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

The topological matrix model of c=1 string

We derive a Kontsevich-type matrix model for the c=1 string directly from the W-infinity solution of the theory. The model that we obtain is different from previous proposals, which are proven to be incorrect. Our matrix model contains the Penner and Kontsevich cases, and we study its quantum effective action. The simplicity of our model leads to an encouraging interpretation in the context of background-independent noncritical string field theory

Topological anomalies for Seifert 3-manifolds

We study globally supersymmetric 3d gauge theories on curved manifolds by describing the coupling of 3d topological gauge theories, with both Yang-Mills and Chern-Simons terms in the action, to background topological gravity. In our approach the Seifert condition for manifolds supporting global supersymmetry is elegantly deduced from the topological gravity BRST transformations. A cohomological characterization of the geometrical moduli which affect the partition function is obtained. In the Seifert context Chern-Simons topological (framing) anomaly is BRST trivial. We compute explicitly the corresponding local Wess-Zumino functional. As an application, we obtain the dependence on the Seifert moduli of the partition function of 3d supersymmetric gauge theory on the squashed sphere by solving the anomalous topological Ward identities, in a regularization independent way and without the need of evaluating any functional determinant.Comment: 31 pages; v2: some comments added, references added; v3: published version, 1+34 pages, one appendix explaining the relation with the supergravity approach added, minor comments and two references adde

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

A lagrangian formulation of 2-dimensional topological gravity and Cech-de Rham cohomology

We present a very simplified analysis of how one can overcome the Gribov problem in a non-abelian gauge theory. Our formulae, albeit quite simplified, show that possible breakdowns of the Slavnov-Taylor identity could in principle come from singularities in space of gauge orbits. To test these ideas we exhibit the calculation of a very simple correlation function of 2-dimensional topological gravity and we show how in this model the singularities of the moduli space induce a breakdown of the Slavnov-Taylor identity. We comment on the technical relevance of the possibility of including the singularities into a finite number of cells of the moduli space

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

Superconformal anomalies from superconformal Chern-Simons polynomials

We consider the 4-dimensional $\mathcal{N}=1$ Lie superconformal algebra and search for completely "symmetric" (in the graded sense) 3-index invariant tensors. The solution we find is unique and we show that the corresponding invariant polynomial cubic in the generalized curvatures of superconformal gravity vanishes. Consequently, the associated Chern-Simons polynomial is a non-trivial anomaly cocycle. We explicitly compute this cocycle to all orders in the independent fields of superconformal gravity and establish that it is BRST equivalent to the so-called superconformal $a$-anomaly. We briefly discuss the possibility that the superconformal $c$-anomaly also admits a similar Chern-Simons formulation.Comment: 44 page

Holomorphic Chern-Simons theory coupled to off-shell Kodaira-Spencer gravity

We construct an action for holomorphic Chern-Simons theory that couples the gauge field to off-shell gravitational backgrounds, comprising the complex structure and the (3,0)-form of the target space. Gauge invariance of the off-shell action is achieved by enlarging the field space to include an appropriate system of Lagrange multipliers, ghost and ghost-for-ghost fields. Both the BRST transformations and the BV action are compactly and neatly written in terms of superfields which include fields, backgrounds and their antifields. We show that the anti-holomorphic target space derivative can be written as a BRST-commutator on a functional space containing the anti-fields of both the dynamical fields and the gravitational backgrounds. We derive from this result a Ward identity that determines the anti-holomorphic dependence of physical correlators.Comment: 21 page

Superconformal anomalies from superconformal Chern-Simons polynomials

We consider the 4-dimensional N = 1 Lie superconformal algebra and search for completely “symmetric” (in the graded sense) 3-index invariant tensors. The solution we find is unique and we show that the corresponding invariant polynomial cubic in the generalized curvatures of superconformal gravity vanishes. Consequently, the associated Chern-Simons polynomial is a non-trivial anomaly cocycle. We explicitly compute this cocycle to all orders in the independent fields of superconformal gravity and establish that it is BRST equivalent to the so-called superconformal a-anomaly. We briefly discuss the possibility that the superconformal c-anomaly also admits a similar Chern-Simons formulation and the potential holographic, 5-dimensional, interpretation of our results