Integrability of Vortex Equations on Riemann Surfaces

The Abelian Higgs model on a compact Riemann surface \Sigma of genus g is considered. We show that for g > 1 the Bogomolny equations for multi-vortices at critical coupling can be obtained as compatibility conditions of two linear equations (Lax pair) which are written down explicitly. These vortices correspond precisely to SO(3)-symmetric Yang-Mills instantons on the (conformal) gravitational instanton \Sigma\times S^2 with a scalar-flat Kahler metric. Thus, the standard methods of constructing solutions and studying their properties by using Lax pairs (twistor approach, dressing method etc.) can be applied to the vortex equations on \Sigma. In the twistor description, solutions of the integrable vortex equations correspond to rank-2 holomorphic vector bundles over the complex 3-dimensional twistor space of \Sigma\times S^2. We show that in the general (nonintegrable) case there is a bijection between the moduli spaces of solutions to vortex equations on \Sigma and of pseudo-holomorphic bundles over the almost complex twistor space.Comment: 16 pages; v2: typos fixed, clarifying comments added, published versio

Hidden Symmetries and Integrable Hierarchy of the N=4 Supersymmetric Yang-Mills Equations

We describe an infinite-dimensional algebra of hidden symmetries of N=4 supersymmetric Yang-Mills (SYM) theory. Our derivation is based on a generalization of the supertwistor correspondence. Using the latter, we construct an infinite sequence of flows on the solution space of the N=4 SYM equations. The dependence of the SYM fields on the parameters along the flows can be recovered by solving the equations of the hierarchy. We embed the N=4 SYM equations in the infinite system of the hierarchy equations and show that this SYM hierarchy is associated with an infinite set of graded symmetries recursively generated from supertranslations. Presumably, the existence of such nonlocal symmetries underlies the observed integrable structures in quantum N=4 SYM theory.Comment: 24 page

The Topological B-model on a Mini-Supertwistor Space and Supersymmetric Bogomolny Monopole Equations

In the recent paper hep-th/0502076, it was argued that the open topological B-model whose target space is a complex (2|4)-dimensional mini-supertwistor space with D3- and D1-branes added corresponds to a super Yang-Mills theory in three dimensions. Without the D1-branes, this topological B-model is equivalent to a dimensionally reduced holomorphic Chern-Simons theory. Identifying the latter with a holomorphic BF-type theory, we describe a twistor correspondence between this theory and a supersymmetric Bogomolny model on R^3. The connecting link in this correspondence is a partially holomorphic Chern-Simons theory on a Cauchy-Riemann supermanifold which is a real one-dimensional fibration over the mini-supertwistor space. Along the way of proving this twistor correspondence, we review the necessary basic geometric notions and construct action functionals for the involved theories. Furthermore, we discuss the geometric aspect of a recently proposed deformation of the mini-supertwistor space, which gives rise to mass terms in the supersymmetric Bogomolny equations. Eventually, we present solution generating techniques based on the developed twistorial description together with some examples and comment briefly on a twistor correspondence for super Yang-Mills theory in three dimensions.Comment: 55 pages; v2: typos fixed, published versio

Reticulocyte binding protein homologues are key adhesins during erythrocyte invasion by Plasmodium falciparum

The Apicomplexan parasite responsible for the most virulent form of malaria, Plasmodium falciparum, invades human erythrocytes through multiple ligand–receptor interactions. The P. falciparum reticulocyte-binding protein homologue (PfRh or PfRBL) family have been implicated in the invasion process but their exact role is unknown. PfRh1 and PfRh4, members of this protein family, bind to red blood cells and function in merozoite invasion during which they undergo a series of proteolytic cleavage events before and during entry into the host cell. The ectodomain of PfRh1 and PfRh4 are processed to produce fragments consistent with cleavage in the transmembrane domain and released into the supernatant, at about the time of invasion, in a manner consistent with rhomboid protease cleavage. Processing of both PfRh1 and PfRh4, and by extrapolation all membrane-bound members of this protein family, is important for function and release of these proteins on the merozoite surface and they along with EBA-175 are important components of the tight junction, the transient structure that links the erythrocyte via receptor–ligand interactions to the actin–myosin motor in the invading merozoite

Identification of a New Rhoptry Neck Complex RON9/RON10 in the Apicomplexa Parasite Toxoplasma gondii

Apicomplexan parasites secrete and inject into the host cell the content of specialized secretory organelles called rhoptries, which take part into critical processes such as host cell invasion and modulation of the host cell immune response. The rhoptries are structurally and functionally divided into two compartments. The apical duct contains rhoptry neck (RON) proteins that are conserved in Apicomplexa and are involved in formation of the moving junction (MJ) driving parasite invasion. The posterior bulb contains rhoptry proteins (ROPs) unique to an individual genus and, once injected in the host cell act as effector proteins to co-opt host processes and modulate parasite growth and virulence. We describe here two new RON proteins of Toxoplasma gondii, RON9 and RON10, which form a high molecular mass complex. In contrast to the other RONs described to date, this complex was not detected at the MJ during invasion and therefore was not associated to the MJ complex RON2/4/5/8. Disruptions of either RON9 or RON10 gene leads to the retention of the partner in the ER followed by subsequent degradation, suggesting that the RON9/RON10 complex formation is required for proper sorting to the rhoptries. Finally, we show that the absence of RON9/RON10 has no significant impact on the morphology of rhoptry, on the invasion and growth in fibroblasts in vitro or on virulence in vivo. The conservation of RON9 and RON10 in Coccidia and Cryptosporidia suggests a specific relation with development in intestinal epithelial cells

Export of a Toxoplasma gondii Rhoptry Neck Protein Complex at the Host Cell Membrane to Form the Moving Junction during Invasion

One of the most conserved features of the invasion process in Apicomplexa parasites is the formation of a moving junction (MJ) between the apex of the parasite and the host cell membrane that moves along the parasite and serves as support to propel it inside the host cell. The MJ was, up to a recent period, completely unknown at the molecular level. Recently, proteins originated from two distinct post-Golgi specialised secretory organelles, the micronemes (for AMA1) and the neck of the rhoptries (for RON2/RON4/RON5 proteins), have been shown to form a complex. AMA1 and RON4 in particular, have been localised to the MJ during invasion. Using biochemical approaches, we have identified RON8 as an additional member of the complex. We also demonstrated that all RON proteins are present at the MJ during invasion. Using metabolic labelling and immunoprecipitation, we showed that RON2 and AMA1 were able to interact in the absence of the other members. We also discovered that all MJ proteins are subjected to proteolytic maturation during trafficking to their respective organelles and that they could associate as non-mature forms in vitro. Finally, whereas AMA1 has previously been shown to be inserted into the parasite membrane upon secretion, we demonstrated, using differential permeabilization and loading of RON-specific antibodies into the host cell, that the RON complex is targeted to the host cell membrane, where RON4/5/8 remain associated with the cytoplasmic face. Globally, these results point toward a model of MJ organization where the parasite would be secreting and inserting interacting components on either side of the MJ, both at the host and at its own plasma membranes

Non-Abelian Vortices on Riemann Surfaces: an Integrable Case

We consider U(n+1) Yang-Mills instantons on the space \Sigma\times S^2, where \Sigma is a compact Riemann surface of genus g. Using an SU(2)-equivariant dimensional reduction, we show that the U(n+1) instanton equations on \Sigma\times S^2 are equivalent to non-Abelian vortex equations on \Sigma. Solutions to these equations are given by pairs (A,\phi), where A is a gauge potential of the group U(n) and \phi is a Higgs field in the fundamental representation of the group U(n). We briefly compare this model with other non-Abelian Higgs models considered recently. Afterwards we show that for g>1, when \Sigma\times S^2 becomes a gravitational instanton, the non-Abelian vortex equations are the compatibility conditions of two linear equations (Lax pair) and therefore the standard methods of integrable systems can be applied for constructing their solutions.Comment: 8 pages; v2: typos fixe

Measurement of the cosmic ray spectrum above 4×10184{\times}10^{18} eV using inclined events detected with the Pierre Auger Observatory

A measurement of the cosmic-ray spectrum for energies exceeding $4{\times}10^{18}$ eV is presented, which is based on the analysis of showers with zenith angles greater than $60^{\circ}$ detected with the Pierre Auger Observatory between 1 January 2004 and 31 December 2013. The measured spectrum confirms a flux suppression at the highest energies. Above $5.3{\times}10^{18}$ eV, the "ankle", the flux can be described by a power law $E^{-\gamma}$ with index $\gamma=2.70 \pm 0.02 \,\text{(stat)} \pm 0.1\,\text{(sys)}$ followed by a smooth suppression region. For the energy ($E_\text{s}$) at which the spectral flux has fallen to one-half of its extrapolated value in the absence of suppression, we find $E_\text{s}=(5.12\pm0.25\,\text{(stat)}^{+1.0}_{-1.2}\,\text{(sys)}){\times}10^{19}$ eV.Comment: Replaced with published version. Added journal reference and DO