Diagrammatics for Bose condensation in anyon theories

Phase transitions in anyon models in (2+1)-dimensions can be driven by condensation of bosonic particle sectors. We study such condensates in a diagrammatic language and explicitly establish the relation between the states in the fusion spaces of the theory with the condensate, to the states in the parent theory using a new set of mathematical quantities called vertex lifting coefficients (VLCs). These allow one to calculate the full set of topological data ($S$-, $T$-, $R$- and $F$-matrices) in the condensed phase. We provide closed form expressions of the topological data in terms of the VLCs and provide a method by which one can calculate the VLCs for a wide class of bosonic condensates. We furthermore furnish a concrete recipe to lift arbitrary diagrams directly from the condensed phase to the original phase, such that they can be evaluated using the data of the original theory and a limited number of VLCs. Some representative examples are worked out in detail.Comment: 20 pages, 1 figure, many diagram

The modular S-matrix as order parameter for topological phase transitions

We study topological phase transitions in discrete gauge theories in two spatial dimensions induced by the formation of a Bose condensate. We analyse a general class of euclidean lattice actions for these theories which contain one coupling constant for each conjugacy class of the gauge group. To probe the phase structure we use a complete set of open and closed anyonic string operators. The open strings allow one to determine the particle content of the condensate, whereas the closed strings enable us to determine the matrix elements of the modular $S$-matrix, also in the broken phase. From the measured broken $S$-matrix we may read off the sectors that split or get identified in the broken phase, as well as the sectors that are confined. In this sense the modular $S$-matrix can be employed as a matrix valued non-local order parameter from which the low-energy effective theories that occur in different regions of parameter space can be fully determined. To verify our predictions we studied a non-abelian anyon model based on the quaternion group $H=\bar{D_2}$ of order eight by Monte Carlo simulation. We probe part of the phase diagram for the pure gauge theory and find a variety of phases with magnetic condensates leading to various forms of (partial) confinement in complete agreement with the algebraic breaking analysis. Also the order of various transitions is established.Comment: 37 page

Defect mediated melting and the breaking of quantum double symmetries

In this paper, we apply the method of breaking quantum double symmetries to some cases of defect mediated melting. The formalism allows for a systematic classification of possible defect condensates and the subsequent confinement and/or liberation of other degrees of freedom. We also show that the breaking of a double symmetry may well involve a (partial) restoration of an original symmetry. A detailed analysis of a number of simple but representative examples is given, where we focus on systems with global internal and external (space) symmetries. We start by rephrasing some of the well known cases involving an Abelian defect condensate, such as the Kosterlitz-Thouless transition and one-dimensional melting, in our language. Then we proceed to the non-Abelian case of a hexagonal crystal, where the hexatic phase is realized if translational defects condense in a particular rotationally invariant state. Other conceivable phases are also described in our framework.Comment: 10 pages, 4 figures, updated reference

Monitoring of UV spectral irradiance at Thessaloniki (1990?2005): data re-evaluation and quality control

International audienceWe present a re-evaluation and quality control of spectral ultraviolet irradiance measurements from two Brewer spectroradiometers operating regularly at Thessaloniki, Greece. The calibration history of the two instruments was re-examined and data flaws were identified by comparing quasi synchronous measurements. Analysis of the sensitivity of both instruments to variations of their internal temperature revealed that they have temperature coefficients of different sign. These coefficients exhibit small variability during the 15-year period. Using averaged temperature coefficients, we corrected both datasets. Corrections were applied for the angular response error using two different approaches depending on the availability of required ancillary data. The uncertainties associated with the measurements have been estimated and presented. Finally, the two datasets are compared using ratios of irradiance integrals at various bands in the UV, in order to assess any dependencies on the internal instrument temperature, solar zenith angle and wavelength

The Large N 't Hooft Limit of Kazama-Suzuki Model

We consider N=2 Kazama-Suzuki model on CP^N=SU(N+1)/SU(N)xU(1). It is known that the N=2 current algebra for the supersymmetric WZW model, at level k, is a nonlinear algebra. The N=2 W_3 algebra corresponding to N=2 was recovered from the generalized GKO coset construction previously. For N=4, we construct one of the higher spin currents, in N=2 W_5 algebra, with spins (2, 5/2, 5/2, 3). The self-coupling constant in the operator product expansion of this current and itself depends on N as well as k explicitly. We also observe a new higher spin primary current of spins (3, 7/2, 7/2, 4). From the behaviors of N=2, 4 cases, we expect the operator product expansion of the lowest higher spin current and itself in N=2 W_{N+1} algebra. By taking the large (N, k) limit on the various operator product expansions in components, we reproduce, at the linear order, the corresponding operator product expansions in N=2 classical W_{\infty}^{cl}[\lambda] algebra which is the asymptotic symmetry of the higher spin AdS_3 supergravity found recently.Comment: 44 pages; the two typos in the first paragraph of page 23 corrected and to appear in JHE

The Operator Product Expansion of the Lowest Higher Spin Current at Finite N

For the N=2 Kazama-Suzuki(KS) model on CP^3, the lowest higher spin current with spins (2, 5/2, 5/2,3) is obtained from the generalized GKO coset construction. By computing the operator product expansion of this current and itself, the next higher spin current with spins (3, 7/2, 7/2, 4) is also derived. This is a realization of the N=2 W_{N+1} algebra with N=3 in the supersymmetric WZW model. By incorporating the self-coupling constant of lowest higher spin current which is known for the general (N,k), we present the complete nonlinear operator product expansion of the lowest higher spin current with spins (2, 5/2, 5/2, 3) in the N=2 KS model on CP^N space. This should coincide with the asymptotic symmetry of the higher spin AdS_3 supergravity at the quantum level. The large (N,k) 't Hooft limit and the corresponding classical nonlinear algebra are also discussed.Comment: 62 pages; the footnotes added, some redundant appendices removed, the presentations in the whole paper improved and to appear in JHE

SU(3) monopoles and their fields

Some aspects of the fields of charge two SU(3) monopoles with minimal symmetry breaking are discussed. A certain class of solutions look like SU(2) monopoles embedded in SU(3) with a transition region or ``cloud'' surrounding the monopoles. For large cloud size the relative moduli space metric splits as a direct product AH\times R^4 where AH is the Atiyah-Hitchin metric for SU(2) monopoles and R^4 has the flat metric. Thus the cloud is parametrised by R^4 which corresponds to its radius and SO(3) orientation. We solve for the long-range fields in this region, and examine the energy density and rotational moments of inertia. The moduli space metric for these monopoles, given by Dancer, is also expressed in a more explicit form.Comment: 17 pages, 3 figures, latex, version appearing in Phys. Rev.

Estimation of photolysis frequencies from TOMS satellite measurements and routine meteorological observations

A study on the estimation of J(O<sup>1</sup>D) and J(NO<sub>2</sub>) photolysis frequencies when limited ground based measurements (or even no measurements at all), are available is presented in this work. Photolysis frequencies can be directly measured by chemical actinometry and filter radiometry or can be calculated from actinic flux measurements. In several meteorological stations, none of the methods above are applicable due to the absence of sophisticated instruments such as actinometers, radiometers or spectroradiometers. In this case, it is possible to calculate photolysis frequencies with reasonable uncertainty using either a) standard meteorological observations, such as ozone, cloud coverage and horizontal visibility, available in various ground based stations, as input for a radiative transfer model or b) satellite observations of solar global irradiance available worldwide, in combination with an empirical method for the conversion of irradiance in photolysis frequencies. Both methods can provide photolysis frequencies with a standard deviation between 20% and 30%. The absolute level of agreement of the retrieved frequencies to those calculated from actual actinic flux measurements, for data from all meteorological conditions, is within ±5% for J(O<sup>1</sup>D) and less than 1% for J(NO<sub>2</sub>) for the first method, while for the second method it rises up to 25% for the case of J(O<sup>1</sup>D) and 12% for J(NO<sub>2</sub>), reflecting the overestimation of TOMS satellite irradiance when compared to ground based measurements of irradiance for the respective spectral regions. Due to the universality of the methods they can be practically applied to almost any station, thus overcoming problems concerning the availability of instruments measuring photolysis frequencies

Comparison of UV-B measurements performed with a Brewer spectrophotometer and a new UVB-1 broad band detector

Measurements of the UV-B erythemal dose, based on solar spectra acquired with a Brewer spectrophotometer at Thessaloniki, Greece, are compared to measurements performed with the recently introduced, by the Yankee Environmental Systems, (Robertson type) broad band solar UV-B detector. The spectral response function of this detector, when applied to the Brewer spectral UV-B measurements, results in remarkably comparable estimates of the erythemal UV-B dose. The two instruments provide similar information on the UV-B dose when they are cross-examined under a variety of meteorological and atmospheric conditions and over the a large range of solar zenith angles and total ozone