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Mirror symmetry
About: Mirror symmetry is a research topic. Over the lifetime, 2422 publications have been published within this topic receiving 90786 citations.
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TL;DR: In this paper, the authors studied half-BPS line operators in 3d = 4 gauge theories, focusing in particular on the algebras of local operators at their junctions.
Abstract: We study half-BPS line operators in 3d $$ \mathcal{N} $$
= 4 gauge theories, focusing in particular on the algebras of local operators at their junctions. It is known that there are two basic types of such line operators, distinguished by the SUSY subalgebras that they preserve; the two types can roughly be called “Wilson lines” and “vortex lines,” and are exchanged under 3d mirror symmetry. We describe a large class of vortex lines that can be characterized by basic algebraic data, and propose a mathematical scheme to compute the algebras of local operators at their junctions — including monopole operators — in terms of this data. The computation generalizes mathematical and physical definitions/analyses of the bulk Coulomb-branch chiral ring. We fully classify the junctions of half-BPS Wilson lines and of half-BPS vortex lines in abelian gauge theories with sufficient matter. We also test our computational scheme in a non-abelian quiver gauge theory, using a 3d-mirror-map of line operators from work of Assel and Gomis.
60 citations
TL;DR: In this article, the mirror of a hypersurface of general type (and more generally varieties of non-negative Kodaira dimension) is described as the critical locus of the zero fibre of a certain Landau-Ginzburg potential.
60 citations
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TL;DR: In this paper, Kontsevich's mirror conjecture for a quartic surface in P^3 was shown to hold for a 4-approximation of the manifold, on the other hand.
Abstract: This proves Kontsevich's mirror conjecture for (on the symplectic side) a quartic surface in P^3.
60 citations
TL;DR: In this paper, the quilt formalism of Mau-Wehrheim-Woodward was used to give a sufficient condition for a finite collection of Lagrangian submanifolds to split-generate the Fukaya category, and deduce homological mirror symmetry for the standard 4-torus.
Abstract: We use the quilt formalism of Mau-Wehrheim-Woodward to give a sufficient condition for a finite collection of Lagrangian submanifolds to split-generate the Fukaya category, and deduce homological mirror symmetry for the standard 4-torus. As an application, we study Lagrangian genus two surfaces of Maslov class zero, deriving numerical restrictions on the intersections of such a surface with linear Lagrangian 2-tori in in the 4-torus.
59 citations
TL;DR: In this paper, a Givental-style mirror theorem for toric Deligne-Mumford stacks X was proved for genus-zero Gromov-Witten invariants.
Abstract: We prove a Givental-style mirror theorem for toric Deligne–Mumford stacks X . This determines the genus-zero Gromov–Witten invariants of X in terms of an explicit hypergeometric function, called the I-function, that takes values in the Chen–Ruan orbifold cohomology of X .
59 citations