(Non)-integrability of geodesics in D-brane backgrounds
Yuri Chervonyi,Oleg Lunin +1 more
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In this paper, it was shown that the Hamilton-Jacobi equation for massless geodesics can only separate in elliptic or spherical coordinates, and all known integrable backgrounds are covered by this separation.Abstract:
Motivated by the search for new backgrounds with integrable string theories, we classify the D-brane geometries leading to integrable geodesics. Our analysis demonstrates that the Hamilton-Jacobi equation for massless geodesics can only separate in elliptic or spherical coordinates, and all known integrable backgrounds are covered by this separation. In particular, we identify the standard parameterization of AdSp × Sq with elliptic coordinates on a flat base. We also find new geometries admitting separation of the Hamilton-Jacobi equation in the elliptic coordinates. Since separability of this equation is a necessary condition for integrability of strings, our analysis gives severe restrictions on the potential candidates for integrable string theories.read more
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Electrodynamics Of Continuous Media
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Superisometries and integrability of superstrings
TL;DR: In this paper, a Lax connection for supergravity backgrounds with superisometries was constructed up to fourth order in Θ for the superstring in AdS 2 and AdS 3 backgrounds with a D(2, 1; α) isometry group.
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Integrability and Black-Hole Microstate Geometries
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On marginal deformations and non-integrability
TL;DR: In this paper, the authors study the interplay between a particular marginal deformation of the super Yang-Mills theory, the β deformation, and integrability in the holographic setting and find that, when the β parameter takes imaginary values, classical string trajectories on the dual background become non-integrable.
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TL;DR: In this article, the propagation of electromagnetic waves and X-ray diffraction of X rays in crystals are discussed. But they do not consider the effects of superconductivity on superconducting conductors.
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