved version of the paper published in JHE

Forms on Vector Bundles Over Hyperbolic Manifolds and the Conformal Anomaly

We study gauge theories based on abelian $p-$forms on real compact hyperbolic manifolds. An explicit formula for the conformal anomaly corresponding to skew--symmetric tensor fields is obtained, by using zeta--function regularization and the trace tensor kernel formula. Explicit exact and numerical values of the anomaly for $p-$forms of order up to $p=4$ in spaces of dimension up to $n=10$ are then calculated.Comment: 13 pages, 2 table

Fluid Biomarkers for Synaptic Dysfunction and Loss

Synapses are the site for brain communication where information is transmitted between neurons and stored for memory formation. Synaptic degeneration is a global and early pathogenic event in neurodegenerative disorders with reduced levels of pre- and postsynaptic proteins being recognized as a core feature of Alzheimer’s disease (AD) pathophysiology. Together with AD, other neurodegenerative and neurodevelopmental disorders show altered synaptic homeostasis as an important pathogenic event, and due to that, they are commonly referred to as synaptopathies. The exact mechanisms of synapse dysfunction in the different diseases are not well understood and their study would help understanding the pathogenic role of synaptic degeneration, as well as differences and commonalities among them and highlight candidate synaptic biomarkers for specific disorders. The assessment of synaptic proteins in cerebrospinal fluid (CSF), which can reflect synaptic dysfunction in patients with cognitive disorders, is a keen area of interest. Substantial research efforts are now directed toward the investigation of CSF synaptic pathology to improve the diagnosis of neurodegenerative disorders at an early stage as well as to monitor clinical progression. In this review, we will first summarize the pathological events that lead to synapse loss and then discuss the available data on established (eg, neurogranin, SNAP-25, synaptotagmin-1, GAP-43, and α-syn) and emerging (eg, synaptic vesicle glycoprotein 2A and neuronal pentraxins) CSF biomarkers for synapse dysfunction, while highlighting possible utilities, disease specificity, and technical challenges for their detection

Vacuum Polarization in an Anti-de Sitter Space as an Origin for a Cosmological Constant in a Brane World

In this Letter we show that the vacuum polarization of quantum fields in an anti-de Sitter space naturally gives rise to a small but nonzero cosmological constant in a brane world living in it. To explain the extremely small ratio of mass density in the cosmological constant to the Planck mass density in our universe (\approx 10^{-123}) as suggested by cosmological observations, all we need is a four-dimensional brane world (our universe) living in a five-dimensional anti-de Sitter space with a curvature radius r_0 \sim 10^{-3}cm and a fundamental Planck energy M_P \sim 10^9 GeV, and a scalar field with a mass m \sim r_0^{-1}\sim 10^{-2}eV. Probing gravity down to a scale \sim 10^{-3}cm, which is attainable in the near future, will provide a test of the model.Comment: 10 pages, including 1 figur

Graviton 1-loop partition function for 3-dimensional massive gravity

The graviton 1-loop partition function in Euclidean topologically massive gravity (TMG) is calculated using heat kernel techniques. The partition function does not factorize holomorphically, and at the chiral point it has the structure expected from a logarithmic conformal field theory. This gives strong evidence for the proposal that the dual conformal field theory to TMG at the chiral point is indeed logarithmic. We also generalize our results to new massive gravity.Comment: 19 pages, v2: major revision, considerably stronger conclusions, added comparison with LCFT partition function, confirmation of LCFT conjecture, added autho

A Model of Curvature-Induced Phase Transitions in Inflationary Universe

Chiral phase transitions driven by space-time curvature effects are investigated in de Sitter space in the supersymmetric Nambu-Jona-Lasinio model with soft supersymmetry breaking. The model is considered to be suitable for the analysis of possible phase transitions in inflationary universe. It is found that a restoration of the broken chiral symmetry takes place in two patterns for increasing curvature : the first order and second order phase transition respectively depending on initial settings of the four-body interaction parameter and the soft supersymmetry breaking parameter. The critical curves expressing the phase boundaries in these parameters are obtained. Cosmological implications of the result are discussed in connection with bubble formations and the creation of cosmic strings during the inflationary era.Comment: 12 pages, 3 figures, REVTe

Neuroligin-1 in brain and CSF of neurodegenerative disorders: investigation for synaptic biomarkers

Synaptic pathology is a central event in Alzheimer’s disease (AD) and other neurodegenerative conditions, and investigation of synaptic proteins can provide valuable tools to follow synaptic dysfunction and loss in these diseases. Neuroligin-1 (Nlgn1) is a postsynaptic cell adhesion protein, important for synapse stabilization and formation. Nlgn1 has been connected to cognitive disorders, and specifically to AD, as target of the synaptotoxic effect of amyloid-β (Aβ) oligomers and Aβ fibrils. To address changes in Nlgn1 expression in human brain, brain regions in different neurological disorders were examined by Western blot and mass spectrometry. Brain specimens from AD (n = 23), progressive supranuclear palsy (PSP, n = 11), corticobasal degeneration (CBD, n = 10), and Pick’s disease (PiD, n = 9) were included. Additionally, cerebrospinal fluid (CSF) samples of AD patients (n = 43) and non-demented controls (n = 42) were analysed. We found decreased levels of Nlgn1 in temporal and parietal cortex (~ 50–60% reductions) in AD brains compared with controls. In frontal grey matter the reduction was not seen for AD patients; however, in the same region, marked reduction was found for PiD (~ 77%), CBD (~ 66%) and to a lesser extent for PSP (~ 43%), which could clearly separate these tauopathies from controls. The Nlgn1 level was reduced in CSF from AD patients compared to controls, but with considerable overlap. The dramatic reduction of Nlgn1 seen in the brain extracts of tauopathies warrants further investigation regarding the potential use of Nlgn1 as a biomarker for these neurodegenerative diseases

Bundles over Nearly-Kahler Homogeneous Spaces in Heterotic String Theory

We construct heterotic vacua based on six-dimensional nearly-Kahler homogeneous manifolds and non-trivial vector bundles thereon. Our examples are based on three specific group coset spaces. It is shown how to construct line bundles over these spaces, compute their properties and build up vector bundles consistent with supersymmetry and anomaly cancelation. It turns out that the most interesting coset is $SU(3)/U(1)^2$. This space supports a large number of vector bundles which lead to consistent heterotic vacua, some of them with three chiral families.Comment: 32 pages, reference adde

Logarithmic Corrections to N=2 Black Hole Entropy: An Infrared Window into the Microstates

Logarithmic corrections to the extremal black hole entropy can be computed purely in terms of the low energy data -- the spectrum of massless fields and their interaction. The demand of reproducing these corrections provides a strong constraint on any microscopic theory of quantum gravity that attempts to explain the black hole entropy. Using quantum entropy function formalism we compute logarithmic corrections to the entropy of half BPS black holes in N=2 supersymmetric string theories. Our results allow us to test various proposals for the measure in the OSV formula, and we find agreement with the measure proposed by Denef and Moore if we assume their result to be valid at weak topological string coupling. Our analysis also gives the logarithmic corrections to the entropy of extremal Reissner-Nordstrom black holes in ordinary Einstein-Maxwell theory.Comment: LaTeX file, 66 page