Conformal Invariance in the Long-Range Ising Model

We consider the question of conformal invariance of the long-range Ising model at the critical point. The continuum description is given in terms of a nonlocal field theory, and the absence of a stress tensor invalidates all of the standard arguments for the enhancement of scale invariance to conformal invariance. We however show that several correlation functions, computed to second order in the epsilon expansion, are nontrivially consistent with conformal invariance. We proceed to give a proof of conformal invariance to all orders in the epsilon expansion, based on the description of the long-range Ising model as a defect theory in an auxiliary higher-dimensional space. A detailed review of conformal invariance in the d-dimensional short-range Ising model is also included and may be of independent interest.Comment: 52pp; V2: refs added; V3: ref added, published versio

Giant FAZ10 is required for flagellum attachment zone stabilization and furrow positioning in Trypanosoma brucei

The flagellum and flagellum attachment zone (FAZ) are important cytoskeletal structures in trypanosomatids, being required for motility, cell division and cell morphogenesis. Trypanosomatid cytoskeletons contain abundant high molecular mass proteins (HMMPs), but many of their biological functions are still unclear. Here, we report the characterization of the giant FAZ protein, FAZ10, in Trypanosoma brucei, which, using immunoelectron microscopy, we show localizes to the intermembrane staples in the FAZ intracellular domain. Our data show that FAZ10 is a giant cytoskeletal protein essential for normal growth and morphology in both procyclic and bloodstream parasite life cycle stages, with its depletion leading to defects in cell morphogenesis, flagellum attachment, and kinetoplast and nucleus positioning. We show that the flagellum attachment defects are probably brought about by reduced tethering of the proximal domain of the paraflagellar rod to the FAZ filament. Further, FAZ10 depletion also reduces abundance of FAZ flagellum domain protein, ClpGM6. Moreover, ablation of FAZ10 impaired the timing and placement of the cleavage furrow during cytokinesis, resulting in premature or asymmetrical cell division