Correlation Functions of a Conformal Field Theory in Three Dimensions

We derive explicit forms of the two--point correlation functions of the $O(N)$ non-linear sigma model at the critical point, in the large $N$ limit, on various three dimensional manifolds of constant curvature. The two--point correlation function, $G(x, y)$, is the only $n$-point correlation function which survives in this limit. We analyze the short distance and long distance behaviour of $G(x, y)$. It is shown that $G(x, y)$ decays exponentially with the Riemannian distance on the spaces $R^2 \times S^1,~S^1 \times S^1 \times R, ~S^2 \times R,~H^2 \times R$. The decay on $R^3$ is of course a power law. We show that the scale for the correlation length is given by the geometry of the space and therefore the long distance behaviour of the critical correlation function is not necessarily a power law even though the manifold is of infinite extent in all directions; this is the case of the hyperbolic space where the radius of curvature plays the role of a scale parameter. We also verify that the scalar field in this theory is a primary field with weight $\delta=-{1 \over 2}$; we illustrate this using the example of the manifold $S^2 \times R$ whose metric is conformally equivalent to that of $R^3-\{0\}$ up to a reparametrization.Comment: 15 pages, Late

Improvement of irregular dtm for sph modelling of flow-like landslides

Irregular topography of real slopes largely affects the propagation stage of flowlike landslides and accurate digital terrain models (DTMs) are absolutely necessary for realistic simulations and assessments. In this paper a simple yet effective method is proposed to improve the accuracy of existing DTMs which is applied to the topographical models used in well equipped laboratory experiments. Aimed at evaluating the effects of different DTMs in the results of the propagation modelling, a depth-integrated SPH model is used to simulate two series of laboratory tests referring to a frictional rheological model while using either the available DTM or the DTM improved through the proposed procedure. The obtained results show that the proposed method provides a more accurate topographical model for all the analyzed cases. Particularly, the new topographical model allows better reproducing the laboratory evidences in terms of run-out distances, inundated areas and geometrical characteristics of the final deposits. Furthermore, SPH analyses with progressively finer topographical inputs outline the role of DTM’s precision towards the accuracy of the numerical simulations

Alternative Canonical Formalism for the Wess-Zumino-Witten Model

We study a canonical quantization of the Wess--Zumino--Witten (WZW) model which depends on two integer parameters rather than one. The usual theory can be obtained as a contraction, in which our two parameters go to infinity keeping the difference fixed. The quantum theory is equivalent to a generalized Thirring model, with left and right handed fermions transforming under different representations of the symmetry group. We also point out that the classical WZW model with a compact target space has a canonical formalism in which the current algebra is an affine Lie algebra of non--compact type. Also, there are some non--unitary quantizations of the WZW model in which there is invariance only under half the conformal algebra (one copy of the Virasoro algebra).Comment: 22 pages; UR-133

Machine-learning nonstationary noise out of gravitational-wave detectors

Signal extraction out of background noise is a common challenge in high-precision physics experiments, where the measurement output is often a continuous data stream. To improve the signal-to-noise ratio of the detection, witness sensors are often used to independently measure background noises and subtract them from the main signal. If the noise coupling is linear and stationary, optimal techniques already exist and are routinely implemented in many experiments. However, when the noise coupling is nonstationary, linear techniques often fail or are suboptimal. Inspired by the properties of the background noise in gravitational wave detectors, this work develops a novel algorithm to efficiently characterize and remove nonstationary noise couplings, provided there exist witnesses of the noise source and of the modulation. In this work, the algorithm is described in its most general formulation, and its efficiency is demonstrated with examples from the data of the Advanced LIGO gravitational-wave observatory, where we could obtain an improvement of the detector gravitational-wave reach without introducing any bias on the source parameter estimation

Measuring the LISA test mass magnetic proprieties with a torsion pendulum

Achieving the low frequency LISA sensitivity requires that the test masses acting as the interferometer end mirrors are free-falling with an unprecedented small degree of deviation. Magnetic disturbances, originating in the interaction of the test mass with the environmental magnetic field, can significantly deteriorate the LISA performance and can be parameterized through the test mass remnant dipole moment $\vec{m}_r$ and the magnetic susceptibility $\chi$. While the LISA test flight precursor LTP will investigate these effects during the preliminary phases of the mission, the very stringent requirements on the test mass magnetic cleanliness make ground-based characterization of its magnetic proprieties paramount. We propose a torsion pendulum technique to accurately measure on ground the magnetic proprieties of the LISA/LTP test masses.Comment: 6 pages, 3 figure

On-ground tests of LISA PathFinder thermal diagnostics system

Thermal conditions in the LTP, the LISA Technology Package, are required to be very stable, and in such environment precision temperature measurements are also required for various diagnostics objectives. A sensitive temperature gauging system for the LTP is being developed at IEEC, which includes a set of thermistors and associated electronics. In this paper we discuss the derived requirements applying to the temperature sensing system, and address the problem of how to create in the laboratory a thermally quiet environment, suitable to perform meaningful on-ground tests of the system. The concept is a two layer spherical body, with a central aluminium core for sensor implantation surrounded by a layer of polyurethane. We construct the insulator transfer function, which relates the temperature at the core with the laboratory ambient temperature, and evaluate the losses caused by heat leakage through connecting wires. The results of the analysis indicate that, in spite of the very demanding stability conditions, a sphere of outer diameter of the order one metre is sufficient. We provide experimental evidence confirming the model predictions.Comment: 18 pages, 5 figures, LaTeX2e (compile with pdflatex), sumbitted to CQG. This paper is a significant extension of gr-qc/060109

Upper limits to surface force disturbances on LISA proof masses and the possibility of observing galactic binaries

We report on the measurement of parasitic surface force noise on a hollow replica of a LISA (Laser Interferometer Space Antenna for the observation of gravitational waves) proof mass surrounded by a faithful representation of its in flight surroundings, namely the capacitive sensor used to detect proof-mass motion. Parasitic forces are detected through the corresponding torque exerted on the proof mass and measured with a torsion pendulum in the frequency range 0.1 30 mHz. The sensor electrodes, electrode housing and associated readout electronics have the same nominal design as for the flight hardware, including 4 mm gaps around the proof mass along the sensitive laser interferometry axis. We show that the measured upper limit for surface forces would allow detection of a number of galactic binaries signals with signal to noise ratio up to approximately 40 for 1 year integration. We also discuss how the flight test under development, LISA Pathfinder, will substantially improve this limit, approaching the performance required for LISA.Comment: 3 Figures. Submitted to Physical Review Letter