Related papers: Instantons and branes in manifolds with vector cro…
Here we study the deformations of associative submanifolds inside a G_2 manifold M^7 with a calibration 3-form \phi. A choice of 2-plane field \Lambda on M (which always exits) splits the tangent bundle of M as a direct sum of a…
By analyzing qualitative aspects of NS5-brane instanton corrections, we determine the topology of the hypermultiplet moduli space M_H in Calabi-Yau compactifications of type II string theories at fixed value of the dilaton and of the…
Generalizing the construction of the Maslov class for a Lagrangian embedding in a symplectic vector space, we prove that it is possible to give a consistent definition of this class for any Lagrangian submanifold of a Calabi-Yau manifold.…
We discuss D-branes of the topological A-model (A-branes), which are believed to be closely related to the Fukaya category. We give string theory arguments which show that A-branes are not necessarily Lagrangian submanifolds in the…
We study the Cahen-Gutt moment map on the space of symplectic connections of a symplectic manifold. On a K\"ahler manifold, we define a Calabi-type functional $\mathscr{F}$ on the space of K\"ahler metrics in a given K\"ahler class. We…
By using the global deformation of almost complex structures which are compatible with a symplectic form off a Lebesgue measure zero subset, we construct a (measurable) Lipschitz Kahler metric such that the one-form type Calabi-Yau equation…
We study special Lagrangian submanifolds in the Calabi-Yau manifold $T^*S^n$ with the Stenzel metric, as well as calibrated submanifolds in the $\text{G}_2$-manifold $\Lambda^2_-(T^*X)$ $(X^4 = S^4, \mathbb{CP}^2)$ and the…
We calculate the topological string amplitudes of Calabi-Yau toric threefolds corresponding to 4D, N=2, SU(2) gauge theory with N_f=0,1,2,3,4 fundamental hypermultiplets by using the method of the geometric transition and show that they…
Compactifications of M-theory on manifolds with reduced holonomy arise as the local eleven-dimensional description of D6-branes wrapped on supersymmetric cycles in manifolds of lower dimension with a different holonomy group. Whenever the…
We study the asymptotic structure of instantons on multi-centered Taub-NUT manifolds, calorons, and monopoles on R^3. We show that, without any assumptions on symmetry breaking, these instantons and monopoles asymptotically decompose as a…
This paper deals with rational curves and birational contractions on irreducible holomorphically symplectic manifold. We survey some recent results about minimal rational curves, their deformations, extremal rays associated with these…
We report on progress towards the construction of SM-like gauge theories on the world-volume of D-branes at a Calabi-Yau singularity. In particular, we work out the topological conditions on the embedding of the singularity inside a compact…
We study D-branes on Calabi-Yau manifolds, carrying charges which are torsion elements of the K-theory. Interesting physics ensues when we follow these branes into nongeometrical phases of the compactification. On the level of K-theory, we…
As a first step towards computing instanton-generated superpotentials in heterotic standard model vacua, we determine the Gromov-Witten invariants for a Calabi-Yau threefold with fundamental group pi_1(X)=Z_3 x Z_3. We find that the curves…
In this review we describe the general geometrical framework of brane world constructions in orientifolds of type IIA string theory with D6-branes wrapping 3-cycles in a Calabi-Yau 3-fold. These branes generically intersect in points on the…
We address the issue why Calabi-Yau manifolds exist with a mirror pair. We observe that the irreducible spinor representation of the Lorentz group Spin(6) requires us to consider the vector spaces of two-forms and four-forms on an equal…
We review how D-brane instantons can generate open string couplings of stringy hierarchy in the superpotential which violate global abelian symmetries and are therefore perturbatively forbidden. We discuss the main ingredients of this…
We review some aspects of D-instantons in intersecting D-brane models. In particular, we present applications of the recently proposed instanton calculus to computations of charged matter superpotential couplings and corrections to the…
Effective field theories in type I and II superstring theories for D-branes located at points in the orbifold C^2/Z_n are supersymmetric gauge theories whose field content is conveniently summarized by a `quiver diagram,' and whose…
We reconsider the study of the geometric transitions and brane/flux dualities in various dimensions. We first give toric interpretations of the topology changing transitions in the Calabi-Yau conifold and the $Spin(7)$ manifold. The latter,…