Charges of Exceptionally Twisted Branes

The charges of the exceptionally twisted (D4 with triality and E6 with charge conjugation) D-branes of WZW models are determined from the microscopic/CFT point of view. The branes are labeled by twisted representations of the affine algebra, and their charge is determined to be the ground state multiplicity of the twisted representation. It is explicitly shown using Lie theory that the charge groups of these twisted branes are the same as those of the untwisted ones, confirming the macroscopic K-theoretic calculation. A key ingredient in our proof is that, surprisingly, the G2 and F4 Weyl dimensions see the simple currents of A2 and D4, respectively.Comment: 19 pages, 2 figures, LaTex2e, complete proofs of all statements, updated bibliograph

On the Classification of Diagonal Coset Modular Invariants

We relate in a novel way the modular matrices of GKO diagonal cosets without fixed points to those of WZNW tensor products. Using this we classify all modular invariant partition functions of $su(3)_k\oplus su(3)_1/su(3)_{k+1}$ for all positive integer level $k$, and $su(2)_k\oplus su(2)_\ell/su(2)_{k+\ell}$ for all $k$ and infinitely many $\ell$ (in fact, for each $k$ a positive density of $\ell$). Of all these classifications, only that for $su(2)_k\oplus su(2)_1/su(2)_{k+1}$ had been known. Our lists include many new invariants.Comment: 24 pp (plain tex

Lie group weight multiplicities from conformal field theory

Dominant weight multiplicities of simple Lie groups are expressed in terms of the modular matrices of Wess-Zumino-Witten conformal field theories, and related objects. Symmetries of the modular matrices give rise to new relations among multiplicities. At least for some Lie groups, these new relations are strong enough to completely fix all multiplicities.Comment: 12 pages, Plain TeX, no figure

Modular differential equations for torus one-point functions

It is shown that in a rational conformal field theory every torus one-point function of a given highest weight state satisfies a modular differential equation. We derive and solve these differential equations explicitly for some Virasoro minimal models. In general, however, the resulting amplitudes do not seem to be expressible in terms of standard transcendental functions.Comment: 19 pages, LaTeX; reference adde

Some Comments on Gravitational Entropy and the Inverse Mean Curvature Flow

The Geroch-Wald-Jang-Huisken-Ilmanen approach to the positive energy problem to may be extended to give a negative lower bound for the mass of asymptotically Anti-de-Sitter spacetimes containing horizons with exotic topologies having ends or infinities of the form $\Sigma_g \times {\Bbb R}$, in terms of the cosmological constant. We also show how the method gives a lower bound for for the mass of time-symmetric initial data sets for black holes with vectors and scalars in terms of the mass, $|Z(Q,P)|$ of the double extreme black hole with the same charges. I also give a lower bound for the area of an apparent horizon, and hence a lower bound for the entropy in terms of the same function $|Z(Q,P)|$. This shows that the so-called attractor behaviour extends beyond the static spherically symmetric case. and underscores the general importance of the function $|Z(Q,P)|$. There are hints that higher dimensional generalizations may involve the Yamabe conjectures.Comment: 13pp. late

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

Topology of Event Horizons and Topological Censorship

We prove that, under certain conditions, the topology of the event horizon of a four dimensional asymptotically flat black hole spacetime must be a 2-sphere. No stationarity assumption is made. However, in order for the theorem to apply, the horizon topology must be unchanging for long enough to admit a certain kind of cross section. We expect this condition is generically satisfied if the topology is unchanging for much longer than the light-crossing time of the black hole. More precisely, let $M$ be a four dimensional asymptotically flat spacetime satisfying the averaged null energy condition, and suppose that the domain of outer communication \C_K to the future of a cut $K$ of \Sm is globally hyperbolic. Suppose further that a Cauchy surface $\Sigma$ for \C_K is a topological 3-manifold with compact boundary $\partial\S$ in $M$, and $\S'$ is a compact submanifold of \bS with spherical boundary in $\S$ (and possibly other boundary components in $M/\S$). Then we prove that the homology group $H_1(\Sigma',Z)$ must be finite. This implies that either $\partial\S'$ consists of a disjoint union of 2-spheres, or $\S'$ is nonorientable and $\partial\S'$ contains a projective plane. Further, \partial\S=\partial\Ip[K]\cap\partial\Im[\Sp], and $\partial \Sigma$ will be a cross section of the horizon as long as no generator of \partial\Ip[K] becomes a generator of \partial\Im[\Sp]. In this case, if $\S$ is orientable, the horizon cross section must consist of a disjoint union of 2-spheres.}Comment: 11 pages, plain latex (minor revision: $\Sigma$ replaced by its closure in various places.

On the complete classification of the unitary N=2 minimal superconformal field theories

Aiming at a complete classification of unitary N=2 minimal models (where the assumption of space-time supersymmetry has been dropped), it is shown that each modular invariant candidate of a partition function for such a theory is indeed the partition function of a minimal model. A family of models constructed via orbifoldings of either the diagonal model or of the space-time supersymmetric exceptional models demonstrates that there exists a unitary N=2 minimal model for every one of the allowed partition functions in the list obtained from Gannon's work. Kreuzer and Schellekens' conjecture that all simple current invariants can be obtained as orbifolds of the diagonal model, even when the extra assumption of higher-genus modular invariance is dropped, is confirmed in the case of the unitary N=2 minimal models by simple counting arguments.Comment: 53 pages; Latex; minor changes in v2: intro expanded, references added, typos corrected, footnote added on p31; renumbering of sections; main theorem reformulated for clarity, but contents unchanged. Minor revisions in v3: typos corrected, footnotes 5, 6 added, lemma 1 and section 3.3.2 rewritten for greater generality, section 3.3 review removed. To appear in Comm. Math. Phy

The effects of visual priming on information processing in child sexual offenders

Child sexual offenders are hypothesized to hold offence-supportive beliefs that set them apart from others. The current study seeks support for this view via a cognitive-experimental approach. Child sexual offenders and offender controls were exposed to pictures of semi-clothed children (priming condition) or clothed, mature adults (control condition). Participants then read ambiguous sentences describing children\u27s actions that could be interpreted in a sexualized manner. Next, participants completed a surprise recognition test in which half the sentences were re-presented in an unambiguously sexual form, and half in an unambiguously non-sexual form. Contrary to hypotheses, primed and/or control child sexual offenders did not show a memory bias for sexualized sentences, suggesting that they did not interpret the original sentences in line with offence-supportive beliefs. Results raise questions about whether child sexual offenders universally hold abnormal beliefs that facilitate their offending. Results also highlight the need for further experimental research within this field

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