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The large volume scenario has been an important issue for flux compactifications with T-dual non-geometric fluxes. As one solution to this issue, to naturally embed duality in string compactification, we investigate in self-mirror…
Superstring theories are the most promising theories for unified description of all fundamental interactions including gravity. However, these theories are formulated consistently only in 10 spacetime dimensions. Therefore, to connect to…
The TS/ST correspondence relates the spectral theory of certain quantum mechanical operators, to topological strings on toric Calabi-Yau threefolds. So far the correspondence has been formulated for real values of Planck's constant. In this…
In this paper, the numbers of rational curves on general complete intersection Calabi-Yau threefolds in complex projective spaces are computed up to degree six. The results are all in agreement with the predictions made from mirror…
String theory appears to admit a group of discrete field transformations -- called $S$ dualities -- as exact non-perturbative quantum symmetries. Mathematically, they are rather analogous to the better-known $T$ duality symmetries, which…
The string landscape satisfies interesting finiteness properties imposed by supersymmetry and string-theoretical consistency conditions. We study N=1 supersymmetric compactifications of Type IIB string theory on smooth elliptically fibered…
It has been proposed recently that topological A-model string amplitudes for toric Calabi-Yau 3-folds in non self-dual graviphoton background can be caluculated by a diagrammatic method that is called the ``refined topological vertex''. We…
We propose that the grand canonical topological string partition functions satisfy finite-difference equations in the closed string moduli. In the case of genus one mirror curve these are conjectured to be the q-difference Painlev\'e…
Topological strings on Calabi--Yau manifolds are known to undergo phase transitions at small distances. We study this issue in the case of perturbative topological strings on local Calabi--Yau threefolds given by a bundle over a two-sphere.…
Non-simply connected Calabi-Yau threefolds play a central role in the study of string compactifications. Such manifolds are usually described by quotienting a simply connected Calabi-Yau variety by a freely acting discrete symmetry. For the…
In this article we prove completeness results for Sobolev metrics with nonconstant coefficients on the space of immersed curves and on the space of unparametrized curves. We provide necessary as well as sufficient conditions for the…
We consider superstring compactifications where both the classical description, in terms of a Calabi-Yau manifold, and also the quantum theory is known in terms of a Landau-Ginzburg orbifold model. In particular, we study (smooth)…
We study the action of mirror symmetry on two-dimensional N=(2,2) effective theories obtained by compactifying Type IIA string theory on Calabi-Yau fourfolds. Our focus is on fourfold geometries with non-trivial three-form cohomology. The…
The quantum Cram\'er-Rao (QCR) bound sets the ultimate local precision limit for unbiased multiparameter estimation. Yet, unlike in the single-parameter case, its saturability is not generally guaranteed and is often assessed through…
We present solutions for the higher genus topological string amplitudes on Calabi-Yau-manifolds, which are realized as complete intersections in Grassmannians. We solve the B-model by direct integration of the holomorphic anomaly equations…
We study local mirror symmetry on non-compact Calabi-Yau manifolds (conifold type of singularities) in the presence of D3 brane probes. Using an intermediate brane setup of NS 5-branes `probed' by D4 resp. D5 branes, we can explicitly…
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…
We derive topological string amplitudes on local Calabi-Yau manifolds in terms of polynomials in finitely many generators of special functions. These objects are defined globally in the moduli space and lead to a description of mirror…
We analyze the moduli spaces of Calabi-Yau threefolds and their associated conformally invariant nonlinear sigma-models and show that they are described by an unexpectedly rich geometrical structure. Specifically, the Kahler sector of the…
It was recently shown that integrating out M2 states on Calabi-Yau manifolds captures non-perturbative topological string physics in the free energy. In this note, we show that the resulting expression manifests a certain duality symmetry:…