Related papers: Foliated eight-manifolds for M-theory compactifica…
Borrowing ideas from elliptic complex geometry, we approach M-theory compactifications on real toric fibrations. Precisely, we explore real toric equations rather than complex ones exploited in F-theory and related dual models. These…
In this paper we describe the heterotic dual of the type IIB theory compactified to four dimensions on a toroidal orientifold in the presence of fluxes. The type IIB background is most easily described in terms of an M-theory…
In this paper, we demonstrate that any asymptotically flat manifold $(M^n, g)$ with $4\leq n\leq 7$ can be foliated by a family of area-minimizing hypersurfaces, each of which is asymptotic to Cartesian coordinate hyperplanes defined at an…
Let $X$ be a connected non-compact $2$-dimensional manifold possibly with boundary and $\Delta$ be a foliation on $X$ such that each leaf $\omega\in\Delta$ is homeomorphic to $\mathbb{R}$ and has a trivially foliated neighborhood. Such…
We consider an embedded general complex torus $C_n$ into a complex manifold $M_{n+d}$ with a unitary flat normal bundle $N_C$. We show the existence of (non-singular) holomorphic foliation in a neighborhood of $C$ in $M$ having $C$ as leaf…
It is well known that a foliation F of a smooth manifold M gives rise to a rich cohomological theory, its characteristic (i.e., leafwise) cohomology. Characteristic cohomologies of F may be interpreted, to some extent, as functions on the…
It is shown that many of the conjectured dualities involving orbifold compactification of M-theory follow from the known dualities involving M-theory and string theory in ten dimensions, and the ansatz that orbifolding procedure commutes…
We study the moduli space of M-theories compactified on G_2 manifolds which are asymptotic to a cone over quotients of S^3 x S^3. We show that the moduli space is composed of several components, each of which interpolates smoothly among…
A compactification over $\overline{M}_g$ of $M_{g,n}$ is obtained by considering the relative Fulton-MacPherson configuration space of the universal curve. The resulting compactification differs from the Deligne-Mumford space…
We study T^{11-D-q}xT^q/Z_n orbifold compactifications of 11D supergravity and M-theory by a purely algebraic method. Using the mapping between scalar fields of toroidally compactified maximal supergravity and generators of the U-duality…
We show that a smooth 1-parameter family of foliations by circles of a closed 3-manifold, deforming the foliation whose leaves are the fibers of a circle bundle, is trivial, i.e. all the foliations of the family arise from circle bundles…
We discuss the possible realisation in string/M theory of the recently discovered family of four-dimensional maximal $SO(8)$ gauged supergravities, and of an analogous family of seven-dimensional half-maximal $SO(4)$ gauged supergravities.…
We obtain the vacuum solutions for M-theory compactified on eight-manifolds with non-vanishing four-form flux by analyzing the scalar potential appearing in the three-dimensional theory. Many of these vacua are not supersymmetric and yet…
We review properties of closed meromorphic $1$-forms and of the foliations defined by them. We present and explain classical results from foliation theory, like index theorems, the existence of separatrices, and resolution of singularities…
We prove a compactness theorem for holomorphic curves in 4-dimensional symplectizations that have embedded projections to the underlying 3-manifold. It strengthens the cylindrical case of the SFT compactness theorem by using intersection…
M theory compactifications on G_2 holonomy manifolds, whilst supersymmetric, require singularities in order to obtain non-Abelian gauge groups, chiral fermions and other properties necessary for a realistic model of particle physics. We…
We investigate the orbifold limits of string theory compactifications with geometric and non-geometric fluxes. Exploiting the connection between internal fluxes and structure constants of the gaugings in the reduced supergravity theory, we…
Magnetic flux plays an important role in compactifications of field and string theories in two ways, it generates a multiplicity of chiral fermion zero modes and it can break supersymmetry. We derive the complete four-dimensional effective…
We study the Matrix theory description of M-theory compactified on $T^4$ and $T^5$. M-theory on $T^4$ is described by the six dimensional (2,0) fixed point field theory compactified on a five torus, $\widetilde T^5$. For M-theory on $T^5$…
We argue that T-duality and F-theory appear automatically in the E_8 gauge bundle perspective of M-theory. The 11-dimensional supergravity four-form determines an E_8 bundle. If we compactify on a two-torus, this data specifies an LLE_8…