Mirror symmetry

About: Mirror symmetry is a research topic. Over the lifetime, 2422 publications have been published within this topic receiving 90786 citations.

Hurwitz numbers, matrix models and enumerative geometry

Abstract: We propose a new, conjectural recursion solution for Hurwitz numbers at all genera. This conjecture is based on recent progress in solving type B topological string theory on the mirrors of toric Calabi-Yau manifolds, which we briefly review to provide some background for our conjecture. We show in particular how this B-model solution, combined with mirror symmetry for the one-leg, framed topological vertex, leads to a recursion relation for Hodge integrals with three Hodge class insertions. Our conjecture in Hurwitz theory follows from this recursion for the framed vertex in the limit of infinite framing.

Atomic structure of the (310) twin in niobium: Experimental determination and comparison with theoretical predictions.

Abstract: The atomic structure of the (310) twin in Nb was predicted using interatomic potentials derived from the embedded atom method (EAM), Finnis-Sinclair theory (FS), and the model generalized pseudopotential theory (MGPT). The EAM and FS predicted structures with crystal translations which break mirror symmetry. The MGPT predicted one stable structure which possessed mirror symmetry. This defect was experimentally determined to have mirror symmetry. These findings emphasize that the angular dependent interactions modeled by the MGPT are important for determining defect structures in bcc transition metals.

The N=2 wonderland : from Calabi-Yau manifolds to topological field-theories

Abstract: An introduction to the subject supergravity and Kahler geometry Calabi-Yau manifolds N=2 field theories in two dimensions Gepner tensor products moduli spaces and special geometry topological field theories mirror symmetry Picard-Fuchs equations monodromy and duality groups

Gauge theory and mirror symmetry

Abstract: Author(s): Teleman, C | Abstract: Outlined here is a description of equivariance in the world of 2-dimensional extended topological quantum field theories, under a topological action of compact Lie groups. In physics language, I am gauging the theories-coupling them to a principal bundle on the surface world-sheet. I describe the data needed to gauge the theory, as well as the computation of the gauged theory, the result of integrating over all bundles. The relevant theories are 'A-models', such as arise from the Gromov-Witten theory of a symplectic manifold with Hamiltonian group action, and the mathematical description starts with a group action on the generating category (the Fukaya category, in this example) which is factored through the topology of the group. Their mirror description involves holomorphic symplectic manifolds and Lagrangians related to the Langlands dual group. An application recovers the complex mirrors of flag varieties proposed by Rietsch.

Mathematical Aspects of Mirror Symmetry

Abstract: Lecture notes from 1993 Park City lectures and 1994 Trento lectures. The focus of these lectures is on giving a mathematical description of the A-model and B-model correlation functions on a Calabi--Yau manifold, and a precise mathematical conjecture relating these for a pair of mirror manifolds.