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Derived Equivalences of K3 Surfaces and Twined Elliptic Genera

We use the unique canonically-twisted module over a certain distinguished super vertex operator algebra---the moonshine module for Conway's group---to attach a weak Jacobi form of weight zero and index one to any symplectic derived equivalence of a projective complex K3 surface that fixes a stability condition in the distinguished space identified by Bridgeland. According to work of Huybrechts, following Gaberdiel--Hohenegger--Volpato, any such derived equivalence determines a conjugacy class in Conway's group, the automorphism group of the Leech lattice. Conway's group acts naturally on the module we consider. In physics the data of a projective complex K3 surface together with a suitable stability condition determines a supersymmetric non-linear sigma model, and supersymmetry preserving automorphisms of such an object may be used to define twinings of the K3 elliptic genus. Our construction recovers the K3 sigma model twining genera precisely in all available examples. In particular, the identity symmetry recovers the usual K3 elliptic genus, and this signals a connection to Mathieu moonshine. A generalization of our construction recovers a number of the Jacobi forms arising in umbral moonshine. We demonstrate a concrete connection to supersymmetric non-linear K3 sigma models by establishing an isomorphism between the twisted module we consider and the vector space underlying a particular sigma model attached to a certain distinguished K3 surface.Comment: 62 pages including 7 pages of tables; updated references and minor editing in v.2; to appear in Research in the Mathematical Science

The Moonshine Module for Conway's Group

We exhibit an action of Conway's group---the automorphism group of the Leech lattice---on a distinguished super vertex operator algebra, and we prove that the associated graded trace functions are normalized principal moduli, all having vanishing constant terms in their Fourier expansion. Thus we construct the natural analogue of the Frenkel--Lepowsky--Meurman moonshine module for Conway's group. The super vertex operator algebra we consider admits a natural characterization, in direct analogy with that conjectured to hold for the moonshine module vertex operator algebra. It also admits a unique canonically-twisted module, and the action of the Conway group naturally extends. We prove a special case of generalized moonshine for the Conway group, by showing that the graded trace functions arising from its action on the canonically-twisted module are constant in the case of Leech lattice automorphisms with fixed points, and are principal moduli for genus zero groups otherwise.Comment: 54 pages including 11 pages of tables; minor revisions in v2, submitte

Kinetics of the HO_2 + BrO reaction over the temperature range 233–348 K

The reaction BrO + HO_2 → products is the rate-limiting step in a key catalytic ozone destruction cycle in the lower stratosphere. In this study a discharge-flow reactor coupled with molecular beam mass spectrometry has been used to study the BrO + HO_2 reaction over the temperature range 233-348 K. Rate constants were measured under pseudo-first-order conditions in separate experiments with first HO_2 and then BrO in excess in an effort to identify possible complications in the reaction conditions. At 298 K, the rate constant was determined to be (1.73 ± 0.61) x 10^(-11) cm^3 molecule^(-1) s^(-1) with HO_2 in excess and (2.05 ± 0.64) x 10^(-11) cm^3 molecule^(-1) s^(-1) with BrO in excess. The combined results of the temperature-dependent experiments gave the following fit to the Arrhenius expression : k = (3.13 ± 0.33)]10^(-12) exp(536 ± 206/T) where the quoted uncertainties represent two standard deviations. The reaction mechanism is discussed in light of recent ab initio results on the thermochemistry of isomers of possible reaction intermediates

Studies of ClO and BrO reactions important in the polar stratosphere: Kinetics and mechanism of the ClO+BrO and ClO+ClO reactions

The reactions, BrO + ClO yields Br + ClOO (1a) yields Br + OClO (1b) yields BrCl + O2 (1c) and ClO + ClO yields Cl + CiOO (2a) yields Cl + OClO (2b) yields Cl2 + O2 (2c) yields (ClO)2 (2d) have assumed new importance in explaining the unusual springtime depletion of ozone observed in the Antarctic stratosphere. The mechanisms of these reactions involve the formation of metastable intermediates which subsequently decompose through several energetically allowed products providing the motivation to study these reactions using both the discharge flow-mass spectrometric and flash photolysis - ultraviolet absorption techniques. These methods have also been used to explore aspects of the kinetics and spectroscopy of the ClO dimer

The metallicity dependence of WR winds

Wolf-Rayet (WR) stars are the most advanced stage in the evolution of the most massive stars. The strong feedback provided by these objects and their subsequent supernova (SN) explosions are decisive for a variety of astrophysical topics such as the cosmic matter cycle. Consequently, understanding the properties of WR stars and their evolution is indispensable. A crucial but still not well known quantity determining the evolution of WR stars is their mass-loss rate. Since the mass loss is predicted to increase with metallicity, the feedback provided by these objects and their spectral appearance are expected to be a function of the metal content of their host galaxy. This has severe implications for the role of massive stars in general and the exploration of low metallicity environments in particular. Hitherto, the metallicity dependence of WR star winds was not well studied. In this contribution, we review the results from our comprehensive spectral analyses of WR stars in environments of different metallicities, ranging from slightly super-solar to SMC-like metallicities. Based on these studies, we derived empirical relations for the dependence of the WN mass-loss rates on the metallicity and iron abundance, respectively.Comment: 5 pages, 4 figures, to be published in the Proceedings of the IAU Symposium No. 329 "The lives and death-throes of massive stars