An Uplifting Discussion of T-Duality

It is well known that string theory has a T-duality symmetry relating circle compactifications of large and small radius. This symmetry plays a foundational role in string theory. We note here that while T-duality is order two acting on the moduli space of compactifications, it is order four in its action on the conformal field theory state space. More generally, involutions in the Weyl group $W(G)$ which act at points of enhanced $G$ symmetry have canonical lifts to order four elements of $G$, a phenomenon first investigated by J. Tits in the mathematical literature on Lie groups and generalized here to conformal field theory. This simple fact has a number of interesting consequences. One consequence is a reevaluation of a mod two condition appearing in asymmetric orbifold constructions. We also briefly discuss the implications for the idea that T-duality and its generalizations should be thought of as discrete gauge symmetries in spacetime.Comment: 47 pages, claims regarding $Z_4$ valued cocycles remove

Predicting Future Sources of Mass Toxic Tort Litigation

The authors describe the efforts of an expert working group to identify potential sources, over the next five to ten years, of future mass litigation and report on the group\u27s consensus conclusions

Educational Facilities for the Twenty-First Century: Research Analysis and Design Patterns

This handbook examines the relationship between school buildings and educational performance. Following the introductory chapter, Chapter 2 presents findings from empirical studies that have examined the building/performance issue. Research has demonstrated that the physical setting has both direct and mediated effects on prosocial and achievement outcomes. Chapter 3 presents an ecological model that accounts for physical, psychological and social environmental factors that affect student outcomes. The fourth chapter offers an analysis based on a review of empirical research, architectural literature and educational reform literature to inductively develop a set of 27 design patterns. Two patterns based on environment-behavior research are highlighted--small schools and well-defined activity pockets. Chapter 5 discusses implications from the educational reform literature. The complete set of 27 patterns is presented in the sixth chapter. Chapter 7 presents an example that uses patterns to create a prototypical design for a new type of educational facility. The final chapter focuses on the earlier stages of the facility development process, those of feasibility and planning. A reconceptualization of an existing educational facility planning model is offered. A total of 42 figures and 1 table are included.https://dc.uwm.edu/caupr_mono/1031/thumbnail.jp

Bedrock Denudation on Titan: Estimates of Vertical Extent and Lateral Debris Dispersion

Methane rainfall and runoff, along with aeolian activity, have dominated the sculpting of Titan s landscape. A knowledge of the vertical extent of bedrock erosion and the lateral extent of the resulting sediment is useful for several purposes [1]. For instance, what is the magnitude and expression of modification of constructional landforms (e.g., mountains)? Does highland denudation and the filling of basins with sediment cause adjustments (uplift and subsidence) in the crustal ice shell? Here we report preliminary findings of putative eroded craters and the results of landform evolution modeling (Fig. 1) that suggest that approx. 250 m of net bedrock erosion has at least locally taken place and approx.1 km of maximum local erosion