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 article, the effect of strain-induced gauge fields on statistical distribution of energy levels of triangular graphene nanoflakes with zigzag edges was investigated and the corresponding transitions to quantum chaos were rationalized by means of additive random-matrix models.
Abstract: We investigate the effect of strain-induced gauge fields on statistical distribution of energy levels of triangular graphene nanoflakes with zigzag edges. In the absence of strain fields but in the presence of weak potential disorder such systems were found by Rycerz [Phys. Rev. B 85, 245424 (2012)] to display the spectral statistics of the Gaussian unitary ensemble (GUE) due to the effective time-reversal (symplectic) symmetry breaking. Here we show that in the absence of disorder, strain fields may solely lead to spectral fluctuations of GUE providing a nanoflake is deformed such that all its geometric symmetries are broken. In a particular case when a single mirror symmetry is preserved the spectral statistics follow the Gaussian orthogonal ensemble (GOE) rather then GUE. The corresponding transitions to quantum chaos are rationalized by means of additive random-matrix models and the analogy between strain-induced gauge fields and real magnetic fields is discussed.
22 citations
TL;DR: A brief survey of recent advances and open problems in the field of singular geometry and Higgs bundles can be found in this paper, with no intention of being a complete review of the whole subject.
Abstract: This brief survey aims to set the stage and summarize some of the ideas under discussion at the Workshop on Singular Geometry and Higgs Bundles in String Theory, to be held at the American Institute of Mathematics from October 30th to November 3rd, 2017. One of the most interesting aspects of the duality revolution in string theory is the understanding that gauge fields and matter representations can be described by intersection of branes. Since gauge theory is at the heart of our description of physical interactions, it has opened the door to the geometric engineering of many physical systems, and in particular those involving Higgs bundles. This note presents a curated overview of some current advances and open problems in the area, with no intention of being a complete review of the whole subject.
22 citations
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TL;DR: In this paper, the Landau-Ginzburg/Calabi-Yau correspondence for the quintic threefold can be cast into a global mirror symmetry framework, and an analogue conjectural picture featuring all CalabiYau hypersurfaces within weighted projective spaces and certain quotients by finite abelian group actions is provided.
Abstract: We show how the Landau-Ginzburg/Calabi-Yau correspondence for the quintic three-fold can be cast into a global mirror symmetry framework. Then we draw inspiration from Berglund-Hubsch mirror duality construction to provide an analogue conjectural picture featuring all Calabi-Yau hypersurfaces within weighted projective spaces and certain quotients by finite abelian group actions.
22 citations
TL;DR: In this paper, numerical and experimental results of acoustic transmission spectra of bead chains with symmetric and asymmetric Fibonacci-like structures were reported, and a good agreement was observed between the theoretical predictions and the experimental power spectra.
Abstract: This paper reports on numerical and experimental results of acoustic transmission spectra of bead chains with symmetric and asymmetric Fibonacci-like structures. As a matter of comparison, perfect periodic acoustic waveguide structures are also examined. This study shows that Fibonacci structures with mirror symmetry can exhibit localized modes with higher amplitude, due to resonant transmission induced by the presence of dimers inside the 1D structure. A good agreement is observed between the theoretical predictions and the experimental power spectra.
21 citations
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TL;DR: In this article, a two-parameter family of symmetry reductions of the Toda lattice hierarchy is introduced, which are characterized by a rational factorization of the Lax operator into a product of an upper diagonal and the inverse of a lower diagonal formal difference operator.
Abstract: We introduce and study a two-parameter family of symmetry reductions of the two-dimensional Toda lattice hierarchy, which are characterized by a rational factorization of the Lax operator into a product of an upper diagonal and the inverse of a lower diagonal formal difference operator. They subsume and generalize several classical 1 + 1 integrable hierarchies, such as the bigraded Toda hierarchy, the Ablowitz-Ladik hierarchy and E. Frenkel's q-deformed Gelfand-Dickey hierarchy. We establish their characterization in terms of block Toeplitz matrices for the associated factorization problem, and study their Hamiltonian structure. At the dispersionless level, we show how the Takasaki-Takebe classical limit gives rise to a family of non-conformal Frobenius manifolds with flat identity. We use this to generalize the relation of the Ablowitz-Ladik hierarchy to Gromov-Witten theory by proving an analogous mirror theorem for rational reductions: in particular, we show that the dual-type Frobenius manifolds we obtain are isomorphic to the equivariant quantum cohomology of a family of toric Calabi-Yau threefolds obtained from minimal resolutions of the local orbifold line.
21 citations