121043272
Centre and representations of small quantum superalgebras at roots of unity
When the deformation parameter is a root of unity, the centre of a quantum group can be described by a set of generators and non trivial relations. In the case ofUq(sl(N)), these relations simply derive from the expressions of the deformed Casimir operators. In the case ofUq(osp(1|2)), the relation is simple if we use an operator which anticommutes with the fermionic generators and whose square is the quadratic Casimir. This operator also simplifies the classification of finite dimensional irreducible representations. In the case ofUq(sl(1|2)), the relations derive from the (infinite set of) standard Casimir operators.
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.
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.
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
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.
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
123530930
EURECA – THE EUROPEAN UNDERGROUND RARE EVENT CALORIMETER ARRAY
38251987
Solution to the flavor problem of warped extra-dimension models.
A minimal solution to the flavor problem of warped extra-dimension models, i.e., the excessive mixed-chirality contribution to CP violation in K-K ¯ mixing arising from Kaluza-Klein (KK) gluon exchange, is proposed. Extending the strong-interaction gauge group in the bulk by an additional SU(3), and breaking this symmetry to QCD via boundary conditions, the constraints arising from the ε(K) parameter are significantly relaxed. As a result, KK scales M(KK)~2 TeV are consistent with all flavor observables without significant fine-tuning. The model predicts an extended Higgs sector featuring massive color-octet scalars and a tower of KK pseudoaxial gluon resonances, whose existence is not in conflict with recent LHC dijet bounds.
119268040
Constraining RS Models by Future Flavor and Collider Measurements: A Snowmass Whitepaper
Randall-Sundrum models are models of quark flavor, because they explain the hierarchies in the quark masses and mixings in terms of order one localization parameters of extra dimensional wavefunctions. The same small numbers which generate the light quark masses suppress contributions to flavor violating tree level amplitudes. In this note we update universal constraints from electroweak precision parameters and demonstrate how future measurements of flavor violation in ultra rare decay channels of Kaons and B mesons will constrain the parameter space of this type of models. We show how collider signatures are correlated with these flavor measurements and compute projected limits for direct searches at the 14 TeV LHC run, a 14 TeV LHC luminosity upgrade, a 33 TeV LHC energy upgrade, and a potential 100 TeV machine. We further discuss the effects of a warped model of leptons in future measurements of lepton flavor violation.