Finiteness Theorems and Counting Conjectures for the Flux Landscape

In this paper, we explore the string theory landscape obtained from type IIB and F-theory flux compactifications. We first give a comprehensive introduction to a number of mathematical finiteness theorems, indicate how they have been obtained, and clarify their implications for the structure of the locus of flux vacua. Subsequently, in order to address finer details of the locus of flux vacua, we propose three mathematically precise conjectures on the expected number of connected components, geometric complexity, and dimensionality of the vacuum locus. With the recent breakthroughs on the tameness of Hodge theory, we believe that they are attainable to rigorous mathematical tools and can be successfully addressed in the near future. The remainder of the paper is concerned with more technical aspects of the finiteness theorems. In particular, we investigate their local implications and explain how infinite tails of disconnected vacua approaching the boundaries of the moduli space are forbidden. To make this precise, we present new results on asymptotic expansions of Hodge inner products near arbitrary boundaries of the complex structure moduli space.Comment: 47 pages + appendices, 11 figures; v2: formulation of generalized tadpole conjecture improved; v3: refined conjecture

Multiple-beam groundstation reflector antenna system : a prelimary study

A wide-scanning multiple-beam reflector antenna, two systems are investigated. A bifocal antenna, designed with the use of an existing method, appears to be unsuitable for wide-angle scanning. A dual-reflector offset torus-antenna showed promising results. As an illustration of its benefit, a possible application is examined: the simultaneous reception of signals from a number (n) of geostationary direct broadcast satellites with mutual distance of 6 degrees. Using this antenna yields advantage when compared, with respect to the total required reflector area, with n separate antennas.<br/

Introduction

What are the library services and resources that Asian Pacific Americans need? What does it mean to be an Asian Pacific American librarian in the 21st century? In Asian American Librarians and Library Services: Activism, Collaborations, and Strategies, library professionals and scholars share reflections, best practices, and strategies, and convey the critical need for diversity in the LIS field, library programming, and resources to better reflect the rich and varied experiences and information needs of Asian Americans in the US and beyond. The contributors show that they care deeply about diversity, that they acknowledge that it is painfully lacking in so many aspects of libraries and librarianship, and that libraries and the LIS profession must systematically integrate diversity and inclusion into their strategic priorities and practices, indeed, in their very mission, such that the rich diversity of experiences and histories of Asian Americans in library and archival collections, services, and programming are not only validated and recognized, but also valued and celebrated as vital components of the shared American experience. The volume recognizes and honors the creative and intentional work librarians do for their constituent Asian American communities in promoting resources, services, and outreac

Bulk Reconstruction in Moduli Space Holography

It was recently suggested that certain UV-completable supersymmetric actions can be characterized by the solutions to an auxiliary non-linear sigma-model with special asymptotic boundary conditions. The space-time of this sigma-model is the scalar field space of these effective theories while the target space is a coset space. We study this sigma-model without any reference to a potentially underlying geometric description. Using a holographic approach reminiscent of the bulk reconstruction in the AdS/CFT correspondence, we then derive its near-boundary solutions for a two-dimensional space-time. Specifying a set of $Sl(2,\mathbb{R})$ boundary data we show that the near-boundary solutions are uniquely fixed after imposing a single bulk-boundary matching condition. The reconstruction exploits an elaborate set of recursion relations introduced by Cattani, Kaplan, and Schmid in the proof of the $Sl(2)$-orbit theorem. We explicitly solve these recursion relations for three sets of simple boundary data and show that they model asymptotic periods of a Calabi--Yau threefold near the conifold point, the large complex structure point, and the Tyurin degeneration.Comment: 44 pages plus appendices, 1 figur

Finiteness Theorems and Counting Conjectures for the Flux Landscape

In this paper, we explore the string theory landscape obtained from type IIB and F-theory flux compactifications. We first give a comprehensive introduction to a number of mathematical finiteness theorems, indicate how they have been obtained, and clarify their implications for the structure of the locus of flux vacua. Subsequently, in order to address finer details of the locus of flux vacua, we propose three mathematically precise conjectures on the expected number of connected components, geometric complexity, and dimensionality of the vacuum locus. With the recent breakthroughs on the tameness of Hodge theory, we believe that they are attainable to rigorous mathematical tools and can be successfully addressed in the near future. The remainder of the paper is concerned with more technical aspects of the finiteness theorems. In particular, we investigate their local implications and explain how infinite tails of disconnected vacua approaching the boundaries of the moduli space are forbidden. To make this precise, we present new results on asymptotic expansions of Hodge inner products near arbitrary boundaries of the complex structure moduli space

Bi-Yang-Baxter Models and Sl(2)-orbits

We study integrable deformations of two-dimensional non-linear sigma-models and present a new class of classical solutions to critical bi-Yang-Baxter models for general groups. For the simplest example, namely the SL(2,R) bi-Yang-Baxter model, we show that our solutions can be mapped to the known complex uniton solutions of the SU(2) bi-Yang-Baxter model. In general, our solutions are constructed from so-called Sl(2)-orbits that play a central role in the study of asymptotic Hodge theory. This provides further evidence for a close relation between integrable non-linear sigma-models and the mathematical principles underlying Hodge theory. We have also included a basic introduction to the relevant aspects of asymptotic Hodge theory and have provided some simple examples

Bulk reconstruction in moduli space holography

It was recently suggested that certain UV-completable supersymmetric actions can be characterized by the solutions to an auxiliary non-linear sigma-model with special asymptotic boundary conditions. The space-time of this sigma-model is the scalar field space of these effective theories while the target space is a coset space. We study this sigma-model without any reference to a potentially underlying geometric description. Using a holographic approach reminiscent of the bulk reconstruction in the AdS/CFT correspondence, we then derive its near-boundary solutions for a two-dimensional space-time. Specifying a set of Sl(2, R) boundary data we show that the near-boundary solutions are uniquely fixed after imposing a single bulk-boundary matching condition. The reconstruction exploits an elaborate set of recursion relations introduced by Cattani, Kaplan, and Schmid in the proof of the Sl(2)-orbit theorem. We explicitly solve these recursion relations for three sets of simple boundary data and show that they model asymptotic periods of a Calabi-Yau threefold near the conifold point, the large complex structure point, and the Tyurin degeneration