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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: The authors investigated whether vertical mirror symmetry acts as a cue in figure-ground segregation and found that symmetric shapes were easier to detect than asymmetric ones across the different noise levels, indicating that vertical mirror symmetry is indeed used as cue in perceptual grouping.
Abstract: The goal of our study is a better understanding of the role of vertical mirror symmetry in perceptual grouping. With a simple psychophysical task and a set of controlled stimuli, we investigated whether vertical mirror symmetry acts as a cue in figure-ground segregation. We asked participants to indicate which of two sequentially presented Gabor arrays contained a visual shape. The shape was defined by a subset of Gabor elements positioned along the outline of an unfamiliar shape. By adding orientation noise to these Gabor elements, the shape percept became less salient. Across the different noise levels, symmetric shapes were easier to detect than asymmetric ones. This finding indicates that vertical mirror symmetry is indeed used as a cue in perceptual grouping.
132 citations
TL;DR: Experimental evidence of broken time-reversal symmetry for the interaction of light with an artificial nonmagnetic material is reported and has some striking resemblance with the expected features of light scattering on anyon matter.
Abstract: We report unambiguous experimental evidence of broken time-reversal symmetry for the interaction of light with an artificial nonmagnetic material. Polarized color images of planar chiral gold-on-silicon nanostructures consisting of arrays of gammadions show intriguing and unusual symmetry: structures, which are geometrically mirror images, lose their mirror symmetry in polarized light. The symmetry of images can be described only in terms of antisymmetry (black-and-white symmetry) appropriate to a time-odd process. The effect results from a transverse chiral nonlocal electromagnetic response of the structure and has some striking resemblance with the expected features of light scattering on anyon matter.
130 citations
TL;DR: In this article, the authors give a new definition of vertex algebra which includes chiral algebras as a special case, but allows for fields which are neither meromorphic nor anti-meromorphic, and show that for algebraic tori the isomorphism of N=2 SCVA's implies the equivalence of the derived categories of coherent sheaves corresponding to the tori or their noncommutative generalizations.
Abstract: A vertex algebra is an algebraic counterpart of a two-dimensional conformal field theory. We give a new definition of a vertex algebra which includes chiral algebras as a special case, but allows for fields which are neither meromorphic nor anti-meromorphic. To any complex torus equipped with a flat Kahler metric and a closed 2-form we associate an N=2 superconformal vertex algebra (N=2 SCVA) in the sense of our definition. We find a criterion for two different tori to produce isomorphic N=2 SCVA's. We show that for algebraic tori the isomorphism of N=2 SCVA's implies the equivalence of the derived categories of coherent sheaves corresponding to the tori or their noncommutative generalizations (Azumaya algebras over tori). We also find a criterion for two different tori to produce N=2 SCVA's related by a mirror morphism. If the 2-form is of type (1,1), this condition is identical to the one proposed by Golyshev, Lunts, and Orlov, who used an entirely different approach inspired by the Homological Mirror Symmetry Conjecture of Kontsevich. Our results suggest that Kontsevich's conjecture must be modified: coherent sheaves must be replaced with modules over Azumaya algebras, and the Fukaya category must be ``twisted'' by a closed 2-form. We also describe the implications of our results for BPS D-branes on Calabi-Yau manifolds.
130 citations
Posted Content•
TL;DR: In this paper, it was shown that fractional branes corresponding to rational B boundary states in a Gepner model can be seen as fractional BRs in the Landau-Ginzburg orbifold phase of the linear sigma model description.
Abstract: We argue that D-branes corresponding to rational B boundary states in a Gepner model can be understood as fractional branes in the Landau-Ginzburg orbifold phase of the linear sigma model description. Combining this idea with the generalized McKay correspondence allows us to identify these states with coherent sheaves, and to calculate their K-theory classes in the large volume limit, without needing to invoke mirror symmetry. We check this identification against the mirror symmetry results for the example of the Calabi-Yau hypersurface in $\WP^{1,1,2,2,2}$.
130 citations
TL;DR: In this paper, the authors describe the physics of the gauged linear sigma models that formally coincide with the mathematical description of toric stacks and check that physical predictions of those gauged lasso models exactly match the corresponding stacks.
Abstract: In this paper, we will discuss gauged linear sigma model descriptions of toric stacks. Toric stacks have a simple description in terms of (symplectic, GIT) C × quotients of homogeneous coordinates, in exactly the same form as toric varieties. We describe the physics of the gauged linear sigma models that formally coincide with the mathematical description of toric stacks and check that physical predictions of those gauged linear sigma models exactly match the corresponding stacks. We also see in examples that when a given toric stack has multiple presentations in a form accessible as a gauged linear sigma model, that the IR physics of those different presentations matches, so that the IR physics is presentation-independent, making it reasonable to associate CFTs to stacks, not just presentations of stacks. We discuss mirror symmetry for stacks, using Morrison– Plesser–Hori–Vafa techniques to compute mirrors explicitly, and also find a natural generalization of Batyrev’s mirror conjecture. In the process of studying mirror symmetry, we find some new abstract CFTs, involving fields valued in roots of unity.
130 citations