New Methods for Characterizing Phases of 2D Supersymmetric Gauge Theories

We study the physics of two-dimensional N=(2,2) gauged linear sigma models (GLSMs) via the two-sphere partition function. We show that the classical phase boundaries separating distinct GLSM phases, which are described by the secondary fan construction for abelian GLSMs, are completely encoded in the analytic structure of the partition function. The partition function of a non-abelian GLSM can be obtained as a limit from an abelian theory; we utilize this fact to show that the phases of non-abelian GLSMs can be obtained from the secondary fan of the associated abelian GLSM. We prove that the partition function of any abelian GLSM satisfies a set of linear differential equations; these reduce to the familiar A-hypergeometric system of Gel'fand, Kapranov, and Zelevinski for GLSMs describing complete intersections in toric varieties. We develop a set of conditions that are necessary for a GLSM phase to admit an interpretation as the low-energy limit of a non-linear sigma model with a Calabi-Yau threefold target space. Through the application of these criteria we discover a class of GLSMs with novel geometric phases corresponding to Calabi-Yau manifolds that are branched double-covers of Fano threefolds. These criteria provide a promising approach for constructing new Calabi-Yau geometries.Comment: 25 pages + references, appendices. v2: references added, typos corrected. v3: two small typos correcte

Perturbative Corrections to Kahler Moduli Spaces

We propose a general formula for perturbative-in-alpha' corrections to the Kahler potential on the quantum Kahler moduli space of Calabi-Yau n-folds, for any n, in their asymptotic large volume regime. The knowledge of such perturbative corrections provides an important ingredient needed to analyze the full structure of this Kahler potential, including nonperturbative corrections such as the Gromov-Witten invariants of the Calabi-Yau n-folds. We argue that the perturbative corrections take a universal form, and we find that this form is encapsulated in a specific additive characteristic class of the Calabi-Yau n-fold which we call the log Gamma class, and which arises naturally in a generalization of Mukai's modified Chern character map. Our proposal is inspired heavily by the recent observation of an equality between the partition function of certain supersymmetric, two-dimensional gauge theories on a two-sphere, and the aforementioned Kahler potential. We further strengthen our proposal by comparing our findings on the quantum Kahler moduli space to the complex structure moduli space of the corresponding mirror Calabi-Yau geometry.Comment: 28 pages; v2: discussion in section 5 extended and refs. adde

How Leaders Invest Staffing Resources for Learning Improvement

Analyzes staffing challenges that guide school leaders' resource decisions in the context of a learning improvement agenda, staff resource investment strategies that improve learning outcomes equitably, and ways to win support for differential investment

Geophysics

Contains reports on three research projects

Can modified gravity explain accelerated cosmic expansion?

We show that the recently suggested explanations of cosmic acceleration by the modification of gravity at small curvature suffer violent instabilities and strongly disagree with the known properties of gravitational interactions.Comment: 4 pages, no figure, revised version (one footnote added

Geophysics

Contains reports on three research projects

Overview of the spectrometer optical fiber feed for the Habitable-zone Planet Finder

The Habitable-zone Planet Finder (HPF) is a highly stabilized fiber fed precision radial velocity (RV) spectrograph working in the Near Infrared (NIR): 810 - 1280 nm . In this paper we present an overview of the preparation of the optical fibers for HPF. The entire fiber train from the telescope focus down to the cryostat is detailed. We also discuss the fiber polishing, splicing and its integration into the instrument using a fused silica puck. HPF was designed to be able to operate in two modes, High Resolution (HR- the only mode mode currently commissioned) and High Efficiency (HE). We discuss these fiber heads and the procedure we adopted to attach the slit on to the HR fibers.Comment: Presented at 2018 SPIE Astronomical Telescopes + Instrumentation, Austin, Texas, USA. 18 pages, 25 figures, and 2 table

The Impact of Atmospheric Fluctuations on Degree-scale Imaging of the Cosmic Microwave Background

Fluctuations in the brightness of the Earth's atmosphere originating from water vapor are an important source of noise for ground-based instruments attempting to measure anisotropy in the Cosmic Microwave Background. This paper presents a model for the atmospheric fluctuations and derives simple expressions to predict the contribution of the atmosphere to experimental measurements. Data from the South Pole and from the Atacama Desert in Chile, two of the driest places on Earth, are used to assess the level of fluctuations at each site.Comment: 29 pages, 7 figures, 1 table, appears in The Astrophysical Journa