Universal Bounds in Even-Spin CFTs

We prove using invariance under the modular $S$- and $ST$-transformations that every unitary two-dimensional conformal field theory (CFT) of only even-spin operators (with no extended chiral algebra and with central charges $c,\tilde{c}>1$) contains a primary operator with dimension $\Delta_1$ satisfying $0 < \Delta_1 < (c+\tilde{c})/24 + 0.09280...$ After deriving both analytical and numerical bounds, we discuss how to extend our methods to bound higher conformal dimensions before deriving lower and upper bounds on the number of primary operators in a given energy range. Using the AdS$_3$/CFT$_2$ dictionary, the bound on $\Delta_1$ proves the lightest massive excitation in appropriate theories of 3D matter and gravity with cosmological constant $\Lambda < 0$ can be no heavier than $1/(8G_N)+O(\sqrt{-\Lambda})$; the bounds on the number operators are related via AdS/CFT to the entropy of states in the dual gravitational theory. In the flat-space approximation, the limiting mass is exactly that of the lightest BTZ black hole.Comment: arXiv admin note: text overlap with arXiv:0902.2790 by other authors; author note: this work is an extension of arXiv:0902.2790, please refer to it for additional details..new version has corrected typos and reference

Individual Religious Commitment and Interdisciplinary Academic Achievement: Student Religiosity as a Factor in a National Academic Competition

This study included an examination of the differences between the religiosity of students representing both public and private schools that qualified at the state and national levels in the United States Academic Decathlon, a national, interdisciplinary academic competition. The statistical significance of religiosity in relation to achievement scores in the Academic Decathlon was examined. The literature reviewed suggested a positive correlation between religiosity and academic achievement. The Duke University Religion Index (DUREL) instrument was administered to students on both teams to determine religiosity levels. Statistical analysis was applied to the data to test for significant difference. No significant difference between overall competition scores was found in relation to reported student religiosity; neither the public nor private school scored significantly higher or lower in the competition. Significant difference in scores was found for specific subject areas. Further, no significant difference was found between student religiosity in relation to grade point average. The conclusion that student religiosity was not found to have a significant influence on competition scores in the Academic Decathlon suggests that religiosity and academic achievement may not always positively correlate. The implications for Christian education suggest that faith-learning integration should be critically examined across disciplines in Christian school settings, particularly in the subjects of mathematics and science

Combatting Skepticism Towards HR

[Excerpt] When assessing the essentiality of HR within a firm, one must first ask what is meant by the word “essential” within a business context. The trickiness here, however, is that such a definition is highly contingent on the type and size of a particular firm. If one defines “essential” as “indispensable,” then HR is almost certainly not essential in very small firms. In such instances, the work of HR can be done by other managers and the owners themselves. On the other hand, if one defines “essential” as “adding considerable value,” then innovative human resource policies can create a competitive advantage even in the smallest of firms. Instead of relying on a single definition of essentiality, this essay will focus on the reasons why human resources practices are often called into question in the first place. Furthermore, I will propose recommendations on how to combat skepticism toward HR

Bounds on Operator Dimensions in 2D Conformal Field Theories

We extend the work of Hellerman (arxiv:0902.2790) to derive an upper bound on the conformal dimension $\Delta_2$ of the next-to-lowest nontrival primary operator in unitary two-dimensional conformal field theories without chiral primary operators. The bound we find is of the same form as found for $\Delta_1$: $\Delta_2 \leq c_{tot}/12 + O(1)$. We find a similar bound on the conformal dimension $\Delta_3$, and present a method for deriving bounds on $\Delta_n$ for any $n$, under slightly modified assumptions. For asymptotically large $c_{tot}$ and fixed $n$, we show that $\Delta_n \leq \frac{c_{tot}}{12}+O(1)$. We conclude with a brief discussion of the gravitational implications of these results.Comment: Corrected typos; revised arguments (adding detail) for clarity, results unchange

A Cut Principle for Information Flow

We view a distributed system as a graph of active locations with unidirectional channels between them, through which they pass messages. In this context, the graph structure of a system constrains the propagation of information through it. Suppose a set of channels is a cut set between an information source and a potential sink. We prove that, if there is no disclosure from the source to the cut set, then there can be no disclosure to the sink. We introduce a new formalization of partial disclosure, called *blur operators*, and show that the same cut property is preserved for disclosure to within a blur operator. This cut-blur property also implies a compositional principle, which ensures limited disclosure for a class of systems that differ only beyond the cut.Comment: 31 page