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, a mirror symmetry theorem for non-convex Gromov-Witten potentials was proved for a family of potentials named after Fan, Jarvis, Ruan, and Witten's quantum singularity theory.
Abstract: We provide a mirror symmetry theorem in a range of cases where the state-of-the-art techniques relying on concavity or convexity do not apply. More specifically, we work on a family of FJRW potentials named after Fan, Jarvis, Ruan, and Witten's quantum singularity theory and viewed as the counterpart of a non-convex Gromov--Witten potential via the physical LG/CY correspondence. The main result provides an explicit formula for Polishchuk and Vaintrob's virtual cycle in genus zero. In the non-concave case of the so-called chain invertible polynomials, it yields a compatibility theorem with the FJRW virtual cycle and a proof of mirror symmetry for FJRW theory.
32 citations
32 citations
TL;DR: The data support the suggestion that extra axes add ‘goodness’ to symmetrical patterns but not in a monotonic fashion.
Abstract: It has been postulated that as the number of axes of symmetry in a pattern increases, so pattern ‘goodness’ increases. Recently, a distinction was made between two different theoretical accounts of regularity or ‘goodness’ in relation to patterns with mirror symmetry: the ‘transformational’ and the ‘holographic’ models. It was argued that the former predicts a ‘goodness’ ordering of four > three > two > one whereas the latter predicts four > two > three > one, where ‘>’ means greater regularity or goodness. In three experiments, we have tested these predictions. In experiment 1, we measured percentage correct and reaction time to dot patterns which had one, two, three, or four axes of symmetry and were flashed for 150 ms. Experiment 2 was identical except that patterns were presented for 2000 ms. In experiment 3, dot patterns were replaced by solid shapes which also had one, two, three, or four axes of symmetry. Although it was found that stimuli with four axes clearly allowed superior performance to that...
32 citations
TL;DR: In this article, the authors consider various proposed manifestations of mirror matter in our solar system examining in particular how the physics changes for different possible values of the free parameter ϵ and find new evidence for mirror matter coming from the observed sharp reduction in crater rates (for craters less than about 100 m in diameter) on the asteroid 433 Eros.
31 citations
TL;DR: In this article, the authors construct a class of symplectic non-Kaehler and complex non-kaehler string theory vacua, extending and providing evidence for an earlier suggestion by Polchinski and Strominger.
Abstract: We construct a class of symplectic non-Kaehler and complex non-Kaehler string theory vacua, extending and providing evidence for an earlier suggestion by Polchinski and Strominger. The class admits a mirror pairing by construction. Comparing hints from a variety of sources, including ten-dimensional supergravity and KK reduction on SU(3)-structure manifolds, suggests a picture in which string theory extends Reid's fantasy to connect classes of both complex non-Kaehler and symplectic non-Kaehler manifolds.
31 citations