Spectral flow invariants and twisted cyclic theory from the Haar state on SU_q(2)

In [CPR2], we presented a K-theoretic approach to finding invariants of algebras with no non-trivial traces. This paper presents a new example that is more typical of the generic situation. This is the case of an algebra that admits only non-faithful traces, namely SU_q(2), and also KMS states. Our main results are index theorems (which calculate spectral flow), one using ordinary cyclic cohomology and the other using twisted cyclic cohomology, where the twisting comes from the generator of the modular group of the Haar state. In contrast to the Cuntz algebras studied in [CPR2], the computations are considerably more complex and interesting, because there are nontrivial `eta' contributions to this index.Comment: 25 pages, 1 figur

Principal Bundles and the Dixmier Douady Class

A systematic consideration of the problem of the reduction and extension of the structure group of a principal bundle is made and a variety of techniques in each case are explored and related to one another. We apply these to the study of the Dixmier-Douady class in various contexts including string structures, U-res bundles and other examples motivated by considerations from quantum field theory.Comment: 28 pages, latex, no figures, uses amsmath, amsthm, amsfonts. Revised version - only change a lot of irritating typos remove

Twisted K-theory and K-theory of bundle gerbes

In this note we introduce the notion of bundle gerbe K-theory and investigate the relation to twisted K-theory. We provide some examples. Possible applications of bundle gerbe K-theory to the classification of D-brane charges in non-trivial backgrounds are discussed.Comment: 29 pages, corrected typos, added references, included new section on twisted Chern character in non-torsion cas

Comparison of Algorithms and Parameterisations for Infiltration into Organic-Covered Permafrost Soils

Infiltration into frozen and unfrozen soils is critical in hydrology, controlling active layer soil water dynamics and influencing runoff. Few Land Surface Models (LSMs) and Hydrological Models (HMs) have been developed, adapted or tested for frozen conditions and permafrost soils. Considering the vast geographical area influenced by freeze/thaw processes and permafrost, and the rapid environmental change observed worldwide in these regions, a need exists to improve models to better represent their hydrology. In this study, various infiltration algorithms and parameterisation methods, which are commonly employed in current LSMs and HMs were tested against detailed measurements at three sites in Canada’s discontinuous permafrost region with organic soil depths ranging from 0.02 to 3 m. Field data from two consecutive years were used to calibrate and evaluate the infiltration algorithms and parameterisations. Important conclusions include: (1) the single most important factor that controls the infiltration at permafrost sites is ground thaw depth, (2) differences among the simulated infiltration by different algorithms and parameterisations were only found when the ground was frozen or during the initial fast thawing stages, but not after ground thaw reaches a critical depth of 15 to 30 cm, (3) despite similarities in simulated total infiltration after ground thaw reaches the critical depth, the choice of algorithm influenced the distribution of water among the soil layers, and (4) the ice impedance factor for hydraulic conductivity, which is commonly used in LSMs and HMs, may not be necessary once the water potential driven frozen soil parameterisation is employed. Results from this work provide guidelines that can be directly implemented in LSMs and HMs to improve their application in organic covered permafrost soils

Holonomy on D-Branes

This paper shows how to construct anomaly free world sheet actions in string theory with $D$-branes. Our method is to use Deligne cohomology and bundle gerbe theory to define geometric objects which are naturally associated to $D$-branes and connections on them. The holonomy of these connections can be used to cancel global anomalies in the world sheet action.Comment: Corrections made and some typographical errors remove

The spectral shift function and spectral flow

This paper extends Krein's spectral shift function theory to the setting of semifinite spectral triples. We define the spectral shift function under these hypotheses via Birman-Solomyak spectral averaging formula and show that it computes spectral flow.Comment: 47 page

Supersymmetry and the Anomalous Anomalous Magnetic Moment of the Muon

The recently reported measurement of the muon's anomalous magnetic moment differs from the standard model prediction by 2.6 standard deviations. We examine the implications of this discrepancy for supersymmetry. Deviations of the reported magnitude are generic in supersymmetric theories. Based on the new result, we derive model-independent upper bounds on the masses of observable supersymmetric particles. We also examine several model frameworks. The sign of the reported deviation is as predicted in many simple models, but disfavors anomaly-mediated supersymmetry breaking.Comment: 4 pages, 4 figures, version to appear in Phys. Rev. Let