Mirror symmetry

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

Mirror symmetry for open strings

Abstract: The authors discuss the generation of superpotentials in d = 4, N = 1 supersymmetric field theories arising from type IIA D6-branes wrapped on supersymmetric three-cycles of a Calabi-Yau threefold. In general, nontrivial superpotentials arise from sums over disc instantons. They then find several examples of special Lagrangian three-cycles with nontrivial topology which are mirror to obstructed rational curves, conclusively demonstrating the existence of such instanton effects. In addition, they present explicit examples of disc instantons ending on the relevant three-cycles. Finally, they give a preliminary construction of a mirror map for the open string moduli, in a large-radius limit of the type IIA compactification.

S-Duality of Boundary Conditions In N=4 Super Yang-Mills Theory

Abstract: By analyzing brane configurations in detail, and extracting general lessons, we develop methods for analyzing S-duality of supersymmetric boundary conditions in N=4 super Yang-Mills theory. In the process, we find that S-duality of boundary conditions is closely related to mirror symmetry of three-dimensional gauge theories, and we analyze the IR behavior of large classes of quiver gauge theories.

Gkz-generalized hypergeometric systems in mirror symmetry of calabi-yau hypersurfaces

Abstract: We present a detailed study of the generalized hypergeometric system introduced by Gel'fand, Kapranov and Zelevinski (GKZ-hypergeometric system) in the context of toric geometry. GKZ systems arise naturally in the moduli theory of Calabi-Yau toric varieties, and play an important role in applications of the mirror symmetry. We find that the Grobner basis for the so-called toric ideal determines a finite set of differential operators for the local solutions of the GKZ system. At the special point called the large radius limit, we find a close relationship between the principal parts of the operators in the GKZ system and the intersection ring of a toric variety. As applications, we analyze general three dimensional hypersurfaces of Fermat and non-Fermat types with Hodge numbers up toh 1,1=3. We also find and analyze several non-Landau-Ginzburg models which are related to singular models.

Topological mirror symmetry

Abstract: This paper focuses on a topological version on the Strominger-Yau-Zaslow mirror symmetry conjecture. Roughly put, the SYZ conjecture suggests that mirror pairs of Calabi-Yau manifolds are related by the existence of dual special Lagrangian torus fibrations. We explore this conjecture without reference to the special Lagrangian condition. In this setting, natural questions include: does there exist a nice class of T^3-fibrations for which the dual fibration can be constructed? Do such fibrations exist on a manifold such as the quintic threefold? If so, is the dual fibration the mirror? We answer these questions affirmatively. We introduce a class of topological T^3-fibrations for which duals can be constructed, including over the singular fibres. We then construct such a fibration on the quintic threefold, and show that by applying this general dualizing construction to this particular case, one obtains the mirror quintic. Thus we have constructed the mirror quintic topologically with no a priori knowledge of the mirror. This shows that in a non-degenerate (and representative) case, the Strominger-Yau-Zaslow conjecture correctly explains mirror symmetry.

Geometric engineering, mirror symmetry and $ 6{\mathrm{d}}_{\left(1,0\right)}\to 4{\mathrm{d}}_{\left(\mathcal{N}=2\right)} $

Abstract: We study compactification of 6 dimensional (1,0) theories on T 2. We use geometric engineering of these theories via F-theory and employ mirror symmetry technology to solve for the effective 4d $$ \mathcal{N}=2 $$ geometry for a large number of the (1,0) theories including those associated with conformal matter. Using this we show that for a given 6d theory we can obtain many inequivalent 4d $$ \mathcal{N}=2 $$ SCFTs. Some of these respect the global symmetries of the 6d theory while others exhibit SL(2, ℤ) duality symmetry inherited from global diffeomorphisms of the T 2. This construction also explains the 6d origin of moduli space of 4d affine ADE quiver theories as flat ADE connections on T 2. Among the resulting 4d $$ \mathcal{N}=2 $$ CFTs we find theories whose vacuum geometry is captured by an LG theory (as opposed to a curve or a local CY geometry). We obtain arbitrary genus curves of class $$ \mathcal{S} $$ with punctures from toroidal compactification of (1, 0) SCFTs where the curve of the class $$ \mathcal{S} $$ theory emerges through mirror symmetry. We also show that toroidal compactification of the little string version of these theories can lead to class $$ \mathcal{S} $$ theories with no punctures on arbitrary genus Riemann surface.