Global Spinors and Orientable Five-Branes

Fermion fields on an M-theory five-brane carry a representation of the double cover of the structure group of the normal bundle. It is shown that, on an arbitrary oriented Lorentzian six-manifold, there is always an Sp(2) twist that allows such spinors to be defined globally. The vanishing of the arising potential obstructions does not depend on spin structure in the bulk, nor does the six-manifold need to be spin or spin-C. Lifting the tangent bundle to such a generalised spin bundle requires picking a generalised spin structure in terms of certain elements in the integral and modulo-two cohomology of the five-brane world-volume in degrees four and five, respectively.Comment: 18 pages, LaTeX; v2: version to appear in JHE

Thermodynamic metrics and optimal paths

A fundamental problem in modern thermodynamics is how a molecular-scale machine performs useful work, while operating away from thermal equilibrium without excessive dissipation. To this end, we derive a friction tensor that induces a Riemannian manifold on the space of thermodynamic states. Within the linear-response regime, this metric structure controls the dissipation of finite-time transformations, and bestows optimal protocols with many useful properties. We discuss the connection to the existing thermodynamic length formalism, and demonstrate the utility of this metric by solving for optimal control parameter protocols in a simple nonequilibrium model.Comment: 5 page

Syk tyrosine kinase is critical for B cell antibody responses and memory B cell survival

Signals from the BCR are required for Ag-specific B cell recruitment into the immune response. Binding of Ag to the BCR induces phosphorylation of immune receptor tyrosine-based activation motifs in the cytoplasmic domains of the CD79a and CD79b signaling subunits, which subsequently bind and activate the Syk protein tyrosine kinase. Earlier work with the DT40 chicken B cell leukemia cell line showed that Syk was required to transduce BCR signals to proximal activation events, suggesting that Syk also plays an important role in the activation and differentiation of primary B cells during an immune response. In this study, we show that Syk-deficient primary mouse B cells have a severe defect in BCR-induced activation, proliferation, and survival. Furthermore, we demonstrate that Syk is required for both T-dependent and T-independent Ab responses, and that this requirement is B cell intrinsic. In the absence of Syk, Ag fails to induce differentiation of naive B cells into germinal center B cells and plasma cells. Finally, we show that the survival of existing memory B cells is dependent on Syk. These experiments demonstrate that Syk plays a critical role in multiple aspects of B cell Ab responses

The Serre spectral sequence of a noncommutative fibration for de Rham cohomology

For differential calculi on noncommutative algebras, we construct a twisted de Rham cohomology using flat connections on modules. This has properties similar, in some respects, to sheaf cohomology on topological spaces. We also discuss generalised mapping properties of these theories, and relations of these properties to corings. Using this, we give conditions for the Serre spectral sequence to hold for a noncommutative fibration. This might be better read as giving the definition of a fibration in noncommutative differential geometry. We also study the multiplicative structure of such spectral sequences. Finally we show that some noncommutative homogeneous spaces satisfy the conditions to be such a fibration, and in the process clarify the differential structure on these homogeneous spaces. We also give two explicit examples of differential fibrations: these are built on the quantum Hopf fibration with two different differential structures.Comment: LaTeX, 33 page

Loop Groups, Kaluza-Klein Reduction and M-Theory

We show that the data of a principal G-bundle over a principal circle bundle is equivalent to that of a \hat{LG} = U(1) |x LG bundle over the base of the circle bundle. We apply this to the Kaluza-Klein reduction of M-theory to IIA and show that certain generalized characteristic classes of the loop group bundle encode the Bianchi identities of the antisymmetric tensor fields of IIA supergravity. We further show that the low dimensional characteristic classes of the central extension of the loop group encode the Bianchi identities of massive IIA, thereby adding support to the conjectures of hep-th/0203218.Comment: 26 pages, LaTeX, utarticle.cls, v2:clarifications and refs adde

On the integral cohomology of smooth toric varieties

Let $X_\Sigma$ be a smooth, not necessarily compact toric variety. We show that a certain complex, defined in terms of the fan $\Sigma$, computes the integral cohomology of $X_\Sigma$, including the module structure over the homology of the torus. In some cases we can also give the product. As a corollary we obtain that the cycle map from Chow groups to integral Borel-Moore homology is split injective for smooth toric varieties. Another result is that the differential algebra of singular cochains on the Borel construction of $X_\Sigma$ is formal.Comment: 10 page

The chameleon groups of Richard J. Thompson: automorphisms and dynamics

The automorphism groups of several of Thompson's countable groups of piecewise linear homeomorphisms of the line and circle are computed and it is shown that the outer automorphism groups of these groups are relatively small. These results can be interpreted as stability results for certain structures of PL functions on the circle. Machinery is developed to relate the structures on the circle to corresponding structures on the line

A Survey of High Contrast Stellar Flares Observed by Chandra

The X-ray light curves of pre-main sequence stars can show variability in the form of flares altering a baseline characteristic activity level; the largest X-ray flares are characterized by a rapid rise to more than 10 times the characteristic count rate, followed by a slower quasi-exponential decay. Analysis of these high-contrast X-ray flares enables the study of the innermost magnetic fields of pre-main sequence stars. We have scanned the ANCHORS database of Chandra observations of star-forming regions to extend the study of flare events on pre-main sequence stars both in sky coverage and in volume. We developed a sample of 30 high-contrast flares out of the 14,000 stars of various ages and masses available in ANCHORS at the start of our study. Applying methods of time-resolved spectral analysis, we obtain the temperatures, confining magnetic field strengths, and loop lengths of these bright, energetic flares. The results of the flare analysis are compared to the 2MASS and Spitzer data available for the stars in our sample. We find that the longest flare loop lengths (of order several stellar radii) are only seen on stars whose IR data indicates the presence of disks. This suggests that the longest flares may stretch all the way to the disk. Such long flares tend to be more tenuous than the other large flares studied. A wide range of loop lengths are observed, indicating that different types of flares may occur on disked young stellar objects.Comment: 38 pages, 8 figures, 4 table

Locating the Accretion Footprint on a Herbig Ae Star: MWC 480

Accretion is a fundamental process which establishes the dynamics of the protoplanetary disk and the final properties of the forming star. In solar-type stars, the star–disk coupling is determined by the magnetic field structure, which is responsible for funneling material from the disk midplane to higher latitudes on the star. Here, we use pan-chromatic data for the Herbig Ae star MWC 480 to address whether similar processes occur in intermediatemass stars. MWC 480 has X-ray emission typical of actively accreting Herbig Ae stars, but with ∼10× more photoelectric absorption than expected from optical and FUV data. We consider three sources for the absorption: the disk, absorption in a wind or jet, and accretion. While we detect the disk in scattered light in a re-analysis of archival Hubble Space Telescope data, the data are consistent with grazing illumination of the dust disk.We find that MWC 480’s disk is stratified, geometrically thin, and is not responsible for the observed photoelectric absorption. MWC 480 drives a bipolar jet, but with a mass-loss rate that is low compared to other Herbig Ae stars, where the outflow is more favorably oriented and enhanced photoelectric absorption is not seen. This excludes a jet or wind origin for the enhanced photoelectric absorption. We compare MWC 480’s Ovi emission with other Herbig Ae stars. The distribution of the emission in inclination, and lack of a correlation of profile shape and system inclination excludes equatorially confined accretion for the FUSE Herbig Ae stars. The photoelectric absorption data further suggest that the accretion footprint on MWC 480 and other Herbig Ae stars is located at high-temperate, rather than polar, latitudes. These findings support the presence of funneled accretion in MWC 480 and Herbig Ae stars, strengthening the parallel to T Tauri stars

Representation theory of finite W algebras

In this paper we study the finitely generated algebras underlying $W$ algebras. These so called 'finite $W$ algebras' are constructed as Poisson reductions of Kirillov Poisson structures on simple Lie algebras. The inequivalent reductions are labeled by the inequivalent embeddings of $sl_2$ into the simple Lie algebra in question. For arbitrary embeddings a coordinate free formula for the reduced Poisson structure is derived. We also prove that any finite $W$ algebra can be embedded into the Kirillov Poisson algebra of a (semi)simple Lie algebra (generalized Miura map). Furthermore it is shown that generalized finite Toda systems are reductions of a system describing a free particle moving on a group manifold and that they have finite $W$ symmetry. In the second part we BRST quantize the finite $W$ algebras. The BRST cohomology is calculated using a spectral sequence (which is different from the one used by Feigin and Frenkel). This allows us to quantize all finite $W$ algebras in one stroke. Explicit results for $sl_3$ and $sl_4$ are given. In the last part of the paper we study the representation theory of finite $W$ algebras. It is shown, using a quantum version of the generalized Miura transformation, that the representations of finite $W$ algebras can be constructed from the representations of a certain Lie subalgebra of the original simple Lie algebra. As a byproduct of this we are able to construct the Fock realizations of arbitrary finite $W$ algebras.Comment: 62 pages, THU-92/32, ITFA-28-9