3,607 research outputs found

    Topological Invariants and Fibration Structure of Complete Intersection Calabi-Yau Four-Folds

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    We investigate the mathematical properties of the class of Calabi-Yau four-folds recently found in [arXiv:1303.1832]. This class consists of 921,497 configuration matrices which correspond to manifolds that are described as complete intersections in products of projective spaces. For each manifold in the list, we compute the full Hodge diamond as well as additional topological invariants such as Chern classes and intersection numbers. Using this data, we conclude that there are at least 36,779 topologically distinct manifolds in our list. We also study the fibration structure of these manifolds and find that 99.95 percent can be described as elliptic fibrations. In total, we find 50,114,908 elliptic fibrations, demonstrating the multitude of ways in which many manifolds are fibered. A sub-class of 26,088,498 fibrations satisfy necessary conditions for admitting sections. The complete data set can be downloaded at http://www-thphys.physics.ox.ac.uk/projects/CalabiYau/Cicy4folds/index.html .Comment: 25 pages, 7 figures, 1 table. v2: references added and minor changes. Final version accepted for publicatio

    On the Emergence of the Coulomb Forces in Quantum Electrodynamics

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    A simple transformation of field variables eliminates Coulomb forces from the theory of quantum electrodynamics. This suggests that Coulomb forces may be an emergent phenomenon rather than being fundamental. This possibility is investigated in the context of reducible quantum electrodynamics. It is shown that states exist which bind free photon and free electron fields. The binding energy peaks in the long-wavelength limit. This makes it plausible that Coulomb forces result from the interaction of the electron/positron field with long-wavelength transversely polarized photons.Comment: Presented at the 5th Winter Workshop on Non-Perturbative Quantum Field Theory, 22-24 March 2017, Sophia-Antipolis (France

    Gravity and Electromagnetism in Noncommutative Geometry

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    We present a unified description of gravity and electromagnetism in the framework of a Z2Z_2 noncommutative differential calculus. It can be considered as a ``discrete version" of Kaluza-Klein theory, where the fifth continuous dimension is replaced by two discrete points. We derive an action which coincides with the dimensionally reduced one of the ordinary Kaluza-Klein theory.Comment: 1 + 11 pages, Report # SU-4240-566, Few misprints have been correcte
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