Related papers: Integrability of the holomorphic anomaly equations
By introducing a more flexible notion of convexity, we obtain a new Omori-Yau maximum principle for harmonic maps. In the spirit of the Calabi-Yau conjectures, this principle is more suitable for studying the unboundedness of certain…
We show how topological open string theory amplitudes can be computed by using relative stable morphisms in the algebraic category. We achieve our goal by explicitly working through an example which has been previously considered by Ooguri…
In this work, we provide evidence for a duality between 4-dimensional Calabi-Yau compactifications of the heterotic string, in which the base manifolds are linked by a conifold transition. In recent work, a geometric proposal was put…
We define the notion of mirror of a Calabi-Yau manifold with a stable bundle in the context of type II strings in terms of supersymmetric cycles on the mirror. This allows us to relate the variation of Hodge structure for cohomologies…
The presence of RR and NS three-form fluxes in type IIB string compactification on a Calabi-Yau orientifold gives rise to a nontrivial superpotential W for the dilaton and complex structure moduli. This superpotential is computable in terms…
We prove that if a Calabi--Yau manifold $M$ admits a holomorphic Cartan geometry, then $M$ is covered by a complex torus. This is done by establishing the Bogomolov inequality for semistable sheaves on compact K\"ahler manifolds. We also…
We study the stringy genus one partition function of $N=2$ SCFT's. It is shown how to compute this using an anomaly in decoupling of BRST trivial states from the partition function. A particular limit of this partition function yields the…
This thesis is concerned with the geometry of toroidal orbifolds and their applications in string theory. By resolving the orbifold singularities via blow-ups, one arrives at a smooth Calabi-Yau manifold. The systematic method to do so is…
We consider principal fibre bundles with a given connection and construct almost complex structures on the total space if the adjoint bundle is isomorphic to the tangent bundle of the base. We derive the integrability condition. If the…
By properly accounting for the invariance of a Calabi-Yau sigma-model under shifts of the $B$-field by integral amounts (analagous to the $\theta$-angle in QCD), we show that the moduli spaces of such sigma-models can often be enlarged to…
We discuss the use of gauge fields to stabilize complex structure moduli in Calabi-Yau three-fold compactifications of heterotic string and M-theory. The requirement that the gauge fields in such models preserve supersymmetry leads to a…
We study the modular symmetry in heterotic string theory on Calabi-Yau threefolds. In particular, we examine whether moduli-dependent holomorphic Yukawa couplings are described by modular forms in the context of heterotic string theory with…
A holographic perspective to study and characterize field spaces that arise in string compactifications is suggested. A concrete correspondence is developed by studying two-dimensional moduli spaces in supersymmetric string…
We consider the heterotic string on Calabi-Yau manifolds admitting a Strominger-Yau-Zaslow fibration. Upon reducing the system in the $T^3$-directions, the Hermitian Yang-Mills conditions can then be reinterpreted as a complex flat…
The holomorphic anomaly equations describe B-model closed topological strings in Calabi-Yau geometries. Having been used to construct perturbative expansions, it was recently shown that they can also be extended past perturbation theory by…
Topological string theory has multi-instanton sectors which lead to non-perturbative effects in the string coupling constant and control the large order behavior of the perturbative genus expansion. As proposed by Couso, Edelstein, Schiappa…
We show that every connected compact or bordered Riemann surface contains a Cantor set whose complement admits a complete conformal minimal immersion in $\mathbb R^3$ with bounded image. The analogous result holds for holomorphic immersions…
We approach string phenomenology from the perspective of computational algebraic geometry, by providing new and efficient techniques for proving stability and calculating particle spectra in heterotic compactifications. This is done in the…
We develop new techniques to study regularity questions for moduli spaces of pseudoholomorphic curves that are multiply covered. Among the main results, we show that unbranched multiple covers of closed holomorphic curves are generically…
We study the differential polynomial rings which are defined using the special geometry of the moduli spaces of Calabi-Yau threefolds. The higher genus topological string amplitudes are expressed as polynomials in the generators of these…