Abelian Chern-Simons theory with toral gauge group, modular tensor categories, and group categories

Classical and quantum Chern-Simons with gauge group $\text{U}(1)^N$ were classified by Belov and Moore in \cite{belov_moore}. They studied both ordinary topological quantum field theories as well as spin theories. On the other hand a correspondence is well known between ordinary $(2+1)$-dimensional TQFTs and modular tensor categories. We study group categories and extend them slightly to produce modular tensor categories that correspond to toral Chern-Simons. Group categories have been widely studied in other contexts in the literature \cite{frolich_kerler},\cite{quinn},\cite{joyal_street},\cite{eno},\cite{dgno}. The main result is a proof that the associated projective representation of the mapping class group is isomorphic to the one from toral Chern-Simons. We also remark on an algebraic theorem of Nikulin that is used in this paper.Comment: 152 page

Ground State Degeneracy in the Levin-Wen Model for Topological Phases

We study properties of topological phases by calculating the ground state degeneracy (GSD) of the 2d Levin-Wen (LW) model. Here it is explicitly shown that the GSD depends only on the spatial topology of the system. Then we show that the ground state on a sphere is always non-degenerate. Moreover, we study an example associated with a quantum group, and show that the GSD on a torus agrees with that of the doubled Chern-Simons theory, consistent with the conjectured equivalence between the LW model associated with a quantum group and the doubled Chern-Simons theory.Comment: 8 pages, 2 figures. v2: reference added; v3: two appendices adde

MERLIN observations of relativistic ejections from GRS 1915+105

We present high resolution MERLIN radio images of multiple relativistic ejections from GRS 1915+105 in 1997 October / November. The observations were made at a time of complex radio behaviour, corresponding to multiple optically-thin outbursts and several days of rapid radio flux oscillations. The radio imaging resolved four major ejection events from the system. As previously reported from earlier VLA observations of the source, we observe apparent superluminal motions resulting from intrinsically relativistic motions of the ejecta. However, our measured proper motions are significantly greater than those observed on larger angular scales with the VLA. Under the assumption of an intrinsically symmetric ejection, we can place an upper limit on the distance to GRS 1915+105 of 11.2 +/- 0.8 kpc. Solutions for the velocities unambiguously require a higher intrinsic speed by about 0.1c than that derived from the earlier VLA observations, whilst the angle to the line-of-sight is not found to be significantly different. At a distance of 11 kpc, we obtain solutions of v = 0.98 (-0.05,+0.02)c and theta = 66 +/- 2 degrees. The jet also appears to be curved on a scale which corresponds to a period of around 7 days. We observe significant evolution of the linear polarisation of the approaching component, with large rotations in position angle and a general decrease in fractional polarisation. The power input into the formation of the jet is very large, >10^38 erg/s at 11 kpc for a pair plasma. If the plasma contains a cold proton for each electron, then the mass outflow rate, >10^18 g/sec is comparable to inflow rates previously derived from X-ray spectral fits.Comment: 14 pages, 7 figures. Accepted for publication in MNRA

Big Bang Nucleosynthesis with Gaussian Inhomogeneous Neutrino Degeneracy

We consider the effect of inhomogeneous neutrino degeneracy on Big Bang nucleosynthesis for the case where the distribution of neutrino chemical potentials is given by a Gaussian. The chemical potential fluctuations are taken to be isocurvature, so that only inhomogeneities in the electron chemical potential are relevant. Then the final element abundances are a function only of the baryon-photon ratio $\eta$, the effective number of additional neutrinos $\Delta N_\nu$, the mean electron neutrino degeneracy parameter $\bar \xi$, and the rms fluctuation of the degeneracy parameter, $\sigma_\xi$. We find that for fixed $\eta$, $\Delta N_\nu$, and $\bar \xi$, the abundances of helium-4, deuterium, and lithium-7 are, in general, increasing functions of $\sigma_\xi$. Hence, the effect of adding a Gaussian distribution for the electron neutrino degeneracy parameter is to decrease the allowed range for $\eta$. We show that this result can be generalized to a wide variety of distributions for $\xi$.Comment: 9 pages, 3 figures, added discussion of neutrino oscillations, altered presentation of figure

Multiple relativistic outbursts of GRS 1915+105: radio emission and internal shocks

We present 5-GHz MERLIN radio images of the microquasar GRS 1915+105 during two separate outbursts in 2001 March and 2001 July, following the evolution of the jet components as they move outwards from the core of the system. Proper motions constrain the intrinsic jet speed to be >0.57c, but the uncertainty in the source distance prevents an accurate determination of the jet speed. No deceleration is observed in the jet components out to an angular separation of about 300mas. Linear polarisation is observed in the approaching jet component, with a gradual rotation in position angle and a decreasing fractional polarisation with time. Our data lend support to the internal shock model whereby the jet velocity increases leading to internal shocks in the pre-existing outflow before the jet switches off. The compact nuclear jet is seen to re-establish itself within two days, and is visible as core emission at all epochs. The energetics of the source are calculated for the possible range of distances; a minimum power of 1-10 per cent of the Eddington luminosity is required to launch the jet.Comment: 18 pages, 14 figures, accepted for publication in MNRAS. For higher-resolution versions of Figures 3, 5, and 12, see http://remote.science.uva.nl/~jmiller/grs1915/figures.htm

Mutability and mutational spectrum of chromosome transmission fidelity genes

It has been more than two decades since the original chromosome transmission fidelity (Ctf) screen of Saccharomyces cerevisiae was published. Since that time the spectrum of mutations known to cause Ctf and, more generally, chromosome instability (CIN) has expanded dramatically as a result of systematic screens across yeast mutant arrays. Here we describe a comprehensive summary of the original Ctf genetic screen and the cloning of the remaining complementation groups as efforts to expand our knowledge of the CIN gene repertoire and its mutability in a model eukaryote. At the time of the original screen, it was impossible to predict either the genes and processes that would be overrepresented in a pool of random mutants displaying a Ctf phenotype or what the entire set of genes potentially mutable to Ctf would be. We show that in a collection of 136 randomly selected Ctf mutants, >65% of mutants map to 13 genes, 12 of which are involved in sister chromatid cohesion and/or kinetochore function. Extensive screening of systematic mutant collections has shown that ~350 genes with functions as diverse as RNA processing and proteasomal activity mutate to cause a Ctf phenotype and at least 692 genes are required for faithful chromosome segregation. The enrichment of random Ctf alleles in only 13 of ~350 possible Ctf genes suggests that these genes are more easily mutable to cause genome instability than the others. These observations inform our understanding of recurring CIN mutations in human cancers where presumably random mutations are responsible for initiating the frequently observed CIN phenotype of tumors