The Drinfel'd Double and Twisting in Stringy Orbifold Theory

This paper exposes the fundamental role that the Drinfel'd double \dkg of the group ring of a finite group $G$ and its twists \dbkg, \beta \in Z^3(G,\uk) as defined by Dijkgraaf--Pasquier--Roche play in stringy orbifold theories and their twistings. The results pertain to three different aspects of the theory. First, we show that $G$--Frobenius algebras arising in global orbifold cohomology or K-theory are most naturally defined as elements in the braided category of \dkg--modules. Secondly, we obtain a geometric realization of the Drinfel'd double as the global orbifold $K$--theory of global quotient given by the inertia variety of a point with a $G$ action on the one hand and more stunningly a geometric realization of its representation ring in the braided category sense as the full $K$--theory of the stack $[pt/G]$. Finally, we show how one can use the co-cycles $\beta$ above to twist a) the global orbifold $K$--theory of the inertia of a global quotient and more importantly b) the stacky $K$--theory of a global quotient $[X/G]$. This corresponds to twistings with a special type of 2--gerbe.Comment: 35 pages, no figure

On Dijkgraaf-Witten Type Invariants

We explicitly construct a series of lattice models based upon the gauge group $Z_{p}$ which have the property of subdivision invariance, when the coupling parameter is quantized and the field configurations are restricted to satisfy a type of mod-$p$ flatness condition. The simplest model of this type yields the Dijkgraaf-Witten invariant of a $3$-manifold and is based upon a single link, or $1$-simplex, field. Depending upon the manifold's dimension, other models may have more than one species of field variable, and these may be based on higher dimensional simplices.Comment: 18 page

Unifying W-Algebras

We show that quantum Casimir W-algebras truncate at degenerate values of the central charge c to a smaller algebra if the rank is high enough: Choosing a suitable parametrization of the central charge in terms of the rank of the underlying simple Lie algebra, the field content does not change with the rank of the Casimir algebra any more. This leads to identifications between the Casimir algebras themselves but also gives rise to new, `unifying' W-algebras. For example, the kth unitary minimal model of WA_n has a unifying W-algebra of type W(2,3,...,k^2 + 3 k + 1). These unifying W-algebras are non-freely generated on the quantum level and belong to a recently discovered class of W-algebras with infinitely, non-freely generated classical counterparts. Some of the identifications are indicated by level-rank-duality leading to a coset realization of these unifying W-algebras. Other unifying W-algebras are new, including e.g. algebras of type WD_{-n}. We point out that all unifying quantum W-algebras are finitely, but non-freely generated.Comment: 13 pages (plain TeX); BONN-TH-94-01, DFTT-15/9

A deep, high resolution survey of the low frequency radio sky

We report on the first wide-field, very long baseline interferometry (VLBI) survey at 90 cm. The survey area consists of two overlapping 28 deg^2 fields centred on the quasar J0226+3421 and the gravitational lens B0218+357. A total of 618 sources were targeted in these fields, based on identifications from Westerbork Northern Sky Survey (WENSS) data. Of these sources, 272 had flux densities that, if unresolved, would fall above the sensitivity limit of the VLBI observations. A total of 27 sources were detected as far as 2 arcdegrees from the phase centre. The results of the survey suggest that at least 10% of moderately faint (S~100 mJy) sources found at 90 cm contain compact components smaller than ~0.1 to 0.3 arcsec and stronger than 10% of their total flux densities. A ~90 mJy source was detected in the VLBI data that was not seen in the WENSS and NRAO VLA Sky Survey (NVSS) data and may be a transient or highly variable source that has been serendipitously detected. This survey is the first systematic (and non-biased), deep, high-resolution survey of the low-frequency radio sky. It is also the widest field of view VLBI survey with a single pointing to date, exceeding the total survey area of previous higher frequency surveys by two orders of magnitude. These initial results suggest that new low frequency telescopes, such as LOFAR, should detect many compact radio sources and that plans to extend these arrays to baselines of several thousand kilometres are warranted.Comment: Accepted by The Astrophysical Journal. 39 pages, 4 figure

A Compact Extreme Scattering Event Cloud Towards AO 0235+164

We present observations of a rare, rapid, high amplitude Extreme Scattering Event toward the compact BL-Lac AO 0235+164 at 6.65 GHz. The ESE cloud is compact; we estimate its diameter between 0.09 and 0.9 AU, and is at a distance of less than 3.6 kpc. Limits on the angular extent of the ESE cloud imply a minimum cloud electron density of ~ 4 x 10^3 cm^-3. Based on the amplitude and timescale of the ESE observed here, we suggest that at least one of the transients reported by Bower et al. (2007) may be attributed to ESEs.Comment: 11 pages, 2 figure

Observation of Quantum Asymmetry in an Aharonov-Bohm Ring

We have investigated the Aharonov-Bohm effect in a one-dimensional GaAs/GaAlAs ring at low magnetic fields. The oscillatory magnetoconductance of these systems are for the first time systematically studied as a function of density. We observe phase-shifts of $\pi$ in the magnetoconductance oscillations, and halving of the fundamental $h/e$ period, as the density is varied. Theoretically we find agreement with the experiment, by introducing an asymmetry between the two arms of the ring.Comment: 4 pages RevTex including 3 figures, submitted to Phys. Rev.

Higher Algebraic Structures and Quantization

We derive (quasi-)quantum groups in 2+1 dimensional topological field theory directly from the classical action and the path integral. Detailed computations are carried out for the Chern-Simons theory with finite gauge group. The principles behind our computations are presumably more general. We extend the classical action in a d+1 dimensional topological theory to manifolds of dimension less than d+1. We then ``construct'' a generalized path integral which in d+1 dimensions reduces to the standard one and in d dimensions reproduces the quantum Hilbert space. In a 2+1 dimensional topological theory the path integral over the circle is the category of representations of a quasi-quantum group. In this paper we only consider finite theories, in which the generalized path integral reduces to a finite sum. New ideas are needed to extend beyond the finite theories treated here.Comment: 62 pages + 16 figures (revised version). In this revision we make some small corrections and clarification

Triality in Minimal Model Holography

The non-linear W_{\infty}[\mu] symmetry algebra underlies the duality between the W_N minimal model CFTs and the hs[\mu] higher spin theory on AdS_3. It is shown how the structure of this symmetry algebra at the quantum level, i.e. for finite central charge, can be determined completely. The resulting algebra exhibits an exact equivalence (a`triality') between three (generically) distinct values of the parameter \mu. This explains, among other things, the agreement of symmetries between the W_N minimal models and the bulk higher spin theory. We also study the consequences of this triality for some of the simplest W_{\infty}[\mu] representations, thereby clarifying the analytic continuation between the`light states' of the minimal models and conical defect solutions in the bulk. These considerations also lead us to propose that one of the two scalar fields in the bulk actually has a non-perturbative origin.Comment: 29 pages; v2. Typos correcte

Vortices on Higher Genus Surfaces

We consider the topological interactions of vortices on general surfaces. If the genus of the surface is greater than zero, the handles can carry magnetic flux. The classical state of the vortices and the handles can be described by a mapping from the fundamental group to the unbroken gauge group. The allowed configurations must satisfy a relation induced by the fundamental group. Upon quantization, the handles can carry ``Cheshire charge.'' The motion of the vortices can be described by the braid group of the surface. How the motion of the vortices affects the state is analyzed in detail.Comment: 28 pages with 10 figures; uses phyzzx and psfig; Caltech preprint CALT-68-187

The First IRAM/PdBI Polarimetric Millimeter Survey of Active Galactic Nuclei. I. Global Properties of the Sample

We have studied the linear polarization of 86 active galactic nuclei (AGN) in the observed frequency range 80-267 GHz (3.7-1.1mm in wavelength), corresponding to rest-frame frequencies 82-738 GHz, with the IRAM Plateau de Bure Interferometer (PdBI). The large number of measurements, 441, makes our analysis the largest polarimetric AGN survey in this frequency range to date. We extracted polarization parameters via earth rotation polarimetry with unprecedented median precisions of ~0.1% in polarization fractions and ~1.2 degrees in polarization angles. For 73 of 86 sources we detect polarization at least once. The degrees of polarization are as high as ~19%, with the median over all sources being ~4%. Source fluxes and polarizations are typically highly variable, with fractional variabilities up to ~60%. We find that BLLac sources have on average the highest level of polarization. There appears to be no correlation between degree of polarization and redshift, indicating that there has been no substantial change of polarization properties since z~2.4. Our polarization and spectral index distributions are in good agreement with results found from various samples observed at cm/radio wavelengths; thus our frequency range is likely tracing the signature of synchrotron radiation without noticeable contributions from other emission mechanisms. The "millimeter-break" located at frequencies >1 THz appears to be not detectable in the frequency range covered by our survey.Comment: 19 pages, 9 figures, 2 long tables (p. 12-19). Accepted by A&A