From local to global in F-theory model building

On the Passage from Local to Global in Number Theory

Would a reader be able to predict the branch of mathematics that is the subject of this article if its title had not included the phrase “in Number Theory”? The distinction “local” versus “global”, with various connotations, has found a home in almost every part of mathematics, local problems being often a stepping-stone to the more difficult global problems. To illustrate what the earthy geome...

From Local to Global Consistency* from Local to Global Consistency*

In reasoning tasks involving the maintenance of consistent databases (so called "constraint net­ works") it is customary to enforce local consistency conditions in order to simplify the construc­ tion of a globally coherent model of the data. In this paper we present a relationship between the sizes of the variables' domains and the level of local consistency sufficient to ensure global con­ si...

Global F-theory GUTs

We construct global F-theory GUT models on del Pezzo surfaces in compact Calabi-Yau fourfolds realized as complete intersections of two hypersurface constraints. The intersections of the GUT brane and the flavour branes as well as the gauge flux are described by the spectral cover construction. We consider a split S[U(4)×U(1)X ] spectral cover, which allows for the phenomenologically relevant Y...

Global Knot Theory in F

Antibiotic resistance: A link from local bio-pollution cycle to global dissemination

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