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

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

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

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

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.

Gamma-loud quasars: a view with BeppoSAX

We present $Beppo$SAX observations of the $\gamma$-ray emitting quasars 0836+710, 1510-089 and 2230+114. All the objects have been detected in the PDS up to 100 keV and have extremely flat power-law spectra above 2 keV ($\alpha _x$=0.3--0.5). 0836+710 shows absorption higher than the galactic value and marginal evidence for the presence of the redshifted 6.4 keV Iron line. 1510-089 shows a spectral break around 1 keV, with the low energy spectrum steeper ($\alpha_l$=1.6) than the high energy power-law ($\alpha_h$=0.3). The data are discussed in the light of current Inverse Compton models for the high energy emission.Comment: 4 pages, 2 figures, to appear in the proceedings of the conference "X-Ray Astronomy '99", Bologna, Italy, September 199

Sigma models as perturbed conformal field theories

We show that two-dimensional sigma models are equivalent to certain perturbed conformal field theories. When the fields in the sigma model take values in a space G/H for a group G and a maximal subgroup H, the corresponding conformal field theory is the $k\to\infty$ limit of the coset model $(G/H)_k$, and the perturbation is related to the current of G. This correspondence allows us for example to find the free energy for the "O(n)" (=O(n)/O(n-1)) sigma model at non-zero temperature. It also results in a new approach to the CP^{n} model.Comment: 4 pages. v2: corrects typos (including several in the published version

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