Wakimoto Modules for Twisted Affine Lie Algebras

We construct Wakimoto modules for twisted affine Lie algebras, and interpret the construction in terms of vertex algebras and their twisted modules. Using the Wakimoto realization, we prove the Kac-Kazhdan conjecture on the characters of irreducible modules with generic critical highest weights in the twisted case. We provide explicit formulas for the twisted fields in the case of the twisted affine algebra A^{(2)}_{2}.Comment: 19 page

Twisted Modules over Vertex Algebras on Algebraic Curves

We extend the geometric approach to vertex algebras developed by the first author to twisted modules, allowing us to treat orbifold models in conformal field theory. Let $V$ be a vertex algebra, $H$ a finite group of automorphisms of $V$, and $C$ an algebraic curve such that H \subset \on{Aut}(C). We show that a suitable collection of twisted $V$--modules gives rise to a section of a certain sheaf on the quotient $X=C/H$. We introduce the notion of conformal blocks for twisted modules, and analyze them in the case of the Heisenberg and affine Kac-Moody vertex algebras. We also give a chiral algebra interpretation of twisted modules

Supersymmetry of the Chiral de Rham Complex

We present a superfield formulation of the chiral de Rham complex (CDR) of Malikov-Schechtman-Vaintrob in the setting of a general smooth manifold, and use it to endow CDR with superconformal structures of geometric origin. Given a Riemannian metric, we construct an N=1 structure on CDR (action of the N=1 super--Virasoro, or Neveu--Schwarz, algebra). If the metric is K"ahler, and the manifold Ricci-flat, this is augmented to an N=2 structure. Finally, if the manifold is hyperk"ahler, we obtain an N=4 structure. The superconformal structures are constructed directly from the Levi-Civita connection. These structures provide an analog for CDR of the extended supersymmetries of nonlinear sigma-models.Comment: References adde

AP39, A Mitochondrially- Targeted Hydrogen Sulfide Donor, Exerts Protective Effects in Renal Epithelial Cells Subjected to Oxidative Stress in Vitro and in Acute Renal Injury in Vivo.

This is the author's accepted manuscript. The article is published in final form in Shock, DOI: 10.1097/SHK.0000000000000478This study evaluated the effects of AP39 [(10-oxo-10-(4-(3-thioxo-3H-1,2-dithiol-5yl) phenoxy)decyl) triphenyl phosphonium bromide], a mitochondrially targeted donor of hydrogen sulfide (H2S) in an in vitro model of hypoxia/oxidative stress injury in NRK-49F rat kidney epithelial cells (NRK cells) and in a rat model of renal ischemia-reperfusion injury. Renal oxidative stress was induced by the addition of glucose oxidase, which generates hydrogen peroxide in the culture medium at a constant rate. Glucose oxidase (GOx)-induced oxidative stress led to mitochondrial dysfunction, decreased intracellular ATP content, and, at higher concentrations, increased intracellular oxidant formation (estimated by the fluorescent probe 2, 7-dichlorofluorescein, DCF) and promoted necrosis (estimated by the measurement of lactate dehydrogenase release into the medium) of the NRK cells in vitro. Pretreatment with AP39 (30-300 nM) exerted a concentration-dependent protective effect against all of the above effects of GOx. Most of the effects of AP39 followed a bell-shaped concentration-response curve; at the highest concentration of GOx tested, AP39 was no longer able to afford cytoprotective effects. Rats subjected to renal ischemia/reperfusion responded with a marked increase (over 4-fold over sham control baseline) blood urea nitrogen and creatinine levels in blood, indicative of significant renal damage. This was associated with increased neutrophil infiltration into the kidneys (assessed by the myeloperoxidase assay in kidney homogenates), increased oxidative stress (assessed by the malondialdehyde assay in kidney homogenates) and an increase in plasma levels of IL-12. Pretreatment with AP39 (0.1, 0.2 and 0.3 mg/kg) provided a dose-dependent protection against these pathophysiological alterations; the most pronounced protective effect was observed at the 0.3 mg/kg dose of the H2S donor; nevertheless AP39 failed to achieve a complete normalization of any of the injury markers measured. The partial protective effects of AP39 correlated with a partial improvement of kidney histological scores and reduced TUNEL staining (an indicator of DNA damage and apoptosis). In summary, the mitochondria-targeted H2S donor AP39 exerted dose-dependent protective effects against renal epithelial cell injury in vitro and renal ischemia-reperfusion injury in vivo. We hypothesize that the beneficial actions of AP39 are related to the reduction of cellular oxidative stress, and subsequent attenuation of various positive feed-forward cycles of inflammatory and oxidative processes.National Institutes of Healt

On the structure and representations of the insertion-elimination Lie algebra

We examine the structure of the insertion-elimination Lie algebra on rooted trees introduced in \cite{CK}. It possesses a triangular structure \g = \n_+ \oplus \mathbb{C}.d \oplus \n_-, like the Heisenberg, Virasoro, and affine algebras. We show in particular that it is simple, which in turn implies that it has no finite-dimensional representations. We consider a category of lowest-weight representations, and show that irreducible representations are uniquely determined by a "lowest weight" $\lambda \in \mathbb{C}$. We show that each irreducible representation is a quotient of a Verma-type object, which is generically irreducible

The novel mitochondria-targeted hydrogen sulfide (H2S) donors AP123 and AP39 protect against hyperglycemic injury in microvascular endothelial cells in vitro.

The development of diabetic vascular complications is initiated, at least in part, by mitochondrial reactive oxygen species (ROS) production in endothelial cells. Hyperglycemia induces superoxide production in the mitochondria and initiates changes in the mitochondrial membrane potential that leads to mitochondrial dysfunction. Hydrogen sulfide (H2S) supplementation has been shown to reduce the mitochondrial oxidant production and shows efficacy against diabetic vascular damage in vivo. However, the half-life of H2S is very short and it is not specific for the mitochondria. We have therefore evaluated two novel mitochondria-targeted anethole dithiolethione and hydroxythiobenzamide H2S donors (AP39 and AP123 respectively) at preventing hyperglycemia-induced oxidative stress and metabolic changes in microvascular endothelial cells in vitro. Hyperglycemia (HG) induced significant increase in the activity of the citric acid cycle and led to elevated mitochondrial membrane potential. Mitochondrial oxidant production was increased and the mitochondrial electron transport decreased in hyperglycemic cells. AP39 and AP123 (30-300nM) decreased HG-induced hyperpolarisation of the mitochondrial membrane and inhibited the mitochondrial oxidant production. Both H2S donors (30-300nM) increased the electron transport at respiratory complex III and improved the cellular metabolism. Targeting H2S to mitochondria retained the cytoprotective effect of H2S against glucose-induced damage in endothelial cells suggesting that the molecular target of H2S action is within the mitochondria. Mitochondrial targeting of H2S also induced >1000-fold increase in the potency of H2S against hyperglycemia-induced injury. The high potency and long-lasting effect elicited by these H2S donors strongly suggests that these compounds could be useful against diabetic vascular complications