Related papers: C-spaces, generalized geometry and double field th…
We construct in ZFC an L topological vector space -- a topological vector space that is an L space -- and an L field -- a topological field that is an L space. This generalizes results in [5] and [8].
In [1] we introduced the notion of 'structured space', i.e. a space which locally resembles various algebraic structures. In [2] and [3] we studied some cohomology theories related to these space. In this paper we continue in this…
We review double field theory (DFT) with emphasis on the doubled spacetime and its generalized coordinate transformations, which unify diffeomorphisms and b-field gauge transformations. We illustrate how the composition of generalized…
We investigate the patching of double and exceptional field theories. In double field theory the patching conditions imposed on the spacetime after solving the strong section condition imply that the 3-form field strength $H$ is exact. A…
The space $D'_\Lambda$ of distributions having their $C^\infty$ wavefront set in a cone $\Lambda$ has become important in physics because of its role in the formulation of quantum field theory in curved spacetime. It is also a basic object…
We study the duality relationship between M-theory and heterotic string theory at the classical level, emphasising the transformations between the Kaluza-Klein reductions of these two theories on the K3 and T^3 manifolds. Particular…
We construct M-theory on the orbifold C^2/Z_N by coupling 11-dimensional supergravity to a seven-dimensional Yang-Mills theory located on the orbifold fixed plane. It is shown that the resulting action is supersymmetric to leading…
Given a small category C, we show that there is a universal way of expanding C into a model category, essentially by formally adjoining homotopy colimits. The technique of localization becomes a method for imposing `relations' into these…
We generalise the notions of supersymmetry and superspace by allowing generators and coordinates transforming according to more general Lorentz representations than the spinorial and vectorial ones of standard lore. This yields novel…
M-theory suggests the study of 11-dimensional space-times compactified on some 7-manifolds. From its intimate relation to superstrings, one possible class of such 7-manifolds are those that have Calabi-Yau threefolds as boundary. In this…
We develop a description of higher gauge theory with higher groupoids as gauge structure from first principles. This approach captures ordinary gauge theories and gauged sigma models as well as their categorifications on a very general…
We "solve" the Freed-Witten anomaly equation, i.e., we find a geometrical classification of the B-field and A-field configurations in the presence of D-branes that are anomaly-free. The mathematical setting being provided by the geometry of…
We study AKSZ-type BV constructions for the topological A- and B-models within a double field theory formulation that incorporates backgrounds with geometric and non-geometric fluxes. We relate them to a Courant sigma-model, on an open…
We describe how generalized complex geometry, which interpolates between complex and symplectic geometry, is compatible with T-duality, a relation between quantum field theories discovered by physicists. T-duality relates topologically…
Topological quivers generalize the notion of directed graphs in which the sets of vertices and edges are locally compact (second countable) Hausdorff spaces. Associated to a topological quiver $Q$ is a $C^*$-correspondence, and in turn, a…
We discuss the r\^ole of enlarged superspaces in two seemingly different contexts, the structure of the $p$-brane actions and that of the Cremmer-Julia-Scherk eleven-dimensional supergravity. Both provide examples of a common principle: the…
While Calabi-Yau hypersurfaces in toric ambient spaces provide a huge number of examples, theoretical considerations as well as applications to string phenomenology often suggest a broader perspective. With even the question of finiteness…
We study a generalization of the Alexandrov-Kontsevich-Schwarz-Zaboronsky (AKSZ) formulation of the A- and B-models which involves a doubling of coordinates, and can be understood as a complexification of the Poisson $\sigma$-model…
Let G be a discrete group. We give methods to compute for a generalized (co-)homology theory its values on the Borel construction (EG x X)/G of a proper G-CW-complex X satisfying certain finiteness conditions. In particular we give formulas…
We introduce and study central types, which are generalizations of Eilenberg-Mac Lane spaces. A type is central when it is equivalent to the component of the identity among its own self-equivalences. From centrality alone we construct an…