Semi-Flatland, by David Vegh and John McGreevy
In looking up material that was related to the classic novel Flatland (review forthcoming), I came across this paper on non-geometric space that would allow for Type II string theory calculations to work on semi-flat space. Unless you are fond of theoretical mathematics and high-level equations involving string theory, I do not recommend this book for reading. If you are, though, there are definitely some aspects of this paper that are very interesting. For my own purposes, though, this was definitely a disappointment, as I saw a reference to Flatland, one of the classic novels of the late 19th century, and the writers never even commented on the novel itself or the odd mathematics that are resulted in moving between the dimensions even though their whole research and the simplifications of string theory involving the dimensions made the perfect setup for the sort of joke that could have been made about it. Still, this paper exists for its own purposes, and that is for seeking to find progress in compactifying string theory calculations into fewer dimensions by using geometries that go above and beyond the usual extremely simplified models used in many such papers.
This paper is about 80 pages or so and is divided into seven sections and numerous appendices that take up a considerable part of the work as a whole. The paper begins with an introduction (1) and then moves to a discussion of the semi-flat limit in one, two, or three dimensions as well as flat vertices (2). After that the author looks at stringy monodromies, including reduction to seven dimensions and various dualities (3). After that the author uses 4th dimension singularities, non-geometric and asymmetric, as a way of further compacting string theory even further (4). Another chapter discusses several examples of non-geometric modifications and compactifications (5), another discusses chiral Scherk-Schwartz reductions in one or two dimensions (6), and then the paper concludes. After the conclusion there are appendices with further reductions, a contrast between semi-flat and exact solutions, more asymmetric orbifolds in semi-flat space, and various spectra and patterns dealing with certain models. To be sure, most readers will not even have the vaguest idea of what is being discussed here, but if this is your sort of thing, this paper may just be your sort of thing for some light and entertaining reading in novel string theory applications. You can do far worse than read math papers for fun, after all.