The W_N minimal model classification

We first rigourously establish, for any N, that the toroidal modular invariant partition functions for the (not necessarily unitary) W_N(p,q) minimal models biject onto a well-defined subset of those of the SU(N)xSU(N) Wess-Zumino-Witten theories at level (p-N,q-N). This permits considerable simplifications to the proof of the Cappelli-Itzykson-Zuber classification of Virasoro minimal models. More important, we obtain from this the complete classification of all modular invariants for the W_3(p,q) minimal models. All should be realised by rational conformal field theories. Previously, only those for the unitary models, i.e. W_3(p,p+1), were classified. For all N our correspondence yields for free an extensive list of W_N(p,q) modular invariants. The W_3 modular invariants, like the Virasoro minimal models, all factorise into SU(3) modular invariants, but this fails in general for larger N. We also classify the SU(3)xSU(3) modular invariants, and find there a new infinite series of exceptionals.Comment: 25 page

Challenges faced by mental health interpreters in East London: An interpretative phenomenological analysis

Background/Aims/Objectives - The role of an interpreter is instrumental for people not fluent in the new language of their host community or country where they are living. This subject is an important one and not enough is known, especially about the challenges faced by mental health interpreters. Methodology/Methods - The study examined how interpreters drew on direct translation, cultural meanings and non-verbal information while interpreting and how they convey these to both service users and providers. An Interpretative Phenomenological Analysis was adopted to analyse three semi-structured interviews with female mental health interpreters that lasted approximately 60 minutes each. All participants were self-identified as fluent in at least two languages and had attended a minimum of six months training on mental health interpreting. Results/Finding - The challenges of mental health interpreting were revealed in three overarching themes: (i) Sensitive nature of interpreting and challenges associated with ensuring accuracy. (ii) Multitasking to convey literal words, feelings and cultural meanings. (iii) Exposure to the risk of vicarious trauma and insufficient organisational support. Discussion/Conclusion - The study concluded that mental health interpreters should have more access to training and development, organisational support, professional recognition and adequate acknowledgement of their essential role in service provision to people not fluent with the new language of their present community or country

Symmetries of the Kac-Peterson Modular Matrices of Affine Algebras

The characters $\chi_\mu$ of nontwisted affine algebras at fixed level define in a natural way a representation $R$ of the modular group $SL_2(Z)$. The matrices in the image $R(SL_2(Z))$ are called the Kac-Peterson modular matrices, and describe the modular behaviour of the characters. In this paper we consider all levels of $(A_{r_1}\oplus\cdots\oplus A_{r_s})^{(1)}$, and for each of these find all permutations of the highest weights which commute with the corresponding Kac-Peterson matrices. This problem is equivalent to the classification of automorphism invariants of conformal field theories, and its solution, especially considering its simplicity, is a major step toward the classification of all Wess-Zumino-Witten conformal field theories.Comment: 16 pp, plain te

On parity functions in conformal field theories

We examine general aspects of parity functions arising in rational conformal field theories, as a result of Galois theoretic properties of modular transformations. We focus more specifically on parity functions associated with affine Lie algebras, for which we give two efficient formulas. We investigate the consequences of these for the modular invariance problem.Comment: 18 pages, no figure, LaTeX2

Automorphism Modular Invariants of Current Algebras

We consider those two-dimensional rational conformal field theories (RCFTs) whose chiral algebras, when maximally extended, are isomorphic to the current algebra formed from some affine non-twisted Kac--Moody algebra at fixed level. In this case the partition function is specified by an automorphism of the fusion ring and corresponding symmetry of the Kac--Peterson modular matrices. We classify all such partition functions when the underlying finite-dimensional Lie algebra is simple. This gives all possible spectra for this class of RCFTs. While accomplishing this, we also find the primary fields with second smallest quantum dimension.Comment: 32 pages, plain Te

The charges of a twisted brane

The charges of the twisted D-branes of certain WZW models are determined. The twisted D-branes are labelled by twisted representations of the affine algebra, and their charge is simply the ground state multiplicity of the twisted representation. It is shown that the resulting charge group is isomorphic to the charge group of the untwisted branes, as had been anticipated from a K-theory calculation. Our arguments rely on a number of non-trivial Lie theoretic identities.Comment: 27 pages, 1 figure, harvmac (b

Quasars: a supermassive rotating toroidal black hole interpretation

A supermassive rotating toroidal black hole (TBH) is proposed as the fundamental structure of quasars and other jet-producing active galactic nuclei. Rotating protogalaxies gather matter from the central gaseous region leading to the birth of massive toroidal stars whose internal nuclear reactions proceed very rapidly. Once the nuclear fuel is spent, gravitational collapse produces a slender ring-shaped TBH remnant. These events are typically the first supernovae of the host galaxies. Given time the TBH mass increases through continued accretion by several orders of magnitude, the event horizon swells whilst the central aperture shrinks. The difference in angular velocities between the accreting matter and the TBH induces a magnetic field that is strongest in the region of the central aperture and innermost ergoregion. Due to the presence of negative energy states when such a gravitational vortex is immersed in an electromagnetic field, circumstances are near ideal for energy extraction via non-thermal radiation including the Penrose process and superradiant scattering. This establishes a self-sustaining mechanism whereby the transport of angular momentum away from the quasar by relativistic bi-directional jets reinforces both the modulating magnetic field and the TBH/accretion disk angular velocity differential. Quasar behaviour is extinguished once the BH topology becomes spheroidal. Similar mechanisms may be operating in microquasars, SNe and GRBs when neutron density or BH tori arise. In certain circumstances, long-term TBH stability can be maintained by a negative cosmological constant, otherwise the classical topology theorems must somehow be circumvented. Preliminary evidence is presented that Planck-scale quantum effects may be responsible.Comment: 26 pages, 14 figs, various corrections and enhancements, final versio

Ecology of Sphaerotilus in an experimental outdoor channel

This paper describes ecological investigations performed in an outdoor experimental channel receiving Huron River water and beet sugar or crude molasses during two summers of operation (1965 and 1966).The channel was assembled in two lengths, 645 ft (1965) and 704 ft (1966), with sampling stations located one near the beginning, one in the middle and one near the end. At each station, three strands of knitting yarn were suspended and allowed to remain for 24 hr. After this time, the strands were removed, together with attached growth, and fresh strings replaced. The replicate strings were cut into 10 cm sections, with one-half of these sections used for dry weight determinations.The attached organisms were removed by violently shaking the strings suspended in a measured quantity of water. One drop was then removed and direct microscopic counts and identification made immediately. Dry weights were obtained by drying the strings in aluminum weighing pans overnight at 90[deg]C.A total of 12 experiments was run, the duration of each being in most cases five days.In the first series of experiments flow through the channel was at 100 g/min. at an essentially uniform velocity of 1 ft/sec. Nutrient concentration was varied from 1 mg/l as sucrose.In the last series of experiments, nutrient concentration was held at 5 mg/l and velocity varied at the three stations by altering the height of an overflow weir between 0.0 and 0.6 ft, and changing the flow between 25 and 200 g/min. This provided a range of velocities at the station from 0.09 to 1.49 ft/sec.The results of attached organism determinations are presented following each experiment and their response to nutrient concentration and velocity summarized in the Discussion.Sphaerotilus-dominated biological flocs were stimulated to bloom proportions within 30 hr after the addition of as little as 1 mg/l of sucrose. Maximum growth was obtained at a concentration of 5 mg/l at velocities from 0.58 to 1.49 ft/sec in the temperature range of 20-28[deg] C after around 72 hr of feeding. About this time, detaching and floating material was equivalent to new material being formed, and the term "saturation population" was proposed to describe this condition.The biological floc community was composed chiefly of Sphaerotilus natans, Melosira varians, M. granulata, Nitzschia sp., Navicula sp., Cosmarium sp., Euglena sp., and the protozoans, Bodo sp., Tetrahymena pyriformis, Colipidium colpoda, and Amoeba sp., tendipedid and simuliid larval forms also apparently found a mutualistic association within the flocs.Saturation population and classical Sphaerotilus flocs could not be obtained at temperatures below 17[deg] C. The typical form was replaced in dominance at low temperatures by an unidentified filamentous bacillus, the total mass of which never approached that of the classical growth.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/33316/1/0000711.pd

The Cosmic Censor Forbids Naked Topology

For any asymptotically flat spacetime with a suitable causal structure obeying (a weak form of) Penrose's cosmic censorship conjecture and satisfying conditions guaranteeing focusing of complete null geodesics, we prove that active topological censorship holds. We do not assume global hyperbolicity, and therefore make no use of Cauchy surfaces and their topology. Instead, we replace this with two underlying assumptions concerning the causal structure: that no compact set can signal to arbitrarily small neighbourhoods of spatial infinity (``$i^0$-avoidance''), and that no future incomplete null geodesic is visible from future null infinity. We show that these and the focusing condition together imply that the domain of outer communications is simply connected. Furthermore, we prove lemmas which have as a consequence that if a future incomplete null geodesic were visible from infinity, then given our $i^0$-avoidance assumption, it would also be visible from points of spacetime that can communicate with infinity, and so would signify a true naked singularity.Comment: To appear in CQG, this improved version contains minor revisions to incorporate referee's suggestions. Two revised references. Plain TeX, 12 page