Topic
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, a rigid analytic space M 0 ∨ over the Novikov field is constructed, which is a deformation of the semi-flat complex structure of the dual torus fibration over the smooth locus B 0 ⊂ B of π.
48 citations
TL;DR: Using toric geometry, lattice theory, and elliptic surface techniques, this paper computed the Picard lattice of certain K3 surfaces and examined the generic member of each of M Reid's list of 95 families of Gorenstein k3 surfaces which occur as hypersurfaces in weighted projective 3-spaces.
Abstract: Using toric geometry, lattice theory, and elliptic surface techniques, we compute the Picard Lattice of certain K3 surfaces In particular, we examine the generic member of each of M Reid's list of 95 families of Gorenstein K3 surfaces which occur as hypersurfaces in weighted projective 3-spaces As an application, we are able to determine whether the mirror family (in the sense of mirror symmetry for K3 surfaces) for each one is also on Reid's list
48 citations
TL;DR: In this article, an exotic monotone Lagrangian torus was constructed in CP2 using techniques motivated by mirror symmetry, and it was shown that this exotic torus is not Hamiltonian isotopic to the known Cliffordand Chekanov tori.
Abstract: We construct an exotic monotone Lagrangian torus in CP2 using techniques motivated by mirror symmetry. We show that it bounds 10 families of Maslov index 2 holomorphic discs, and it follows that this exotic torus is not Hamiltonian isotopic to the known Cliffordand Chekanov tori.
47 citations
TL;DR: In this article, the authors used 3D mirror symmetry and Type IIB S-duality to construct Abelian gauge theories corresponding to D3 branes ending on both sides of a pq-web made of many coincident N S5s intersecting one D5.
Abstract: D3 branes stretching between webs of (p,q) 5branes provide an interesting class of 3d $$ \mathcal{N} $$
= 2 theories. For generic pq-webs however the low energy field theory is not known. We use 3d mirror symmetry and Type IIB S-duality to construct Abelian gauge theories corresponding to D3 branes ending on both sides of a pq-web made of many coincident N S5’s intersecting one D5. These theories contain chiral monopole operators in the superpotential and enjoy a non trivial pattern of global symmetry enhancements. In the special case of the pq-web with one D5 and one N S5, the 3d low energy SCFT admits three dual formulations. This triality can be applied locally inside bigger quiver gauge theories. We prove our statements using partial mirror symmetry a la Kapustin-Strassler, showing the equality of the S
3
partition functions and studying the quantum chiral rings.
47 citations
Journal Article•
TL;DR: In this article, the effect of electron interactions in topological crystalline insulators (TCIs) protected by mirror symmetry was studied and a microscopic interaction Hamiltonian was constructed to gap eight flavors of Dirac fermions on the TCI surface while preserving the mirror symmetry.
Abstract: We study the effect of electron interactions in topological crystalline insulators (TCIs) protected by mirror symmetry, which are realized in the SnTe material class and host multivalley Dirac fermion surface states. We find that interactions reduce the integer classification of noninteracting TCIs in three dimensions, indexed by the mirror Chern number, to a finite group Z8. In particular, we explicitly construct a microscopic interaction Hamiltonian to gap eight flavors of Dirac fermions on the TCI surface, while preserving the mirror symmetry. Our construction builds on interacting edge states of U (1) × Z2 symmetry-protected topological phases of fermions in two dimensions, which we classify. Our work reveals a deep connection between three-dimensional topological phases protected by spatial symmetries and two-dimensional topological phases protected by internal symmetries.
47 citations