Related papers: Non-geometric Calabi-Yau compactifications and fra…
Compactifications with fluxes and branes motivate us to study various enumerative invariants of Calabi-Yau manifolds. In this paper, we study non-perturbative corrections depending on both open and closed string moduli for a class of…
$\mathcal{G}$-structures, where $\mathcal{G}$ is a Lie group, are a uniform characterisation of many differential geometric structures of interest in supersymmetric compactifications of string theories. Calabi-Yau $n$-folds are instances of…
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…
In this paper we propose a systematic construction of mirrors of nonabelian two dimensional (2,2) supersymmetric gauge theories. Specifically, we propose a construction of B-twisted Landau-Ginzburg orbifolds whose correlation functions…
We define and investigate deformed n-Calabi-Yau completions of homologically smooth differential graded (=dg) categories. Important examples are: deformed preprojective algebras of connected non Dynkin quivers, Ginzburg dg algebras…
We show how the full holomorphic geometry of local Calabi-Yau threefold compactifications with N=1 supersymmetry can be obtained from matrix models. In particular for the conifold geometry we relate F-terms to the general amplitudes of c=1…
We show that supersymmetric M-theory compactifications to three-dimensional Minkowski space-time preserving $\mathcal{N}=2$ supersymmetry allow for a class of internal manifolds more general than the Calabi-Yau one, namely the class of…
We perform dimensional reductions of type IIA and type IIB double field theory in the flux formulation on Calabi-Yau three-folds and on $K3\times T^2$. In addition to geometric and non-geometric three-index fluxes and Ramond-Ramond fluxes,…
We show that the exact N=1 superpotential of a class of 4d string compactifications is computed by the closed topological string compactified to two dimensions. A relation to the open topological string is used to define a special geometry…
We consider F-theory compactifications on a mirror pair of elliptic Calabi-Yau threefolds. This yields two different six-dimensional theories, each of them being nonperturbatively equivalent to some compactification of heterotic strings on…
We study limits of four-dimensional type II Calabi-Yau compactifications with vanishing four-cycle singularities, which are dual to $\IT^2$ compactifications of the six-dimensional non-critical string with $E_8$ symmetry. We define proper…
In Calabi-Yau fourfold compactifications of M-theory with flux, we investigate the possibility of partial supersymmetry breaking in the three-dimensional effective theory. To this end, we place the effective theory in the framework of…
We study mirror symmetry of Calabi-Yau manifolds within the framework of the Gauss-Manin system. Applying the flat coordinates to the Gauss-Manin system for the periods, we derive differential equations for the mirror map in addition to the…
We construct Calabi-Yau geometries with wrapped D6 branes which realize ${\cal N}=1$ supersymmetric $A_r$ quiver theories, and study the corresponding geometric transitions. This also yields new large $N$ dualities for topological strings…
We study the Coulomb-Higgs duality of N=2 supersymmetric Abelian Chern-Simons theories in 2+1 dimensions, by compactifying dual pairs on a circle of radius R and comparing the resulting N=(2,2) theories in 1+1 dimensions. Below the…
Using mirror pairs (M_3, W_3) in type II superstring compactifications on Calabi-Yau threefolds, we study, geometrically, F-theory duals of M-theory on seven manifolds with G_2 holonomy. We first develop a way for getting Landau Ginzburg…
Using mirror symmetry, we show that Chern-Simons theory on certain manifolds such as lens spaces reduces to a novel class of Hermitian matrix models, where the measure is that of unitary matrix models. We show that this agrees with the more…
We review the major mathematical concepts involved in the dimensional reduction of D=11 N=1 supergravity theory over a Calabi-Yau manifold with non-trivial complex structure moduli resulting in ungauged D=5 N=2 supergravity theory with…
We review N=(2,2) supersymmetric non-linear sigma-models in two dimensions and their relation to generalized Kahler and Calabi-Yau geometry. We illustrate this with an explicit non-trivial example.
We study black hole attractor equations for one-(complex structure)modulus Calabi-Yau spaces which are the mirror dual of Fermat Calabi-Yau threefolds (CY_{3}s). When exploring non-degenerate solutions near the Landau-Ginzburg point of the…