SL(2,R) Chern-Simons Theories with Rational Charges and Two-dimensional Conformal Field Theories

This paper (completed March 1992) is an extensively revised and expanded version of work which appeared July 1991 on the initial incarnation of the hepth bulletin board, and which was published in the Proceedings of the Workshop on String Theory, Trieste, March 1991. Abstract We present a hamiltonian quantization of the $SL(2,R)$ 3-dimensional Chern-Simons theory with fractional coupling constant $k=s/r$ on a space manifold with torus topology in the ``constrain-first'' framework. By generalizing the ``Weyl-odd'' projection to the fractional charge case, we obtain multi-components holomorphic wave functions whose components are the Kac-Wakimoto characters of the modular invariant admissible representations of ${\hat A}_1$ current algebra with fractional level. The modular representations carried by the quantum Hilbert space satisfy both Verlinde's and Vafa's constraints coming from conformal field theory. They are the ``square-roots'' of the representations associated to the conformal $(r,s)$ minimal models. Our results imply that Chern-Simons theory with $SO(2,2)$ as gauge group, which describes $2+1$-dimensional gravity with negative cosmological constant, has the modular properties of the Virasoro discrete series. On the way, we show that the 2-dimensional counterparts of Chern-Simons $SU(2)$ theories with half-integer charge $k=p/2$Comment: 29 pages, GEF-TH-92-

Weak Coupling Expansion of Yang-Mills Theory on Recursive Infinite Genus Surfaces

We analyze the partition function of two dimensional Yang-Mills theory on a family of surfaces of infinite genus. These surfaces have a recursive structure, which was used by one of us to compute the partition function that results in a generalized Migdal formula. In this paper we study the `small area' (weak coupling) expansion of the partition function, by exploiting the fact that the generalized Migdal formula is analytic in the (complexification of the) Euler characteristic. The structure of the perturbative part of the weak coupling expansion suggests that the moduli space of flat connections (of the SU(2) and SO(3) theories) on these infinite genus surfaces are well defined, perhaps in an appropriate regularization.Comment: 1+18 pages, 2 figure

A Functional and Lagrangian Formulation of Two-Dimensional Topological Gravity

We reconsider two-dimensional topological gravity in a functional and lagrangian framework. We derive its Slavnov-Taylor identities and discuss its (in)dependence on the background gauge. Correlators of reparamerization invariant observables are shown to be globally defined forms on moduli space. The potential obstruction to their gauge-independence is the non-triviality of the line bundle on moduli space ${\cal L}_x$, whose first Chern-class is associated to the topological invariants of Mumford, Morita and Miller. Based on talks given at the Fubini Fest, Torino, 24-26 February 1994, and at the Workshop on String Theory, Trieste, 20-22 April 1994.Comment: 11 pages, harvmac, CERN-TH-7302/94, GEF-Th-6/199

New Supersymmetric Localizations from Topological Gravity

Supersymmetric field theories can be studied exactly on suitable off-shell supergravity backgrounds. We show that in two dimensions such backgrounds are identifiable with BRST invariant backgrounds of topological gravity coupled to an abelian topological gauge multiplet. This latter background is required for the consistent coupling of the topological `matter' YM theory to topological gravity. We make use of this topological point of view to obtain, in a simple and straightforward way, a complete classification of localizing supersymmetric backgrounds in two dimensions. The BRST invariant topological backgrounds are parametrized by both Killing vectors and $S^1$-equivariant cohomology of the 2-dimensional world-sheet. We reconstruct completely the supergravity backgrounds from the topological data: some of the supergravity fields are twisted versions of the topological backgrounds, but others are "composite", i.e. they are non-linear functionals of them. We recover all the known localizing 2-dimensional backgrounds and (infinitely) many more that have not been explored so far. We show that the supersymmetric $\Omega$-deformation is nothing but the background value of the ghost-for-ghost of topological gravity, a result which holds for other dimensions too. The new localizing backgrounds are characterized by non-trivial fluxes for both the graviphotons of the supergravity multiplet.Comment: 45 pages, 2 figures, revised introduction, version published on JHE

Mesothelioma and thymic tumors: Treatment challenges in (outside) a network setting

The management of patients with mesothelioma and thymic malignancy requires continuous multidisciplinary expertise at any step of the disease. A dramatic improvement in our knowledge has occurred in the last few years, through the development of databases, translational research programs, and clinical trials. Access to innovative strategies represents a major challenge, as there is a lack of funding for clinical research in rare cancers and their rarity precludes the design of robust clinical trials that could lead to specific approval of drugs. In this context, patient-centered initiatives, such as the establishment of dedicated networks, are warranted. International societies, such as IMIG (International Mesothelioma Interest Group) and ITMIG (International Thymic Malignancy Interest Group) provide infrastructure for global collaboration, and there are many advantages to having strong regional groups working on the same issues. There may be regional differences in risk factors, susceptibility, management and outcomes. The ability to address questions both regionally as well as globally is ideal to develop a full understanding of mesothelioma and thymic malignancies. In Europe, through the integration of national networks with EURACAN, the collaboration with academic societies and international groups, the development of networks in thoracic oncology provides multiplex integration of clinical care and research, ultimately ensuring equal access to high quality care to all patients, with the opportunity of conducting high level clinical and translational research projects

Chiral QED in Terms of Chiral Boson with a Generalized Fadeevian Regularization

Chiral QED with a generalized Fadeevian regularization is considered. Imposing a chiral constraint a gauged version of Floranini-Jackiw lagrangian is constructed. The imposition of the chiral constarint has spoiled t he manifestly Lorentz covariance of the theory. The phase space structure for this theory has been det ermined. It is found that spectrum changes drastically but it is Lorentz invariant. Chiral fermion di sappears from the spectra and the photon anquire mass as well. Poincare algebra has been calculated to show physicial Lorentz invariance explicitely.Comment: 11 page

Investigational treatments for neurodegenerative diseases caused by inheritance of gene mutations: lessons from recent clinical trials

: We reviewed recent major clinical trials with investigational drugs for the treatment of subjects with neurodegenerative diseases caused by inheritance of gene mutations or associated with genetic risk factors. Specifically, we discussed randomized clinical trials in subjects with Alzheimer's disease, Huntington's disease and amyotrophic lateral sclerosis bearing pathogenic gene mutations, and glucocerebrosidase-associated Parkinson's disease. Learning potential lessons to improve future therapeutic approaches is the aim of this review. Two long-term, controlled trials on three anti-β-amyloid monoclonal antibodies (solanezumab, gantenerumab and crenezumab) in subjects carrying Alzheimer's disease-linked mutated genes encoding for amyloid precursor protein or presenilin 1 or presenilin 2 failed to show cognitive or functional benefits. A major trial on tominersen, an antisense oligonucleotide designed to reduce the production of the huntingtin protein in subjects with Huntington's disease, was prematurely interrupted because the drug failed to show higher efficacy than placebo and, at highest doses, led to worsened outcomes. A 28-week trial of tofersen, an antisense oligonucleotide for superoxide dismutase 1 in patients with amyotrophic lateral sclerosis with superoxide dismutase 1 gene mutations failed to show significant beneficial effects but the 1-year open label extension of this study indicated better clinical and functional outcomes in the group with early tofersen therapy. A trial of venglustat, a potent and brain-penetrant glucosylceramide synthase inhibitor, in Parkinson's disease subjects with heterozygous glucocerebrosidase gene mutations revealed worsened clinical and cognitive performance of patients on the enzyme inhibitor compared to placebo. We concluded that clinical trials in neurodegenerative diseases with a genetic basis should test monoclonal antibodies, antisense oligonucleotides or gene editing directed against the mutated enzyme or the mutated substrate without dramatically affecting physiological wild-type variants

The Kontsevich Connection on the Moduli Space of FZZT Liouville Branes

We point out that insertions of matrix fields in (connected amputated) amplitudes of (generalized) Kontsevich models are given by covariant derivatives with respect to the Kontsevich moduli. This implies that correlators are sections of symmetric products of the (holomorphic) tangent bundle on the (complexified) moduli space of FZZT Liouville branes. We discuss the relation of Kontsevich parametrization of moduli space with that provided by either the (p,1) or the (1,p) boundary conformal field theories. It turns out that the Kontsevich connection captures the contribution of contact terms to open string amplitudes of boundary cosmological constant operators in the (1,p) minimal string models. The curvature of the connection is of type (1,1) and has delta-function singularities at the points in moduli space where Kontsevich kinetic term vanishes. We also outline the extention of our formalism to the c=1 string at self-dual radius and discuss the problems that have to be understood to reconciliate first and second quantized approaches in this case.Comment: 34 pages, 2 eps figures, LaTex; typos corrected (including title); more typos fixed, including those in Eqs.(72) and (132