Mirror symmetry

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

Electrically Tunable Conductance and Edge Modes in Topological Crystalline Insulator Thin Films: Tight-Binding Model Analysis

Abstract: We propose a minimal tight-binding model for thin films made of topological crystalline insulator (TCI) on the basis of the mirror and discrete rotational symmetries. The basic term consists of the spin-orbit interaction describing a Weyl semimetal, where gapless Dirac cones emerge at all the high symmetry points in the momentum space. We then introduce the mass term providing gaps to Dirac cones at our disposal. They simulate the thin films made of the [001], [111] and [110] TCI surfaces. TCI thin films are topological insulators protected by the mirror symmetry. We analyze the mirror-Chern number, the edge modes and the conductance by breaking the mirror symmetry with the use of electric field. We propose a multi-digit topological field-effect transistor by applying electric field independently to the right and left edges of a nanoribbon. Our results will open a new way to topological electronics.

Mirror symmetry and tropical geometry

Abstract: Using tropical geometry we propose a mirror construction for monomial degenerations of Calabi-Yau varieties in toric Fano varieties. The construction reproduces the mirror constructions by Batyrev for Calabi-Yau hypersurfaces and by Batyrev and Borisov for Calabi-Yau complete intersections. We apply the construction to Pfaffian examples and recover the mirror given by Rodland for the degree 14 Calabi-Yau threefold in PP^6 defined by the Pfaffians of a general linear 7x7 skew-symmetric matrix. We provide the necessary background knowledge entering into the tropical mirror construction such as toric geometry, Groebner bases, tropical geometry, Hilbert schemes and deformations. The tropical approach yields an algorithm which we illustrate in a series of explicit examples.

Geometric Engineering of Quantum Field Theories

Abstract: Using the recent advances in our understanding of non-perturbative aspects of type II strings we show how non-trivial exact results for $N=2$ quantum field theories can be reduced to T-dualities of string theory. This is done by constructing a local geometric realization of quantum field theories together with a local application of mirror symmetry. This construction is not based on any duality conjecture and thus reduces non-trivial quantum field theory results to much better understood T-dualities of type II strings. Moreover it can be used in principle to construct in a systematic way the vacuum structure for arbitrary $N=2$ gauge theories with matter representations.

Mirror symmetry and deformation quantization

Abstract: In homological mirror symmetry (see [Ko1]) and in the theory of D-modulesone meets similar objects. They are pairs (L,ρ) where L is a Lagrangianmanifold, and ρ is a flat bundle on L (local system). In the framework ofhomological mirror symmetry such pairs are objects of the so-called Fukayacategory, which is the principal mathematical structure of the genus zeropart of the A-model. In the framework of D-modules they are holonomic D-modules (in C