Localization and Diagonalization: A review of functional integral techniques for low-dimensional gauge theories and topological field theories

We review localization techniques for functional integrals which have recently been used to perform calculations in and gain insight into the structure of certain topological field theories and low-dimensional gauge theories. These are the functional integral counterparts of the Mathai-Quillen formalism, the Duistermaat-Heckman theorem, and the Weyl integral formula respectively. In each case, we first introduce the necessary mathematical background (Euler classes of vector bundles, equivariant cohomology, topology of Lie groups), and describe the finite dimensional integration formulae. We then discuss some applications to path integrals and give an overview of the relevant literature. The applications we deal with include supersymmetric quantum mechanics, cohomological field theories, phase space path integrals, and two-dimensional Yang-Mills theory.Comment: 72 pages (60 A4 pages), LaTeX (to appear in the Journal of Mathematical Physics Special Issue on Functional Integration (May 1995)

Depth spreading through empty space induced by sparse disparity cues

A key goal of visual processing is to develop an understanding of the three-dimensional layout of the objects in our immediate vicinity from the variety of incomplete and noisy depth cues available to the eyes. Binocular disparity is one of the dominant depth cues, but it is often sparse, being definable only at the edges of uniform surface regions, and visually resolvable only where the edges have a horizontal disparity component. To understand the full 3D structure of visual objects, our visual system has to perform substantial surface interpolation across unstructured visual space. This interpolation process was studied in an eight-spoke depth spreading configuration corresponding to that used in the neon color spreading effect, which generates a strong percept of a sharp contour extending through empty space from the disparity edges within the spokes. Four hypotheses were developed for the form of the depth surface induced by disparity in the spokes defining an incomplete disk in depth: low-level local (isotropic) depth propagation, mid-level linear (anisotropic) depth-contour interpolation or extrapolation, and high-level (anisotropic) figural depth propagation of a disk figure in depth. Data for both perceived depth and position of the perceived contour clearly rejected the first three hypotheses and were consistent with the high-level figural hypothesis in both uniform disparity and slanted disk configurations. We conclude that depth spreading through empty visual space is an accurately quantifiable perceptual process that propagates depth contours anisotropically along their length and is governed by high-level figural properties of 3D object structure

Defect free global minima in Thomson's problem of charges on a sphere

Given $N$ unit points charges on the surface of a unit conducting sphere, what configuration of charges minimizes the Coulombic energy $\sum_{i>j=1}^N 1/r_{ij}$? Due to an exponential rise in good local minima, finding global minima for this problem, or even approaches to do so has proven extremely difficult. For \hbox{$N = 10(h^2+hk+k^2)+ 2$} recent theoretical work based on elasticity theory, and subsequent numerical work has shown, that for $N \sim >500$--1000 adding dislocation defects to a symmetric icosadeltahedral lattice lowers the energy. Here we show that in fact this approach holds for all $N$, and we give a complete or near complete catalogue of defect free global minima.Comment: Revisions in Tables and Reference

A Compact Extreme Scattering Event Cloud Towards AO 0235+164

We present observations of a rare, rapid, high amplitude Extreme Scattering Event toward the compact BL-Lac AO 0235+164 at 6.65 GHz. The ESE cloud is compact; we estimate its diameter between 0.09 and 0.9 AU, and is at a distance of less than 3.6 kpc. Limits on the angular extent of the ESE cloud imply a minimum cloud electron density of ~ 4 x 10^3 cm^-3. Based on the amplitude and timescale of the ESE observed here, we suggest that at least one of the transients reported by Bower et al. (2007) may be attributed to ESEs.Comment: 11 pages, 2 figure

A multi-modal data resource for investigating topographic heterogeneity in patient-derived xenograft tumors.

Patient-derived xenografts (PDXs) are an essential pre-clinical resource for investigating tumor biology. However, cellular heterogeneity within and across PDX tumors can strongly impact the interpretation of PDX studies. Here, we generated a multi-modal, large-scale dataset to investigate PDX heterogeneity in metastatic colorectal cancer (CRC) across tumor models, spatial scales and genomic, transcriptomic, proteomic and imaging assay modalities. To showcase this dataset, we present analysis to assess sources of PDX variation, including anatomical orientation within the implanted tumor, mouse contribution, and differences between replicate PDX tumors. A unique aspect of our dataset is deep characterization of intra-tumor heterogeneity via immunofluorescence imaging, which enables investigation of variation across multiple spatial scales, from subcellular to whole tumor levels. Our study provides a benchmark data resource to investigate PDX models of metastatic CRC and serves as a template for future, quantitative investigations of spatial heterogeneity within and across PDX tumor models

Sigma models as perturbed conformal field theories

We show that two-dimensional sigma models are equivalent to certain perturbed conformal field theories. When the fields in the sigma model take values in a space G/H for a group G and a maximal subgroup H, the corresponding conformal field theory is the $k\to\infty$ limit of the coset model $(G/H)_k$, and the perturbation is related to the current of G. This correspondence allows us for example to find the free energy for the "O(n)" (=O(n)/O(n-1)) sigma model at non-zero temperature. It also results in a new approach to the CP^{n} model.Comment: 4 pages. v2: corrects typos (including several in the published version

Observation of Quantum Asymmetry in an Aharonov-Bohm Ring

We have investigated the Aharonov-Bohm effect in a one-dimensional GaAs/GaAlAs ring at low magnetic fields. The oscillatory magnetoconductance of these systems are for the first time systematically studied as a function of density. We observe phase-shifts of $\pi$ in the magnetoconductance oscillations, and halving of the fundamental $h/e$ period, as the density is varied. Theoretically we find agreement with the experiment, by introducing an asymmetry between the two arms of the ring.Comment: 4 pages RevTex including 3 figures, submitted to Phys. Rev.

Vortices on Higher Genus Surfaces

We consider the topological interactions of vortices on general surfaces. If the genus of the surface is greater than zero, the handles can carry magnetic flux. The classical state of the vortices and the handles can be described by a mapping from the fundamental group to the unbroken gauge group. The allowed configurations must satisfy a relation induced by the fundamental group. Upon quantization, the handles can carry ``Cheshire charge.'' The motion of the vortices can be described by the braid group of the surface. How the motion of the vortices affects the state is analyzed in detail.Comment: 28 pages with 10 figures; uses phyzzx and psfig; Caltech preprint CALT-68-187

On Thermodynamical Properties of Some Coset CFT Backgrounds

We investigate the thermodynamical features of two Lorentzian signature backgrounds that arise in string theory as exact CFTs and possess more than two disconnected asymptotic regions: the 2-d charged black hole and the Nappi-Witten cosmological model. We find multiple smooth disconnected Euclidean versions of the charged black hole background. They are characterized by different temperatures and electro-chemical potentials. We show that there is no straightforward analog of the Hartle-Hawking state that would express these thermodynamical features. We also obtain multiple Euclidean versions of the Nappi-Witten cosmological model and study their singularity structure. It suggests to associate a non-isotropic temperature with this background.Comment: 1+39 pages, harvmac, 8 eps figure