Related papers: Integrability of the holomorphic anomaly equations
We study a flat connection defined on the open-closed deformation space of open string mirror symmetry for type II compactifications on Calabi-Yau threefolds with D-branes. We use flatness and integrability conditions to define…
Recent work on four dimensional effective descriptions of the heterotic string has identified the moduli of such systems as being given by kernels of maps between ordinary Dolbeault cohomology groups. The maps involved are defined by the…
We study various properties of a nonperturbative partition function which can be associated to any spectral curve. When the spectral curve arises from a matrix model, this nonperturbative partition function is given by a sum of matrix…
This thesis contributes with a number of topics to the subject of string compactifications. In the first half of the work, I discuss the Hodge plot of Calabi-Yau threefolds realised as hypersurfaces in toric varieties. The intricate…
Moduli stabilisation in superstring compactifications on Calabi-Yau orientifolds remains a key challenge in the search for realistic string vacua. In particular, odd moduli arising from the reduction of 2-forms $(B_2,C_2)$ in type IIB are…
We describe an explicit action of the prop of the chains on the moduli space of Riemann surfaces on the Hochschild complex of a Calabi-Yau elliptic space. One example of such an elliptic space extends the known string topology operations,…
The c-map relates classical hypermultiplet moduli spaces in compactifications of type II strings on a Calabi-Yau threefold to vector multiplet moduli spaces via a further compactification on a circle. We give an off-shell description of the…
We develop the deformation theory of Calabi-Yau threefolds, by which we mean 3-dimensional complex manifolds with a nowhere-vanishing holomorphic 3-form, on manifolds with boundary. The boundary data is a closed, real 3-form on the…
We prove the existence of global sections trivializing the Hodge bundles on the Hodge metric completion space of the Torelli space of Calabi--Yau manifolds, a global splitting property of these Hodge bundles. We also prove that a compact…
We analyze the phase structure of topological Calabi--Yau manifolds defined on the moduli space of instantons. We show in this framework that topological vacua describe new phases of the Heterotic String theory in which the flat directions…
The moduli dependence of $(2,2)$ superstring compactifications based on Calabi--Yau hypersurfaces in weighted projective space has so far only been investigated for Fermat-type polynomial constraints. These correspond to Landau-Ginzburg…
Compactification of the heterotic string on toroidal orbifolds is a promising set-up for the construction of realistic unified models of particle physics. The target space dynamics of such models, however, drives them slightly away from the…
This paper describes the reconstruction of the topological string partition function for certain local Calabi-Yau (CY) manifolds from the quantum curve, an ordinary differential equation obtained by quantising their defining equations.…
Generating functions $h_r(\tau)$ of D4-D2-D0 BPS indices, appearing in Calabi-Yau compactifications of type IIA string theory and identical to rank 0 Donaldson-Thomas invariants, are known to be higher depth mock modular forms satisfying a…
Let $f$ be a holomorphic mapping between compact complex manifolds. We give a criterion for $f$ to have {\it unobstructed deformations}, i.e. for the local moduli space of $f$ to be smooth: this says, roughly speaking, that the group of…
In arXiv:0905.3629 we described a new class of N=2 topological amplitudes that depends both on vector and hypermultiplet moduli. Here we find that this class is actually a particular case of much more general topological amplitudes which…
We study noncompact Calabi-Yau threefolds, their moduli spaces of vector bundles and deformation theory. We present Calabi-Yau threefolds that have infinitely many distinct deformations, constructing them explicitily, and describe the…
We present a new class of dualities relating non-geometric Calabi-Yau compactifications of type II string theory to T-fold compactifications of the heterotic string, both preserving four-dimensional $\mathcal{N}=2$ supersymmetry. The…
We study low-degree curves on one-parameter Calabi-Yau hypersurfaces, and their contribution to the space-time superpotential in a superstring compactification with D-branes. We identify all lines that are invariant under at least one…
We introduce a moment map picture for holomorphic string algebroids where the Hamiltonian gauge action is described by means of inner automorphisms of Courant algebroids. The zero locus of our moment map is given by the solutions of the…