Related papers: JKLMR conjecture and Batyrev construction
Mirror symmetry has proven to be a powerful tool to study several properties of higher dimensional superconformal field theories upon compactification to three dimensions. We propose a quiver description for the mirror theories of the…
The Gamma-series of Gel'fand-Kapranov-Zelevinsky are adapted so that they give solutions for certain resonant systems of GKZ hypergeometric differential equations. For this some complex parameters in the Gamma-series are replaced by…
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…
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…
In the SYZ program, the mirror of $Y$ is the moduli space of Lagrangian branes in $Y$. When $Y$ is equipped with a Hamiltonian $G$-action, we prove that its mirror determines a canonical complex Lagrangian subvariety in the Coulomb branch…
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…
The connections amongst (1) quivers whose representation varieties are Calabi-Yau, (2) the combinatorics of bipartite graphs on Riemann surfaces, and (3) the geometry of mirror symmetry have engendered a rich subject at whose heart is the…
N = 2 supersymmetry in four space-time dimensions is intimately related to hyperkahler and quaternionic Kahler geometries. On one hand, the target spaces for rigid supersymmetric sigma-models are necessarily hyperkahler manifolds. On the…
We prove equivalences of derived categories for the various mirrors in the Batyrev-Borisov construction. In particular, we obtain a positive answer to a conjecture of Batyrev and Nill. The proof involves passing to an associated category of…
We propose and prove a mirror theorem for the elliptic quasimap invariants for smooth Calabi-Yau complete intersections in projective spaces. The theorem combined with the wall-crossing formula appeared in paper (arXiv:1308.6377) implies…
The disk partition function of certain 3d N=2 supersymmetric gauge theories computes a quantum K-theoretic ring for Kahler manifolds X. We study the 3d gauge theory/quantum K-theory correspondence for global and local Calabi-Yau manifolds…
The $tt^*$ equations define a flat connection on the moduli spaces of $2d, \mathcal{N}=2$ quantum field theories. For conformal theories with $c=3d$, which can be realized as nonlinear sigma models into Calabi-Yau d-folds, this flat…
In mirror symmetry, after the work by J. Walcher, the number of holomorphic disks with boundary on the real quintic lagrangian in a general quintic threefold is related to the periods of the mirror quintic family with boundary on two…
We prove homological mirror symmetry for the quintic Calabi-Yau 3-fold. The proof follows that for the quartic surface by Seidel (arXiv:math/0310414) closely, and uses a result of Sheridan (arXiv:1012.3238). In contrast to Sheridan's…
This contribution to the 2015 AMS Summer Institute in Algebraic Geometry (Salt Lake City) announces a general mirror construction. This construction applies to log Calabi-Yau pairs (X,D) with maximal boundary D or to maximally unipotent…
We develop techniques for obtaining the mirror of Calabi-Yau supermanifolds as super-Landau-Ginzburg theories. In some cases the dual can be equivalent to a geometry. We apply this to some examples. In particular we show that the mirror of…
In this paper, we revisit the A-twisted gauged linear sigma models (GLSMs) whose geometric phases are complex K\"ahler supermanifolds. For abelian models without superpotentials we propose an explicit orbifold description of the…
We present a method based on mutations of helices which leads to the construction (in the large volume limit) of exceptional coherent sheaves associated with the $(\sum_al_a=0)$ orbits in Gepner models. This is explicitly verified for a few…
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…
In this paper, we verify a part of the Mirror Symmetry Conjecture for Schoen's Calabi-Yau 3-fold, which is a special complete intersection in a toric variety. We calculate a part of the prepotential of the A-model Yukawa couplings of the…