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, mirror symmetry of three-dimensional N = 1 supersymmetric gauge theories can be used to determine the theory on the world volume of a D2-brane probe of manifolds with G_2 holonomy.
Abstract: We describe how mirror symmetry of three-dimensional N=1 supersymmetric gauge theories can be used to determine the theory on the world volume of a D2-brane probe of manifolds with G_2 holonomy.
23 citations
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TL;DR: In this article, it was shown that the product of a six-manifold M × hat M is doubly fibered by supersymmetric three-tori, with both sets of fibers transverse to M and hat M, and the mirror map is then realized by T-dualizing the fibers.
Abstract: Fibrations of flux backgrounds by supersymmetric cycles are investigated. For an internal six-manifold M with static SU(2) structure and mirror hat M, it is argued that the product M × hat M is doubly fibered by supersymmetric three-tori, with both sets of fibers transverse to M and hat M. The mirror map is then realized by T-dualizing the fibers. Mirror-symmetric properties of the fluxes, both geometric and non-geometric, are shown to agree with previous conjectures based on the requirement of mirror symmetry for Killing prepotentials. The fibers are conjectured to be destabilized by fluxes on generic SU(3) × SU(3) backgrounds, though they may survive at type-jumping points. T-dualizing the surviving fibers ensures the exchange of pure spinors under mirror symmetry.
23 citations
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TL;DR: Using natural patterns to measure salience of symmetry in diverse contexts produces new insights into symmetry perception and its possible neural circuits, and reveals why perceptual symmetry can differ from mathematical characterizations.
Abstract: Symmetry is a biologically relevant, mathematically involving, and aesthetically compelling visual phenomenon. Mirror symmetry detection is considered particularly rapid and efficient, based on experiments with random noise. Symmetry detection in natural settings, however, is often accomplished against structured backgrounds. To measure salience of symmetry in diverse contexts, we assembled mirror symmetric patterns from 101 natural textures. Temporal thresholds for detecting the symmetry axis ranged from 28 to 568 ms indicating a wide range of salience (1/Threshold). We built a model for estimating symmetry-energy by connecting pairs of mirror-symmetric filters that simulated cortical receptive fields. The model easily identified the axis of symmetry for all patterns. However, symmetry-energy quantified at this axis correlated weakly with salience. To examine context effects on symmetry detection, we used the same model to estimate approximate symmetry resulting from the underlying texture throughout the image. Magnitudes of approximate symmetry at flanking and orthogonal axes showed strong negative correlations with salience, revealing context interference with symmetry detection. A regression model that included the context-based measures explained the salience results, and revealed why perceptual symmetry can differ from mathematical characterizations. Using natural patterns thus produces new insights into symmetry perception and its possible neural circuits.
23 citations
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TL;DR: Here it is found that a J π = 5/2 − spin assignment is needed to explain the proton-emission pattern observed from the T Â= 3/2 isobaric-analogue state in rubidium-73, which is identical to the ground state of strontium-73.
Abstract: Conservation laws are deeply related to any symmetry present in a physical system1,2. Analogously to electrons in atoms exhibiting spin symmetries3, it is possible to consider neutrons and protons in the atomic nucleus as projections of a single fermion with an isobaric spin (isospin) of t = 1/2 (ref. 4). Every nuclear state is thus characterized by a total isobaric spin T and a projection Tz—two quantities that are largely conserved in nuclear reactions and decays5,6. A mirror symmetry emerges from this isobaric-spin formalism: nuclei with exchanged numbers of neutrons and protons, known as mirror nuclei, should have an identical set of states7, including their ground state, labelled by their total angular momentum J and parity π. Here we report evidence of mirror-symmetry violation in bound nuclear ground states within the mirror partners strontium-73 and bromine-73. We find that a J π = 5/2− spin assignment is needed to explain the proton-emission pattern observed from the T = 3/2 isobaric-analogue state in rubidium-73, which is identical to the ground state of strontium-73. Therefore the ground state of strontium-73 must differ from its J π = 1/2− mirror bromine-73. This observation offers insights into charge-symmetry-breaking forces acting in atomic nuclei. Observations of the decay of 73Sr, when compared to its mirror nucleus 73Br, indicate that the spin assignment of their ground states differ, demonstrating mirror-symmetry violation.
23 citations