Related papers: Recent Developments in (0,2) Mirror Symmetry
We study mirror symmetry (A-side vs B-side) in the framework of quantum differential systems. We focuse on the logarithmic and non-resonant case, which describes the geometric situation. We show that quantum differential systems provide a…
We study mirror symmetry of type II strings on manifolds with the exceptional holonomy groups $G_2$ and Spin(7). Our central result is a construction of mirrors of Spin(7) manifolds realized as generalized connected sums. In parallel to…
N=(2,1) heterotic string theory provides clues about hidden structure in M-theory related to string duality; in effect it geometrizes some aspects of duality. The program whereby one may deduce this hidden structure is outlined, together…
The celebrated Mirror Theorem states that the genus zero part of the A model (quantum cohomology, rational curves counting) of the Fermat quintic threefold is equivalent to the B model (complex deformation, variation of Hodge structure) of…
These notes are aimed at mathematicians working on topics related to mirror symmetry, but are unfamiliar with the physical origins of this subject. We explain the physical concepts that enable this surprising duality to exist, using the…
We study homological mirror symmetry for $(\mathbb{P}^2, \Omega)$ viewed as an object of birational geometry, with $\Omega$ the standard meromorphic volume form. First, we construct universal objects on the two sides of mirror symmetry,…
We give some simple examples of mirror Calabi-Yau fourfolds in Type II string theory. These are realised as toroidal orbifolds. Motivated by the Strominger, Yau, Zaslow argument we give explicitly the mirror transformation which maps Type…
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…
Chiral gauge theories in two dimensions with (0,2) supersymmetry admit a much broader, and more interesting, class of vacuum solutions than their better studied (2,2) counterparts. In this thesis, we will explore some of the possibilities…
We study the worldsheet CFTs of type II strings on compact $G_2$ orbifolds obtained as quotients of a product of a Calabi-Yau threefold and a circle. For such models, we argue that the Calabi-Yau mirror map implies a mirror map for the…
Mirror symmetry is a type of infrared duality in 3D quantum field theory that relates the low-energy dynamics of two distinct ultraviolet descriptions. Though first discovered in the supersymmetric context, it has far-reaching implications…
Some aspects of Mirror symmetry are reviewed, with an emphasis on more recent results extending mirror transform to higher genus Riemann surfaces and its relation to the Kodaira-Spencer theory of gravity (talk given in the Geometry and…
We analyze global aspects of the moduli space of K\"ahler forms for $N$=(2,2) conformal $\sigma$-models. Using algebraic methods and mirror symmetry we study extensions of the mathematical notion of length (as specified by a K\"ahler…
We compute certain one-loop corrections to F^4 couplings of the heterotic string compactified on T^2, and show that they can be characterized by holomorphic prepotentials. We then discuss how some of these couplings can be obtained in…
We study (0,2) deformations of N=2 Liouville field theory and its mirror duality. A gauged linear sigma model construction of the ultraviolet theory connects (0,2) deformations of Liouville field theory and (0,2) deformations of N=2…
The most impressively prolific exploration of superstring models (aiming for our physical reality) has been focused on worldsheet-supersymmetric gauged linear sigma models and the closely associated complex-algebraic toric geometry. Mirror…
We construct a class of exactly solved (0,2) heterotic compactifications, similar to the (2,2) models constructed by Gepner. We identify these as special points in moduli spaces containing geometric limits described by non-linear sigma…
In this paper we give a proposal for mirrors to (0,2) supersymmetric gauged linear sigma models (GLSMs), for those (0,2) GLSMs which are deformations of (2,2) GLSMs. Specifically, we propose a construction of (0,2) mirrors for (0,2) GLSMs…
Active feedback between geometry and physics is woven throughout the study of Nature at its fundamental level, and is of key importance in string theory. Methods of complex algebraic geometry in particular have brought about an unrivaled…
This is a review article on mirror symmetry and aspects of it related to the theory of modular forms. We describe this topic along its historical development and connect to some more recent results toward the end. The article is for…