Related papers: Mirror Symmetry for Two Parameter Models -- I
We study mirror symmetry of a family of Calabi-Yau manifolds fibered by (1,8)-polarized abelian surfaces with Euler characteristic zero. By describing the parameter space globally, we find all expected boundary points (LCSLs), including…
We use mirror symmetry to establish the first concrete arena of spacetime topology change in string theory. In particular, we establish that the {\it quantum theories} based on certain nonlinear sigma models with topologically distinct…
We extend our variant of mirror symmetry for K3 surfaces \cite{GN3} and clarify its relation with mirror symmetry for Calabi-Yau manifolds. We introduce two classes (for the models A and B) of Calabi-Yau manifolds fibrated by K3 surfaces…
We consider an (N-2)-dimensional Calabi-Yau manifold which is defined as the zero locus of the polynomial of degree N (of Fermat type) in CP^{N-1} and its mirror manifold. We introduce the (N-2)-point correlation function (generalized…
We discuss two-dimensional sigma models on moduli spaces of instantons on K3 surfaces. These N=(4,4) superconformal field theories describe the near-horizon dynamics of the D1-D5-brane system and are dual to string theory on AdS_3. We…
Gieseker-Nakajima moduli spaces $M_{k}(n)$ parametrize the charge $k$ noncommutative $U(n)$ instantons on ${\bf R}^{4}$ and framed rank $n$ torsion free sheaves $\mathcal{E}$ on ${\bf C\bf P}^{2}$ with ${\rm ch}_{2}({\mathcal{E}}) = k$.…
We use the recursive structure of the compactification of the instanton moduli space of N=2 Super Yang-Mills theory with gauge group SU(2), to construct, by inductive limit, a universal moduli space which includes all the multi-instanton…
We study a kaehler potential K in the large radius region of a Calabi-Yau d-fold M embedded in CP^{d+1}. It has a kaehler parameter t that describes a deformation of the A-model moduli. Also the metric, curvature and hermitian two-point…
We study generalized anti-self-dual instantons defined over Riemannian manifolds equipped with a parallel codimension-$4$ differential form. In particular, for product Riemannian manifolds possessing such a form, we study dimension…
The rank 4 locus of a general skew-symmetric 7x7 matrix gives the pfaffian variety in P^20 which is not defined as a complete intersection. Intersecting this with a general P^6 gives a Calabi-Yau manifold. An orbifold construction seems to…
In this paper, we present an application of mirror symmetry to arithmetic geometry. The main result is the computation of the period of a mixed Hodge structure, which lends evidence to its expected motivic origin. More precisely, given a…
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…
We investigate Yang--Mills instanton theory over four dimensional asymptotically locally flat (ALF) geometries, including gravitational instantons of this type, by exploiting the existence of a natural smooth compactification of these…
In this paper, we have realized the left-right symmetric model with modular symmetry. We have used $\Gamma$(3) modular group which is isomorphic to non-abelian discrete symmetry group $A_4$. The advantage of using modular symmetry is the…
We describe a simple class of type IIA string compactifications on Calabi-Yau manifolds where background fluxes generate a potential for the complex structure moduli, the dilaton, and the K\"ahler moduli. This class of models corresponds to…
We study quiver gauge theories on the round and squashed seven-spheres, and orbifolds thereof. They arise by imposing $G$-equivariance on the homogeneous space $G/H=\mathrm{SU}(4)/\mathrm{SU}(3)$ endowed with its Sasaki-Einstein structure,…
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…
The study of the geometry of Calabi-Yau fourfolds is relevant for compactifications of string theory, M-theory, and F-theory to various dimensions. In the first part of this thesis, we study the action of mirror symmetry on two-dimensional…
We survey mirror symmetry of Calabi-Yau manifolds from the perspective of families of Calabi-Yau manifolds and their period integrals. Special emphasis is laid on distinguished properties of the hypergeometric series of Gel'fand, Kapranov,…
In this paper we explore contributions to non-perturbative superpotentials arising from instantons wrapping effective divisors in smooth Calabi-Yau four-folds. We concentrate on the case of manifolds constructed as complete intersections in…