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We develop some consequences of the connection between Calabi-Yau structures and torsion-free $G_2$ structures on compact and asymptotically cylindrical six- and seven-dimensional manifolds. Firstly, we improve the known proof that matching…
In this paper we compute the gravitational couplings of the heterotic string compactified on $(K3\times T^2)/\mathbb{Z}_N$ and $E_8\times E_8$ and predict the Gopakumar Vafa invariants of the dual Calabi Yau manifold in presence of Wilson…
We study the physics of globally consistent four-dimensional $\mathcal{N}=1$ supersymmetric M-theory compactifications on $G_2$ manifolds constructed via twisted connected sum; there are now perhaps fifty million examples of these…
A new local, covariant ``counter-term'' is used to construct a variational principle for asymptotically flat spacetimes in any spacetime dimension $ d \ge 4$. The new counter-term makes direct contact with more familiar background…
We study the equivariant generalization of topological strings on toric manifolds, focusing in particular on defining the contributions of constant maps in the genus expansion of the partition function. This approach regularizes the…
In a previous paper we had proposed a specific route to relating the entropy of two charge black holes to the degeneracy of elementary string states in N=4 supersymmetric heterotic string theory in four dimensions. For toroidal…
We are considering the class of heterotic $\mathcal{N}=(2,2)$ Landau-Ginzburg orbifolds with 9 fields corresponding to $A_1^9$ Gepner models. We classify all of its Abelian discrete quotients and obtain 152 inequivalent models closed under…
I show that all FRW models (four dimensional pseudo-Riemannian manifolds with maximally symmetric space) can be embedded in a flat Minkowski manifold with 5 dimensions. The pseudo Riemannian metric of space-time is induced by the flat…
We discuss perturbative four-dimensional compactifications of both the SO(32) heterotic and the Type I string on smooth Calabi-Yau manifolds endowed with general non-abelian and abelian bundles. We analyse the generalized Green-Schwarz…
We introduce the notion of a flat extension of a connection $\theta$ on a principal bundle. Roughly speaking, $\theta$ admits a flat extension if it arises as the pull-back of a component of a Maurer-Cartan form. For trivial bundles over…
By studying phase transitions in supersymmetric gauge theories with Green-Schwarz anomaly cancellation, a natural relation is found between sigma models on certain non-Kahler manifolds with intrinsic torsion and asymmetric Landau-Ginzburg…
Following Ghomi and Tabachnikov we study topological obstructions to totally skew embeddings of a smooth manifold M in Euclidean spaces. This problem is naturally related to the question of estimating the geometric dimension of the stable…
In this paper we consider orbifold compactifications of M-theory on $S^1/{\bf Z}_2\times T^4/{\bf Z}_2$. We discuss solutions of the local anomaly matching conditions by twisted vector, tensor and hypermultiplets confined on the local…
Open topological string amplitudes on compact Calabi-Yau threefolds are shown to satisfy an extension of the holomorphic anomaly equation of Bershadsky, Cecotti, Ooguri and Vafa. The total topological charge of the D-brane configuration…
According to the Campbell-Magaard theorem, any analytical spacetime can be locally and analytically embedded into a five-dimensional pseudo-Riemannian Ricci-flat manifold. We find explicitly this embedding for Godel's universe. The…
We consider compactifications of higher-dimensional supergravities on Riemann-flat manifolds of dimension d ($3 \le d \le 7$) that fully break supersymmetry at the classical level on a resulting D-dimensional Minkowski space. We…
We use local mirror symmetry in type IIA string compactifications on Calabi-Yau n+1 folds $X_{n+1}$ to construct vector bundles on (possibly singular) elliptically fibered Calabi-Yau n-folds Z_n. The interpretation of these data as valid…
We derive the anomaly 8-form of 6-dimensional gauge theories arising in F theory compactifications on elliptic Calabi-Yau threefolds. The result allows to determine the matter content of certain such theories in terms of intersection…
We obtain smooth M-theory solutions whose geometry is a warped product of AdS_5 and a compact internal space that can be viewed as an S^4 bundle over S^2. The bundle can be trivial or twisted, depending on the even or odd values of the two…
The heterotic string compactified on an (n-1)-dimensional elliptically fibered Calabi-Yau Z-->B is conjectured to be dual to F-theory compactified on an n-dimensional Calabi-Yau X-->B, fibered over the same base with elliptic K3 fibers. In…