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

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

Dual-Frequency VSOP Observations of AO 0235+164

AO 0235+164 is a very compact, flat spectrum radio source identified as a BL Lac object at a redshift of z=0.94. It is one of the most violently variable extragalactic objects at both optical and radio wavelengths. The radio structure of the source revealed by various ground-based VLBI observations is dominated by a nearly unresolved compact component at almost all available frequencies. Dual-frequency space VLBI observations of AO 0235+164 were made with the VSOP mission in January-February 1999. The array of the Japanese HALCA satellite and co-observing ground radio telescopes in Australia, Japan, China and South Africa allowed us to study AO 0235+164 with an unprecedented angular resolution at frequencies of 1.6 and 5 GHz. We report on the sub-milliarcsecond structural properties of the source. The 5-GHz observations led to an estimate of T_B > 5.8 x 10^{13} K for the rest-frame brightness temperature of the core, which is the highest value measured with VSOP to date.Comment: 8 pages, 8 figures, to appear in Publ. Astron. Soc. Japa

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

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

Highly Polarized Optically-Selected BL Lacertae Objects

Observations of candidate BL Lacertae objects spectroscopically selected from the Sloan Digital Sky Survey (SDSS) reveal a large fraction with high polarization (P > 3%). This result confirms that synchrotron radiation makes an important contribution to the observed optical continuum for most objects in the sample. The SDSS sample can be divided into separate categories, with objects of undetermined redshift generally having the highest optical polarization. Polarization as high as 23% and the lack of spectral features suggests that the synchrotron continuum completely dominates the spectra of these sources. The mean polarization levels observed for objects having measured redshifts is much lower, with the maximum observed polarization for this group being ~10%. The lower polarizations of these objects are reminiscent of the less spectacular polarization levels shown by BL Lac objects discovered in X-ray surveys. We find no SDSS BL Lac candidates at z > 1 with P > 3%, calling their classification as BL Lac objects into question. In addition, the existence of radio-quiet BL Lac objects is not verified since none of 10 potentially radio-weak BL Lac candidates observed are highly polarized. Regardless of whether the high-redshift and radio-weak objects are included in this optical sample, the overall levels of polarization observed are intermediate between those seen for X-ray and radio-selected BL Lac objects.Comment: 9 pages, 3 figures, 2 table

Generalized diagonal crossed products and smash products for quasi-Hopf algebras. Applications

In this paper we introduce generalizations of diagonal crossed products, two-sided crossed products and two-sided smash products, for a quasi-Hopf algebra H. The results we obtain may be applied to H^*-Hopf bimodules and generalized Yetter-Drinfeld modules. The generality of our situation entails that the "generating matrix" formalism cannot be used, forcing us to use a different approach. This pays off because as an application we obtain an easy conceptual proof of an important but very technical result of Hausser and Nill concerning iterated two-sided crossed products.Comment: 41 pages, no 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

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