119381704
Fusion and singular vectors inA1(1) highest weight cyclic modules
We show how the interplay between the fusion formalism of conformal field theory and the Knizhnik-Zamolodchikov equation leads to explicit formulae for the singular vectors in the highest weight representations ofA1(1).
173517385
A Short Introduction to Critical Interfaces in 2D
These notes are meant as a gentle introduction to the concepts of Loewner chains, local growth, Stochastic Loewner Evolutions (SLE) and their relationships to Conformal Field Theories (CFT). These concepts have played an important role in physics and mathematics during the recent years. The first section describes two discrete examples, the exploration process and loop-erased random walks. It can be read almost without any prerequisites. The aim is to show that even for curves defined purely in geometrical terms, it is useful to have a statistical mechanics viewpoint where the measure on curves is derived from a measure on local degrees of freedom of some model. A third model, diffusion-limited aggregation (DLA) is also introduced. The second section introduces Loewner chains and their relevance for the description of growth processes. A prerequisite is a minimal knowledge of complex analysis. The third section contains the derivation of the relevance of SLE in the description of interfaces when two properties, conformal invariance and the domain Markov property, are assumed/proved. The prerequisites are some knowledge of complex analysis and probability theory. The last section outlines the relation with Conformal Field Theory. This relation is via martingales and singular vectors. Again, the reader is assumed to have some basic knowledge of complex analysis and probability theory, and some familiarity with CFT. The discussion is informal. There is little or no claim at originality. We try to give some intuition based on explicit examples.
115160247
Another derivation of the geometrical KPZ relations
We give a physicist's derivation of the geometrical (in the spirit of Duplantier–Sheffield) KPZ relations, via heat kernel methods. It gives a covariant way to define neighborhoods of fractals in 2D quantum gravity, and shows that these relations are in the realm of conformal field theory.
5911478
Phase transition with the Berezinskii-Kosterlitz-Thouless singularity in the Ising model on a growing network.
We consider the ferromagnetic Ising model on a highly inhomogeneous network created by a growth process. We find that the phase transition in this system is characterized by the Berezinskii-Kosterlitz-Thouless singularity, although critical fluctuations are absent and the mean-field description is exact. Below this infinite order transition, the magnetization behaves as exp((-const/square root of(Tc-T)). We show that the critical point separates the phase with the power-law distribution of the linear response to a local field and the phase where this distribution rapidly decreases. We suggest that this phase transition occurs in a wide range of cooperative models with a strong infinite-range inhomogeneity.
15486552
Comments on the links between SU(3) modular invariants, simple factors in the Jacobian of Fermat curves, and rational triangular billiards
We examine the proposal made recently that the su(3) modular invariant partition functions could be related to the geometry of the complex Fermat curves. Although a number of coincidences and similarities emerge between them and certain algebraic curves related to triangular billiards, their meaning remains obscure. In an attempt to go beyond the su(3) case, we show that any rational conformal field theory determines canonically a Riemann surface. Comment: 56 pages, 4 eps figures, LaTeX, uses epsf
119148126
Scasimir Operator, Scentre and Representations of Uq(osp(1|2))
A bosonic operator of Uq(osp(1|2)) that anticommutes with the fermionic generators appears to be useful to describe the relations in the centre of Uq(osp(1|2)) for q a root of unity (in the unrestricted specialisation). As in the classical case, it also simplifies the classification of finite dimensional irreducible representations.
107502491
Bipolar monolithic preamplifiers for SSC silicon calorimetry
This paper describes preamplifiers designed specifically to address the requirements of silicon calorimetry for the Superconducting Super Collider (SSC). Eight different preamplifiers designed for detector capacitances ranging from 20 pF to 500 pF and operating temperatures from 25{degree}C to {minus}20{degree}C are discussed. The preamplifiers were fabricated with two different high-frequency processes (one with the VTC, Inc. VJ900 process, seven with the Harris Semiconductor VHF Process). The different topologies and their features are discussed in addition to the design methodologies employed. The results for noise, power consumption, speed, and radiation damage effects as well as data for post-damage annealing are presented for the VTC process preamplifier. Simulations for the VHF Process circuits are presented. This work was funded through SSC Generic Detector funding, SSC Detector Subsystem funding, and the Oak Ridge National Laboratory (ORNL) Detector Center.
119268338
Light dark matter, naturalness, and the radiative origin of the electroweak scale
A bstractWe study classically scale invariant models in which the Standard Model Higgs mass term is replaced in the Lagrangian by a Higgs portal coupling to a complex scalar field of a dark sector. We focus on models that are weakly coupled with the quartic scalar couplings nearly vanishing at the Planck scale. The dark sector contains fermions and scalars charged under dark SU(2) × U(1) gauge interactions. Radiative breaking of the dark gauge group triggers electroweak symmetry breaking through the Higgs portal coupling. Requiring both a Higgs boson mass of 125.5 GeV and stability of the Higgs potential up to the Planck scale implies that the radiative breaking of the dark gauge group occurs at the TeV scale. We present a particular model which features a long-range abelian dark force. The dominant dark matter component is neutral dark fermions, with the correct thermal relic abundance, and in reach of future direct detection experiments. The model also has lighter stable dark fermions charged under the dark force, with observable effects on galactic-scale structure. Collider signatures include a dark sector scalar boson with mass ≲ 250 GeV that decays through mixing with the Higgs boson, and can be detected at the LHC. The Higgs boson, as well as the new scalar, may have significant invisible decays into dark sector particles.
121526925
EURECA: The European future of dark matter searches with cryogenic detectors
EURECA (European Underground Rare Event Calorimeter Array) is a new project, searching for dark matter, with largely the present groups of the CRESST and EDELWEISS experiments and already a few new groups. The aim is to explore scalar cross sections in the 10 −9 –10 −10 picobarn region with a target mass of up to one tonne. A major advantage of EURECA is our planned use of more that just one target material (multi target experiment for WIMP identification). In preparation for this large-scale experiment, R&D for EURECA is provided through the current phases of CRESST and EDELWEISS.
118498826
Soft collinear effective theory for heavy WIMP annihilation
A bstractIn a large class of models for Weakly Interacting Massive Particles (WIMPs), the WIMP mass M lies far above the weak scale mW . This work identifies universal Sudakov-type logarithms ∼ α log2(2 M/mW ) that spoil the naive convergence of perturbation theory for annihilation processes. An effective field theory (EFT) framework is presented, allowing the systematic resummation of these logarithms. Another impact of the large separation of scales is that a long-distance wavefunction distortion from electroweak boson exchange leads to observable modifications of the cross section. Careful accounting of momentum regions in the EFT allows the rigorous disentanglement of this so-called Sommerfeld enhancement from the short-distance hard annihilation process. The WIMP is described as a heavy-particle field, while the electroweak gauge bosons are treated as soft and collinear fields. Hard matching coefficients are computed at renormalization scale μ ∼ 2 M , then evolved down to μ ∼ mW , where electroweak symmetry breaking is incorporated and the matching onto the relevant quantum mechanical Hamiltonian is performed. The example of an SU(2)W triplet scalar dark matter candidate annihilating to line photons is used for concreteness, allowing the numerical exploration of the impact of next-to-leading order corrections and log resummation. For M ≃ 3 TeV, the resummed Sommerfeld enhanced cross section is reduced by a factor of ∼ 3 with respect to the treelevel fixed order result.
133716710
New applications of silicon micromachining
The use of photolithography and anisotropic etching of silicon wafers to make strong, thin membranes has created a large family of miniature sensing devices such as pressure transducers and accelerometers. This report describes several entirely new devices in which silicon membranes are used for their strength and for their transparency to certain kinds of radiation. Two applications are described: a rugged alpha detector and a fluid sample cell for small-angle x-ray scattering. 8 refs., 12 figs., 2 tabs.