Limit Cycles and Conformal Invariance

There is a widely held belief that conformal field theories (CFTs) require zero beta functions. Nevertheless, the work of Jack and Osborn implies that the beta functions are not actually the quantites that decide conformality, but until recently no such behavior had been exhibited. Our recent work has led to the discovery of CFTs with nonzero beta functions, more precisely CFTs that live on recurrent trajectories, e.g., limit cycles, of the beta-function vector field. To demonstrate this we study the S function of Jack and Osborn. We use Weyl consistency conditions to show that it vanishes at fixed points and agrees with the generator Q of limit cycles on them. Moreover, we compute S to third order in perturbation theory, and explicitly verify that it agrees with our previous determinations of Q. A byproduct of our analysis is that, in perturbation theory, unitarity and scale invariance imply conformal invariance in four-dimensional quantum field theories. Finally, we study some properties of these new, "cyclic" CFTs, and point out that the a-theorem still governs the asymptotic behavior of renormalization-group flows.Comment: 31 pages, 4 figures. Expanded introduction to make clear that cycles discussed in this work are not associated with unitary theories that are scale but not conformally invarian

Why Calls for Shifting to Brandeisian Economic Theory Are Flawed: An Evaluation of the United States’ and European Union’s Approach to Vertical Mergers

The tech industry has exploded over the last few decades and progressives are advocating for a shift in antitrust review in the United States (US).1 Seeking a modified economic theory based on the writings of the late Justice Louis Brandeis (Brandeisian economic theory), these advocates seek to control the vertical expansion of dominant tech firms such as Amazon.2 On a broad level, this position argues for a shift of US antitrust regulatory review towards the European Union’s (EU) application of antitrust regulation. This paper provides a review of both US and EU antitrust review, provides a primer on vertical merger theory and Chicago school economic theory, and compares and contrasts US and EU review of certain business practices to conclude Brandeisian economics will not achieve its advocates’ goals and will have a negative impact on consumers. Finally, this paper supports a proposal to modify and strengthen consent decrees following merger review in order to use a scalpel—rather than a sledgehammer—to adapt to the changes in the technological environment. Most importantly, this proposal would actually protect consumers, not competitors in the marketplace

DEVELOPING FRENCH LANGUAGE LEARNING LEADERSHIP

This Organizational Improvement Plan analyzes the leadership shortage in a French language school board and the scarcity of qualified, skilled, and knowledgeable principals and vice principals willing to lead schools as learning organizations within minority contexts. French language principals have a unique responsibility for ensuring instructional excellence and learning, and they must lead in ways that transmit the mission and values of Francophone language and culture (Leurebourg, 2013). They must understand the cultural context of leading in minority environments and that organizational survival depends upon adaptability and the capacity to learn as an organization. Organizations should have a long-term strategic succession plan to attract, recruit, hire, and develop potential leaders. However, fewer individuals are willing to lead schools since the responsibilities are taxing, the remunerations are incongruent with the invested time, and the professional supports for leadership development are lacking. Drawing on multiple directions of inquiry to identify and analyze the problem of practice, this OIP proposes a change strategy inspired by Senge’s (2006) Learning Organization, and Cawsey, Deszca and Ingols’ (2016) Change Path Model. Change progress will be measured using a Strategy Map and a Balanced Scorecard (Kaplan & Norton, 2004) that fuses the criteria of Learning Organization Dimensions (Watkins & Marsick, 2017) throughout the various phases of the organizational change strategy

Limit Cycles in Four Dimensions

We present an example of a limit cycle, i.e., a recurrent flow-line of the beta-function vector field, in a unitary four-dimensional gauge theory. We thus prove that beta functions of four-dimensional gauge theories do not produce gradient flows. The limit cycle is established in perturbation theory with a three-loop calculation which we describe in detail.Comment: 12 pages, 1 figure. Significant revision of the interpretation of our result. Improved description of three-loop calculatio

To See Great Wonders: A History of Xavier University, 1831-2006

A history of Xavier University, Cincinnati, Ohio from 1831-2006.https://www.exhibit.xavier.edu/ebooks/1000/thumbnail.jp

Alien Registration- Fortin, Joseph A. (Lewiston, Androscoggin County)

https://digitalmaine.com/alien_docs/29736/thumbnail.jp

Alien Registration- Fortin, Joseph A. (Lewiston, Androscoggin County)

https://digitalmaine.com/alien_docs/29736/thumbnail.jp

Little short of national murder: Forced migration and the making of diasporas in the Atlantic world, 1745--1865

Removal---or, the exile and forced migration of marginalized cultural and racial groups from one region of the British Empire and, later, the United States, to another less volatile region---emerged as a key tool in the construction of the Anglo-American Atlantic World. British officials used removal to secure the empire, ridding the realm of Catholic menaces, black insurgents, challenges to the throne and the brutal conflicts between English colonists and Native Americans. American leaders, after the conclusion of the American Revolution, viewed removal as a viable solution to the problem of slavery and the potential troubles induced by freeing the slaves. Thomas Jefferson, among other Virginians, Britons and West Indians, advocated removing all freed blacks to parts unknown. At the same time, black Masons in New England embarked on the first organized attempt to land free African-Americans in Sierra Leone in 1795/6, calling on free Africans in America to return to their native land to Christianize the continent. By 1812, Paul Cuffe advocated black emigration partly for religious reasons, but also in an effort to open new trade opportunities with West Africa. Later, the American Colonization Society---heavily supported by current and former slaveholders, high profile politicians such as Henry Clay, and moral improvement organizations---motivated some freed blacks to voluntarily go to Africa to settle Liberia. Soon, however, free blacks who formerly supported voluntary emigration began to view the idea as removal, a colonization scheme forced on them by powerful whites. Many blacks such as James Forten and Richard Allen refocused their attention on building strong, free black communities in America, while others looked to black organized and sponsored emigration to Haiti. As the Civil War erupted and the United States faced the prospect of thousands of free blacks, Abraham Lincoln\u27s government joined the growing Haitian colonization movement, sponsoring a colony in Haiti that failed within one year. Lincoln also called for the creation of a colony in South America for newly emancipated African-Americans, revealing the extent to which removal had become a highly racialized and institutionalized ideology that went far beyond the Indian Removal Act of 1830. Indeed, removal and colonization served as a key ingredient in America\u27s plans for territorial expansion throughout the nineteenth century. Men like Thomas Jefferson attempted to replace free blacks with immigrant white Europeans, which they believed made for a more harmonious and stable republic

SM(2,4k) fermionic characters and restricted jagged partitions

A derivation of the basis of states for the $SM(2,4k)$ superconformal minimal models is presented. It relies on a general hypothesis concerning the role of the null field of dimension $2k-1/2$. The basis is expressed solely in terms of $G_r$ modes and it takes the form of simple exclusion conditions (being thus a quasi-particle-type basis). Its elements are in correspondence with $(2k-1)$-restricted jagged partitions. The generating functions of the latter provide novel fermionic forms for the characters of the irreducible representations in both Ramond and Neveu-Schwarz sectors.Comment: 12 page

The hippocampus, prefrontal cortex, and perirhinal cortex are critical to incidental order memory.

Considerable research in rodents and humans indicates the hippocampus and prefrontal cortex are essential for remembering temporal relationships among stimuli, and accumulating evidence suggests the perirhinal cortex may also be involved. However, experimental parameters differ substantially across studies, which limits our ability to fully understand the fundamental contributions of these structures. In fact, previous studies vary in the type of temporal memory they emphasize (e.g., order, sequence, or separation in time), the stimuli and responses they use (e.g., trial-unique or repeated sequences, and incidental or rewarded behavior), and the degree to which they control for potential confounding factors (e.g., primary and recency effects, or order memory deficits secondary to item memory impairments). To help integrate these findings, we developed a new paradigm testing incidental memory for trial-unique series of events, and concurrently assessed order and item memory in animals with damage to the hippocampus, prefrontal cortex, or perirhinal cortex. We found that this new approach led to robust order and item memory, and that hippocampal, prefrontal and perirhinal damage selectively impaired order memory. These findings suggest the hippocampus, prefrontal cortex and perirhinal cortex are part of a broad network of structures essential for incidentally learning the order of events in episodic memory