Related papers: Classical {\it vs.}\ Landau-Ginzburg Geometry of C…
The D-brane spectrum of a $\Zop_2\times\Zop_2$ Calabi-Yau three-fold orbifold of toroidally compactified Type IIA and Type IIB string theory is analysed systematically. The corresponding K-theory groups are determined and complete agreement…
This thesis explores an exotic class of M-theory compactifications in which the compact manifold is taken to be a Calabi-Yau five-fold. The resulting effective theory is a one-dimensional N=2 super-mechanics model that exhibits peculiar…
The structure of stringy quantum corrections to four-dimensional effective theories is particularly interesting for string phenomenology and attempts to stabilize moduli. We consider the heterotic string compactified on a Calabi-Yau space.…
We perform a Hodge theoretic study of parameter dependent families of D-branes on compact Calabi-Yau manifolds in type II and F-theory compactifcations. Starting from a geometric Gauss-Manin connection for B type branes we study the…
We consider the holomorphic twist of the worldvolume theory of flat D$(2k-1)$-branes transversely probing a Calabi--Yau manifold. A chain complex, constructed using the BV formalism, computes the local observables in the holomorphically…
We study M and F theory compactifications on Calabi-Yau four-folds in the presence of non-trivial background flux. The geometry is warped and belongs to the class of p-brane metrics. We solve for the explicit warp factor in the orbifold…
We show that questions concerning the topological B-model on a Calabi-Yau manifold in the Landau-Ginzburg phase can be rephrased in the language of commutative algebra. This yields interesting and very practical methods for analyzing the…
We study the gauged sigma model and its mirror Landau-Ginsburg model corresponding to type IIA on the Fermat degree-24 hypersurface in WCP^4[1,1,2,8,12] (whose blow-up gives the smooth CY_3(3,243)) away from the orbifold singularities, and…
A T6 orbifold compactification is discussed from the somewhat unconventional perspective as the large radius limit of a Landau-Ginzburg model. The features of the model are in principle familiar, but the way they enter here is different…
We study the type II string theories compactified on manifolds of $G_2$ holonomy of the type $({Calabi-Yau 3-fold} \times S^1)/\bz_2$ where $CY_3$ sectors realized by the Gepner models. We construct modular invariant partition functions for…
After orientifold projection, the conifold singularity in hypermultiplet moduli space of Calabi-Yau compactifications cannot be avoided by geometric deformations. We study the non-perturbative fate of this singularity in a local model…
In the context of string dualities, fibration structures of Calabi-Yau manifolds play a prominent role. In particular, elliptic and K3 fibered Calabi-Yau fourfolds are important for dualities between string compactifications with four flat…
There is a large number of different ways of constructing Calabi-Yau manifolds, as well as related non-geometric formulations, relevant in string compactifications. Showcasing this diversity, we discuss explicit deformation families of…
We construct stringy cosmic string solutions corresponding to compactifications of F-theory on several elliptic Calabi-Yau manifolds by solving the equations of motion of low energy effective action of ten dimensional type IIB superstring…
Basics of some topics on perturbative and non-perturbative string theory are reviewed. After a mathematical survey of the Standard Model of particle physics and GUTs, the bosonic string kinematics for the free case and with interaction is…
These are lecture notes on non-K\"ahler complex threefolds presented at the MATRIX program ``The geometry of moduli spaces in string theory''. We review some basics of Calabi-Yau geometry in Section 1, describe topological features of the…
Superstring compactifications have been vigorously studied for over four decades, and have flourished involving an active iterative feedback between physics and (complex) algebraic geometry. This led to an unprecedented wealth of…
We formulate and study a class of massive N=2 supersymmetric gauge field theories coupled to boundary degrees of freedom on the strip. For some values of the parameters, the infrared limits of these theories can be interpreted as open…
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 study compactifications of type IIB supergravity on Calabi-Yau threefolds. The resulting low energy effective Lagrangian is displayed in the large volume limit and its symmetry properties - with specific emphasis on the SL(2,Z) - are…