119377774
2D FRACTIONAL SUPERSYMMETRY FOR RATIONAL CONFORMAL FIELD THEORY : APPLICATION FOR THIRD-INTEGER SPIN STATES
A 2D fractional supersymmetry theory is algebraically constructed. The Lagrangian is derived using an adapted superspace including, in addition to a scalar field, two fields with spins 13, 23 This theory turns out to be a rational conformal field theory. The symmetry of this model goes beyond the super-Virasoro algebra and connects these third-integer spin states. Besides the stress-momentum tensor, we obtain a supercurrent of spin 43. Cubic relations are involved in order to close the algebra; the basic algebra is no longer a Lie or a super-Lie algebra. The central charge of this model is found to be 53 Finally, we analyze the form that a local invariant action should take.
117969814
Mutation of Andreev into Majorana bound states in long superconductor-normal and superconductor-normal-superconductor junctions
We study one-dimensional topological SN and SNS long junctions obtained by placing a topological insulating nanowire in the proximity of either one or two SC finite-size leads. Using the Majorana Polarization order parameter (MP) introduced in Phys. Rev. Lett. 108, 096802 (2012)(arxiv:1109.5697) we find that the extended Andreev bound states (ABS) of the normal part of the wire acquire a finite MP: for a finite-size SN junction the ABS spectrum exhibits a zero-energy extended state which carries a full Majorana fermion, while the ABS of long SNS junctions with phase difference $\pi$ transform into two zero-energy states carrying two Majorana fermions with the same MP. Given their extended character inside the whole normal link, and not only close to an interface, these Majorana-Andreev states can be directly detected in tunneling spectroscopy experiments.
118873533
From Andreev bound states to Majorana fermions in topological wires on superconducting substrates: A story of mutation
We study the proximity effect in a topological nanowire tunnel coupled to an s-wave superconducting substrate. We use a general Green's function approach that allows us to study the evolution of the Andreev bound states in the wire into Majorana fermions. We show that the strength of the tunnel coupling induces a topological transition in which the Majorana fermionic states can be destroyed when the coupling is very strong. Moreover, we provide a phenomenologial study of the effects of disorder in the superconductor on the formation of Majorana fermions. We note a non-trivial effect of a quasiparticle broadening term which can take the wire from a topological into a non-topological phase in certain ranges of parameters. Our results have also direct consequences for a nanowire coupled to an inhomogenous superconductor.
119500460
Coupled critical models: application to Ising-Potts models
Abstract We discuss the critical behaviour of 2 D Ising and q -states Potts models coupled by their energy density. We found new tricritical points. The procedure employed is the renormalisation approach of the perturbations series around conformal field theories representing pure models as already used for disordered spins models. This analysis could be useful to understand the physics of coupled critical models like the fully frustrated XY model.
7559852
A renormalization group study of asymmetrically coupled minimal models
Abstract We investigate the renormalization group flows and fixed point structure of many coupled minimal models. The models are coupled two by two by energy-energy couplings. We take the general approach where the bare couplings are all taken to be independent. New fixed points are found for N models ( N ≥3). At these fixed points, the coupling constants all have the same magnitude, but some are positive while others are negative. By analogy with spin lattices, these can be interpreted as non-frustrated configurations with a maximal number of antiferromagnetic links. The stability of the different fixed points is studied. We compute the critical exponents and spin-spin correlation functions between different models. Our classification is shown to be complete.
14198652
Bosonic-type S -matrix, vacuum instability and CDD ambiguities
Abstract We consider the simplest bosonic-type S -matrix which is usually regarded as unphysical due to the complex values of the finite volume ground state energy. While a standard quantum field theory interpretation of such a scattering theory is precluded, we argue that the physical situation described by this S -matrix is of a massive Ising model perturbed by a particular set of irrelevant operators. The presence of these operators drastically affects the stability of the original vacuum of the massive Ising model and its ultraviolet properties.
14149653
GaBoDS: The Garching-Bonn Deep Survey - VI. Probing galaxy bias using weak gravitational lensing
Aims. An interesting question of contemporary cosmology concerns the relation between the spatial distribution of galaxies and dark matter, which is thought to be the driving force behind the structure formation in the Universe. In this paper, we measure this relation, parameterised by the linear stochastic bias parameters, for a range of spatial scales using the data of the Garching-Bonn Deep Survey (GaBoDS). Methods. The weak gravitational lensing effect is used to infer matter density fluctuations within the field-of-view of the survey fields. This information is employed for a statistical comparison of the galaxy distribution to the total matter distribution. The result of this comparison is expressed by means of the linear bias factor  b , the ratio of density fluctuations, and the correlation factor  r between density fluctuations. The total galaxy sample is divided into three sub-samples using R -band magnitudes and the weak lensing analysis is applied separately for each sub-sample. Together with the photometric redshifts from the related COMBO-17 survey we estimate the typical mean redshifts of these samples with $\bar{z}=0.35, 0.47, 0.61$, respectively. Results. Using a flat $\Lambda\rm CDM$ model with $\Omega_{\rm m}=0.3, \Omega_\Lambda=0.7$ as fiducial cosmology, we obtain values for the galaxy bias on scales between $1^\prime\le\theta_{\rm ap}\le20^\prime$. At $10^\prime$, the median redshifts of the samples correspond roughly to a typical comoving scale of $3,5,7~h^{-1}\,\rm Mpc$ with $h=0.7$, respectively. We find evidence for a scale-dependence of b . Averaging the measurements of the bias over the range $2^\prime\le \theta_{\rm ap}\le 19^\prime$ yields $\bar{b}=0.81\pm0.11, 0.79\pm0.11, 0.81\pm0.11$ ($1\sigma$), respectively. Galaxies are thus less clustered than the total matter on that particular range of scales (anti-biased). As for the correlation factor  r we see no scale-dependence within the statistical uncertainties; the average over the same range is $\bar{r}=0.61\pm0.16, 0.64\pm0.18, 0.58\pm0.19$ ($1\sigma$), respectively. This implies a possible decorrelation between galaxy and dark matter distribution. An evolution of galaxy bias with redshift is not found, the upper limits are: $\Delta b\lesssim0.2$ and $\Delta r\lesssim 0.4(1\sigma)$.
53611492
Spatial matter density mapping of the STAGES Abell A901/2 supercluster field with 3D lensing
We present weak lensing data from the Hubble Space Telescope(HST)/Space Telescope A901/902 Galaxy Evolution Survey (STAGES) survey1 to study the three-dimensional spatial distribution of matter and galaxies in the Abell 901/902 supercluster complex. Our method improves over the existing 3D lensing mapping techniques by calibrating and removing redshift bias and accounting for the effects of the radial elongation of 3D structures. We also include the first detailed noise analysis of a 3D lensing map, showing that even with deep HST-quality data, only the most massive structures, for example M200≳ 1015 M⊙ h−1 at z∼ 0.8, can be resolved in 3D with any reasonable redshift accuracy (Δz≈ 0.15). We compare the lensing map to the stellar mass distribution and find luminous counterparts for all mass peaks detected with a peak significance >3σ. We see structures in and behind the z= 0.165 foreground supercluster, finding structure directly behind the A901b cluster at z∼ 0.6 and also behind the south-west (SW) group at z∼ 0.7. This 3D structure viewed in projection has no significant impact on recent mass estimates of A901b or the SW group components SWa and SWb
8253626
The non-Gaussianity of the cosmic shear likelihood or How odd is the Chandra Deep Field South?
Aims. We study the validity of the approximation of a Gaussian cosmic shear likelihood. We estimate the true likelihood for a fiducial cosmological model from a large set of ray-tracing simulations and investigate the impact of non-Gaussianity on cosmological parameter estimation. We investigate how odd the recently reported very low value of σ8 really is as derived from the Chandra Deep Field South (CDFS) using cosmic shear by taking the non-Gaussianity of the likelihood into account, as well as the possibility of biases coming from the way the CDFS was selected. Methods. A brute force approach to estimating the likelihood from simulations must fail because of the high dimensionality of the problem. We therefore use independent component analysis to transform the cosmic shear correlation functions to a new basis, in which the likelihood approximately factorises into a product of one-dimensional distributions. Results. We find that the cosmic shear likelihood is significantly non-Gaussian. This leads to both a shift of the maximum of the posterior distribution and a significantly smaller credible region compared to the Gaussian case. We re-analyse the CDFS cosmic shear data using the non-Gaussian likelihood in combination with conservative galaxy selection criteria that minimise calibration uncertainties. Assuming that the CDFS is a random pointing, we find σ8 = 0.68 +0.09 −0.16 for fixed Ωm = 0.25. In a WMAP5-like cosmology, a value equal to or lower than this would be expected in ≈5% of the times. Taking biases into account arising from the way the CDFS was selected, which we model as being dependent on the number of haloes in the CDFS, we obtain σ8 = 0.71 +0.10 −0.15 . Combining the CDFS data with the parameter constraints from WMAP5 yields Ωm = 0.26 +0.03 −0.02 and σ8 = 0.79 +0.04 −0.03 for a flat universe.
17142858
GaBoDS: The Garching-Bonn Deep Survey: VI. Cosmic shear analysis
Aims. We present a cosmic shear analysis and data validation of 15 square degree high-quality R-band data of the Garching-Bonn Deep Survey obtained with the Wide Field Imager of the MPG/ESO 2.2m telescope. Methods. We measure the two-point shear correlation functions to calculate the aperture mass dispersion. Both statistics are used to perform the data quality control. Combining the cosmic shear signal with a photometric redshift distribution of a galaxy sub-sample obtained from two square degree of UBVRI-band observations of the Deep Public Survey we determine constraints for the matter density Omega_m, the mass power spectrum normalisation sigma_8 and the dark energy density Omega_Lambda in the magnitude interval R in [21.5,24.5]. In this magnitude interval the effective number density of source galaxies is n=12.5/sq. arcmin, and their mean redshift is z_m=0.78. To estimate the posterior likelihood we employ the Monte Carlo Markov Chain method. Results. Using the aperture mass dispersion we obtain for the mass power spectrum normalisation sigma_8=0.80 +- 0.10 (1 sigma statistical error) at a fixed matter density Omega_m=0.30 assuming a flat universe with negligible baryon content and marginalising over the Hubble parameter and the uncertainties in the fitted redshift distribution.
118682213
Locating the baryon acoustic peak
Forthcoming photometric redshift surveys should provide an accurate probe of the acoustic peak in the two-point galaxy correlation function, in the form of angular clustering of galaxies within a given shell in redshift space. We investigate the form of the anticipated signal, quantifying the distortions that arise due to projection effects, and, in particular, explore the validity of applying the Limber approximation. A single-integral prescription is presented, which provides an alternative to Limber's equation, and produces a significantly improved prediction in the regime of interest. The position of the acoustic peak within the angular correlation function relates to the angular diameter distance to the far side of the redshift bin. Thicker redshift bins therefore shift comoving features toward smaller angular scales. As a result, the value of the photometric redshift error acquires a greater significance, particularly at lower redshifts. In order to recover the dark energy equation of state to a level of 1 %, we find the total redshift dispersion must be determined to within Δ σz ≤ 10 -3 , which may prove challenging to achieve in practice.