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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 introduce the interested reader to homological mirror symmetry and tackle the simplest cases of mirror symmetry, such as curves of genus zero and one, and discuss the current state of the field and mention what homo-logical mirror symmetry has to say about other aspects of symmetry.
Abstract: In this paper, we introduce the interested reader to homological mirror symmetry After recalling a little background knowledge, we tackle the simplest cases of homological mirror symmetry: curves of genus zero and one We close by outlining the current state of the field and mentioning what homo- logical mirror symmetry has to say about other aspects of mirror symmetry
16 citations
TL;DR: A random matrix model of systems with an approximate symmetry is discussed and the spectral fluctuation statistics and eigenvector characteristics for the model are presented and it is found that this transition is well described by therandom matrix model.
Abstract: We discuss a random matrix model of systems with an approximate symmetry and present the spectral fluctuation statistics and eigenvector characteristics for the model. An acoustic resonator like, e.g., an aluminum plate may have an approximate symmetry. We have measured the frequency spectrum and the widths for acoustic resonances in thin aluminum plates, cut in the shape of the so-called three-leaf clover. Due to the mirror symmetry through the middle plane of the plate, each resonance of the plate belongs to one of two mode classes and we show how to separate the modes into these two classes using their measured widths. We compare the spectral statistics of each mode class with results for the Gaussian orthogonal ensemble. By cutting a slit of increasing depth on one face of the plate, we gradually break the mirror symmetry and study the transition that takes place as the two classes are mixed. Presenting the spectral fluctuation statistics and the distribution of widths for the resonances, we find that this transition is well described by the random matrix model.
16 citations
TL;DR: In this paper, the notion of pseudotoric structure on a symplectic manifold was introduced, which can be used to generalize the geometric quantization and mirror symmetry methods that work well in the toric case to a broader class of Fano varieties.
Abstract: We introduce the notion of a pseudotoric structure on a symplectic manifold, generalizing the notion of a toric structure. We show that such a pseudotoric structure can exist on toric and nontoric symplectic manifolds. For the toric manifolds, it describes deformations of the standard toric Lagrangian fibrations; for the nontoric ones, it gives Lagrangian fibrations with singularities that are very close to the toric fibrations. We present examples of toric manifolds with different pseudotoric structures and prove that certain nontoric manifolds (smooth complex quadrics) have such structures. In the future, introducing this new structure can be useful for generalizing the geometric quantization and mirror symmetry methods that work well in the toric case to a broader class of Fano varieties.
16 citations
21 Jan 2019
TL;DR: In this paper, a new type of multi-loop structure was found in AsRhTi that a s-NL touched robustly with a m-NL at some "nexus point" and in the meanwhile a second mNL crossed with the s-NM to form a Hopf-link.
Abstract: Node line band-touchings protected by mirror symmetry (named as m-NLs), the product of inversion and time reversal symmetry S = PT (named as s-NLs), or nonsymmorphic symmetry are nontrivial topological objects of topological semimetals in the Brillouin Zone. In this work, we screened a family of MgSrSi-type crystals using first principles calculations, and discovered that more than 70 members are node-line semimetals. A new type of multi-loop structure was found in AsRhTi that a s-NL touches robustly with a m-NL at some “nexus point”, and in the meanwhile a second m-NL crosses with the s-NL to form a Hopf-link. Unlike the previously proposed Hopf-link formed by two s-NLs or two m-NLs, a Hopf-link formed by a s-NL and a m-NL requires a minimal three-band model to characterize its essential electronic structure. The associated topological surface states on different surfaces of AsRhTi crystal were also obtained. Even more complicated and exotic multi-loop structure of NLs were predicted in AsFeNb and PNiNb. Our work may shed light on search for exotic multi-loop node-line semimetals in real materials.
16 citations
TL;DR: In this paper, the authors calculate the category of branes in the Landau-Ginzburg A-model with background M =Cn and superpotential W =z1⋯zn in the form of microlocal sheaves along a natural Lagrangian skeleton.
Abstract: We calculate the category of branes in the Landau–Ginzburg A-model with background M=Cn and superpotential W=z1⋯zn in the form of microlocal sheaves along a natural Lagrangian skeleton. Our arguments employ the framework of perverse schobers, and our results confirm expectations from mirror symmetry.
16 citations