121411195
Singular vectors of the Virasoro algebra
Abstract We present an explicit construction of the singular (or null) vectors in highest weight Verma modules.
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.
59058647
COVARIANT DIFFERENTIAL EQUATIONS AND SINGULAR VECTORS IN VIRASORO REPRESENTATIONS
Abstract We give explicit expressions for the singular vectors in highest weight representations of the Virasoro algebra using a precise definition of fusion.
121423772
The branching rules of conformal embeddings
After recalling the main properties of a conformal embedding of Lie algebrasg⊃p, which is defined by the equality of the Sugawara central charges on both sides, we launch a systematic study of their branching rules. The bulk of the paper is devoted to the proof of a general formula in the casesu(mn)1⊃su(m)n⊕su(n)m. At the end we give some applications to the construction of modular invariant partition functions.
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.
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.
118156527
Randall-Sundrum Models and Precision Observables
I present a review of phenomenological implications of the Randall-Sundrum (RS) model with bulk fermions and brane-localized Higgs boson. Modifications to the W-boson mass, corrections to the Peskin-Takeuchi parameters and to the Z -> bb couplings will be discussed. From these observables severe bounds on the mass scale of Kaluza-Klein (KK) modes arise. Constraints from all three observables are very sensitive to the exact value of the Higgs boson mass and the bounds can be significantly lowered by allowing for a heavy Higgs boson (m_h ~ 1 TeV). Consequences thereof, as well as other approaches like "little RS" models and models with custodial symmetry will also be briefly discussed.
209431040
Dark Matter Search with CRESST-II
R. Strauss, G. Angloher, M. Bauer, I. Bavykina, A. Bento, C. Bucci, C. Ciemniak, G. Deuter, F. von Feilitzsch, D. Hauff, C. Isaila, J. Jochum, M. Kiefer, M. Kimmerle, J.-C. Lanfranchi, F. Petricca, S. Pfister, W. Potzel, F. Pröbst , F. Reindl , S. Roth, K. Rottler, C. Sailer, K. Schäffner, J. Schmaler, S. Scholl, W. Seidel, M. von Sivers, L. Stodolsky , C. Strandhagen, A. Tanzke, I. Usherov, S. Wawoczny, M. Willers, A. Zöller Physik-Department E15, Technische Universität München, D-85747 Garching, Germany Max-Planck-Institut für Physik, D-80805 München, Germany Eberhard-Karls-Universität Tübingen, D-72076 Tübingen, Germany Laboratori Nazionali del Gran Sasso, INFN, I-67010 Assergi, Italy Departamento de Fisica, Universidade de Coimbra, P3004 516 Coimbra, Portugal
13930079
The recurrent ultra-luminous X-ray transient NGC 253 ULX1
We present the results of ROSAT and XMM-Newton observations of the recurrent ultraluminous X-ray source (ULX) NGC 253 ULX I. This transient is one of the few ULXs that was detected during several outbursts. The luminosity reached 1.4 × 10 39 erg s -1 and 0.5 x 10 39 erg s -1 in the detections by ROSAT and XMM-Newton, respectively, indicating a black hole X-ray binary (BHXRB) with a mass of the compact object of ≥11 M ○. . In the ROSAT detection NGC 253 ULX1 showed significant variability, whereas the luminosity was constant in the detection from XMM-Newton. The XMM-Newton EPIC spectra are well-tit by a hremsstrahlung model (kT = 2.24 keV, N H = 1.74 x 10 20 cm -2 ), which can he used to describe a comptonized plasma. No counterpart was detected in the optical I, R, B, NUV and FUV bands to limits of 22.9, 24.2. 24.3, 22 and 23 mag, respectively, pointing at a XRB with a low mass companion.
122260318
Direct dark matter search with CRESST and EURECA
Abstract The current status of the direct Dark Matter experiments CRESST (Cryogenic Rare Event Search with Superconducting Thermometers) and the planned EURECA (European Underground Rare Event Calorimeter Array) is presented. Both experiments are aimed at the direct detection of WIMPs (Weakly Interacting Massive Particles), potential candidates for the Dark Matter in the universe. New design developments of the cryogenic detectors operated at mK temperatures are investigated to optimize detector performance and to simplify mass production. Thus, CRESST is also providing a basis for the EURECA project, aimed at a ton of cryogenic detectors with a multi-material target.
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.