OPE for null Wilson loops and open spin chains

Maximal helicity-violating scattering amplitudes in N=4 supersymmetric Yang-Mills theory are dual to Wilson loops on closed null polygons. We perform their operator product expansion analysis in two-dimensional kinematics in the soft-collinear approximation which corresponds to the case when some light-cone distances vanish. We construct the expansion in terms of multi-particle "heavy"-light operators, where the "heavy" fields are identified with the Wilson lines defining the OPE channel and the light fields emerge from the curvature of the contour. The correlation function of these define the remainder function. We study the dilatation operator for these operators at one loop order and find that it corresponds to a non-compact open spin chain. This provides an alternative view on elementary excitations propagating on the GKP string at weak coupling, which now correspond to particles traveling along an open spin chain. The factorized structure of the Wilson loop in the soft limit allows one to represent the two-loop correction to the octagon Wilson loop as a convolution formula and find the corresponding remainder function.Comment: 10 pages, 2 figure

Multi-frequency study of DEM L299 in the Large Magellanic Cloud

We have studied the HII region DEM L299 in the Large Magellanic Cloud to understand its physical characteristics and morphology in different wavelengths. We performed a spectral analysis of archived XMM-Newton EPIC data and studied the morphology of DEM L299 in X-ray, optical, and radio wavelengths. We used H alpha, [SII], and [OIII] data from the Magellanic Cloud Emission Line Survey and radio 21 cm line data from the Australia Telescope Compact Array (ATCA) and the Parkes telescope, and radio continuum data from ATCA and the Molonglo Synthesis Telescope. Our morphological studies imply that, in addition to the supernova remnant SNR B0543-68.9 reported in previous studies, a superbubble also overlaps the SNR in projection. The position of the SNR is clearly defined through the [SII]/H alpha flux ratio image. Moreover, the optical images show a shell-like structure that is located farther to the north and is filled with diffuse X-ray emission, which again indicates the superbubble. Radio 21 cm line data show a shell around both objects. Radio continuum data show diffuse emission at the position of DEM L299, which appears clearly distinguished from the HII region N 164 that lies south-west of it. We determined the spectral index of SNR B0543-68.9 to be alpha=-0.34, which indicates the dominance of thermal emission and therefore a rather mature SNR. We determined the basic properties of the diffuse X-ray emission for the SNR, the superbubble, and a possible blowout region of the bubble, as suggested by the optical and X-ray data. We obtained an age of 8.9 (3.5-18.1) kyr for the SNR and a temperature of 0.64 (0.44-1.37) keV for the hot gas inside the SNR, and a temperature of the hot gas inside the superbubble of 0.74 (0.44-1.1) keV. We conclude that DEM L299 consists of a superposition of SNR B0543-68.9 and a superbubble, which we identified based on optical data.Comment: Accepted for publication in Astronomy and Astrophysics. 17 pages, 16 figure

Velocity Level Approximation of Pressure Field Contact Patches

Pressure Field Contact (PFC) was recently introduced as a method for detailed modeling of contact interface regions at rates much faster than elasticity-theory models, while at the same time predicting essential trends and capturing rich contact behavior. The PFC model was designed to work in conjunction with error-controlled integration at the acceleration level. Therefore a vast majority of existent multibody codes using solvers at the velocity level cannot incorporate PFC in its original form. In this work we introduce a discrete in time approximation of PFC making it suitable for use with existent velocity-level time steppers and enabling execution at real-time rates. We evaluate the accuracy and performance gains of our approach and demonstrate its effectiveness in simulating relevant manipulation tasks. The method is available in open source as part of Drake's Hydroelastic Contact model.Comment: 8 pages, 10 figures. Supplementary video can be found at https://youtu.be/AdCnTyqqQP

Comments on Correlation Functions of Large Spin Operators and Null Polygonal Wilson Loops

We discuss the relation between correlation functions of twist-two large spin operators and expectation values of Wilson loops along light-like trajectories. After presenting some heuristic field theoretical arguments suggesting this relation, we compute the divergent part of the correlator in the limit of large 't Hooft coupling and large spins, using a semi-classical worldsheet which asymptotically looks like a GKP rotating string. We show this diverges as expected from the expectation value of a null Wilson loop, namely, as $(\ln{\mu^{-2}})^ 2$, $\mu$ being a cut-off of the theory.Comment: 16+3 pages, 3 figures. Computation in section 4.1 has been clarified. Some comments on the vertex contributions has been added in section 4.2. Some other minor corrections. Version to appear in Nucl. Phys.

Rigorous Probabilistic Analysis of Equilibrium Crystal Shapes

The rigorous microscopic theory of equilibrium crystal shapes has made enormous progress during the last decade. We review here the main results which have been obtained, both in two and higher dimensions. In particular, we describe how the phenomenological Wulff and Winterbottom constructions can be derived from the microscopic description provided by the equilibrium statistical mechanics of lattice gases. We focus on the main conceptual issues and describe the central ideas of the existing approaches.Comment: To appear in the March 2000 special issue of Journal of Mathematical Physics on Probabilistic Methods in Statistical Physic

Isosurface modelling of soft objects in computer graphics.

There are many different modelling techniques used in computer graphics to describe a wide range of objects and phenomena. In this thesis, details of research into the isosurface modelling technique are presented. The isosurface technique is used in conjunction with more traditional modelling techniques to describe the objects needed in the different scenes of an animation. The isosurface modelling technique allows the description and animation of objects that would be extremely difficult, or impossible to describe using other methods. The objects suitable for description using isosurface modelling are soft objects. Soft objects merge elegantly with each other, pull apart, bubble, ripple and exhibit a variety of other effects. The representation was studied in three phases of a computer animation project: modelling of the objects; animation of the objects; and the production of the images. The research clarifies and presents many algorithms needed to implement the isosurface representation in an animation system. The creation of a hierarchical computer graphics animation system implementing the isosurface representation is described. The scalar fields defining the isosurfaces are represented using a scalar field description language, created as part of this research, which is automatically generated from the hierarchical description of the scene. This language has many techniques for combining and building the scalar field from a variety of components. Surface attributes of the objects are specified within the graphics system. Techniques are described which allow the handling of these attributes along with the scalar field calculation. Many animation techniques specific to the isosurface representation are presented. By the conclusion of the research, a graphics system was created which elegantly handles the isosurface representation in a wide variety of animation situations. This thesis establishes that isosurface modelling of soft objects is a powerful and useful technique which has wide application in the computer graphics community