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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 parity-time symmetry in matching electric permittivity to magnetic permeability can be established by considering an effective parity operator involving both mirror symmetry and coupling between electric and magnetic fields.
Abstract: We show that parity-time symmetry in matching electric permittivity to magnetic permeability can be established by considering an effective parity operator involving both mirror symmetry and coupling between electric and magnetic fields. This approach extends the discussion of parity-time symmetry to the situation with more than one material potential. We show that the band structure of a one-dimensional photonic crystal with alternating purely dielectric and purely magnetic slabs can undergo a phase transition between propagation modes and evanescent modes when the balanced gain or loss parameter is varied. The cross matching between different material potentials also allows exceptional points of the constitutive matrix to appear in the long-wavelength limit where they can be used to construct ultrathin metamaterials with unidirectional reflection.
56 citations
TL;DR: In this article, the geometric Langlands correspondence has been interpreted as the mirror symmetry of the Hitchin fibrations for two dual reductive groups, and it has been shown that these mirror symmetry reduces to T -duality on the generic Hitchin fibers, which are smooth tori.
Abstract: The geometric Langlands correspondence has been interpreted as the mirror symmetry of the Hitchin fibrations for two dual reductive groups. This mirror symmetry, in turn, reduces to T -duality on the generic Hitchin fibers, which are smooth tori. In this paper, we study what happens when the Hitchin fibers on the B-model side develop orbifold singularities. These singularities correspond to local systems with finite groups of automorphisms. In the classical Langlands program, local systems of this type are called endoscopic. They play an important role in the theory of automorphic representations, in particular, in the stabilization of the trace formula. Our goal is to use the mirror symmetry of the Hitchin fibrations to expose the special role played by these local systems in the geometric theory. The study of the categories of A-branes on the dual Hitchin fibers allows us to uncover some interesting phenomena associated with the endoscopy in the geometric Langlands correspondence. We then follow our predictions back to the classical theory of automorphic functions. This enables us to test and confirm them. The geometry we use is similar to that which is exploited in recent work by Ngo, a fact which could be significant for understanding the trace formula.
56 citations
TL;DR: Grana et al. as mentioned in this paper showed that the supersymmetry transformations for type II string theories on six-manifolds can be written as differential conditions on a pair of pure spinors, the exponentiated Kahler form e i J and the holomorphic form Ω.
56 citations
TL;DR: In this article, the authors demonstrate a unique valley-like phononic crystal with position-varying Dirac cones at the high-symmetry lines of the Brillouin zone boundary.
Abstract: In condensed matter physics, topologically protected edge transportation has drawn extensive attention over recent years. Thus far, the topological valley edge states have been produced near the Dirac cones fixed at the high-symmetry points of the Brillouin zone. In this paper, we demonstrate a unique valleylike phononic crystal (PnC) with the position-varying Dirac cones at the high-symmetry lines of the Brillouin zone boundary. The emergence of such Dirac cones, characterized by the vortex structure in a momentum space, is attributed to the unavoidable band crossing protected by the mirror symmetry. The Dirac cones can be unbuckled and a complete band gap can be induced through breaking the mirror symmetry. Interestingly, by simply rotating the square columns, we realize the valleylike vortex states and the band inversion effect which leads to the valley Hall phase transition. Along the valleylike PnC interfaces separating two distinct acoustic valley Hall phases, the valleylike protected edge transport of sound in domain walls is observed in both the simulations and the experiments. These results are promising for the exploration of alternative topological phenomena in the valleylike PnCs beyond the graphenelike lattice.
55 citations
TL;DR: In this paper, the homological mirror conjecture for toric del Pezzo surfaces was shown to coincide with the derived Fukaya category of coherent sheaves on the original manifold, where the mirror object is a regular function on an algebraic torus.
Abstract: We prove the homological mirror conjecture for toric del Pezzo surfaces. In this case, the mirror object is a regular function on an algebraic torus Open image in new window We show that the derived Fukaya category of this mirror coincides with the derived category of coherent sheaves on the original manifold.
55 citations