Related papers: Spin(7)-manifolds in compactifications to four dim…
We show that M-theory on spaces with irreducible holonomy represent Type IIA backgrounds in which a collection of D6-branes wrap a supersymmetric cycle in a manifold with a holonomy group different from the one appearing in the M-theory…
We show how supersymmetry conditions for flux compactifications of supergravity and string theory can be described in terms of a flat subalgebra of the Kahler-Atiyah algebra of the compactification space, a description which has…
We study constrained generalized Killing spinors over the metric cone and cylinder of a (pseudo-)Riemannian manifold, developing a toolkit which can be used to investigate certain problems arising in supersymmetric flux compactifications of…
We construct a smooth Deligne-Mumford compactification for the moduli space of curves with an m-tuple of spin structures using line bundles on quasi-stable curves as limiting objects, as opposed to line bundles on stacky curves. For all m,…
We derive the three-dimensional $\mathcal{N}=1$ effective theories obtained by compactifying all five ten-dimensional string theories on generic seven-dimensional manifolds with $G_2$ structure. The resulting flux compactifications are…
The study of fibrations of the target manifolds of string/M/F-theories has provided many insights to the dualities among these theories or even as a tool to build up dualities since the work of Strominger, Yau, and Zaslow on the Calabi-Yau…
Let $LG$ be the loop group of a compact, connected Lie group $G$. We show that the tangent bundle of any proper Hamiltonian $LG$-space $\mathcal{M}$ has a natural completion $\overline{T}\mathcal{M}$ to a strongly symplectic…
Ramond has observed that the massless multiplet of eleven-dimensional supergravity can be generated from the decomposition of certain representation of the exceptional Lie group F4 into those of its maximal compact subgroup Spin(9). The…
In this paper we study compactifications of ADE type conformal matter, N M5 branes probing ADE singularity, on torus with flux for global symmetry. We systematically construct the four dimensional theories by first going to five dimensions…
The nature of M-theory on K3 X I, where I is a line interval, is considered, with a view towards formulating a `matrix theory' representation of that situation. Various limits of this compactification of M-theory yield a number of well…
F-theory on appropriately fibered Spin(7) holonomy manifolds is defined to arise as the dual of M-theory on the same space in the limit of a shrinking fiber. A class of Spin(7) orbifolds can be constructed as quotients of elliptically…
We study compactifications of the 6d E-string theory, the theory of a small E_8 instanton, to four dimensions. In particular we identify N=1 field theories in four dimensions corresponding to compactifications on arbitrary Riemann surfaces…
We first consider M-theory formulated on an open eleven-dimensional spin-manifold. There is then a potential anomaly under gauge transformations on the E_8 bundle that is defined over the boundary and also under diffeomorphisms of the…
We study $\mathrm{Spin}(7)$-manifolds with an effective multi-Hamiltonian action of a four-torus. On an open dense set, we provide a Gibbons-Hawking type ansatz that describes such geometries in terms of a symmetric $4\times4$-matrix of…
F-theory admits 7-branes with exceptional gauge symmetries, which can be compactified to give phenomenological four-dimensional GUT models. Here we study general supersymmetric compactifications of eight-dimensional Yang-Mills theory. They…
We formulate a theory of topological membranes on manifolds with G_2 holonomy. The BRST charges of the theories are the superspace Killing vectors (the generators of global supersymmetry) on the background with reduced holonomy G_2. In the…
We study the types of non-integrable $\mathrm{G}$-structures on Riemannian manifolds. In particular, geometric types admitting a connection with totally skew-symmetric torsion are characterized. 8-dimensional manifolds equipped with a…
We consider manifolds with special holonomy groups SU(3), G2 and Spin(7) as suitable for compactification of superstrings, M-theory and F-theory (with only one time) respectively. The relations of these groups with the octonions are…
This article presents families of 7-dimensional closed and simply-connected manifolds and fold maps on them such that squares of 2nd integral cohomology classes may not be divisible by 2. Fold maps are higher dimensional versions of Morse…
We continue the investigation into non-maximally symmetric compactifications of the heterotic string. In particular, we consider compactifications where the internal space is allowed to depend on two or more external directions. For…