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(Non)-Integrability of Geodesics in D-brane Backgrounds

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arxiv 1311.1521 v2 pith:64IVTGCD submitted 2013-11-06 hep-th

Yuri Chervonyi , Oleg Lunin This is my paper · ORCID
classification hep-th
keywords integrablebackgroundscoordinatesellipticequationgeodesicsanalysisd-brane
verification ladder T0 review T1 audit T2 compute T3 formal
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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 AdS_p X S^q 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.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Berry Picking: Random Wave Chaos Hierarchy for BPS Microstate Geometries

    hep-th 2026-07 conditional novelty 6.0 of 10

    Wave chaos in BPS microstate geometries strengthens toward black-hole-like throats while geodesic chaos weakens, and weak-coupling CFT Renyi entropies do not share that bulk hierarchy.

  2. Cogito, ergo - strings: Supersymmetric ergoregions and their stringy excitations

    hep-th 2025-08 unverdicted novelty 6.0 of 10

    Supersymmetric ergoregions without horizons in NS5-F1-P bound states are shown to admit negative-energy BPS excitations, described via gauged WZW models and mapped holographically to the dual CFT.

  3. Evidence for a $4$-dimensional $\mathcal{N}=1$ integrable quiver in massive type IIA

    hep-th 2024-12 conditional novelty 6.0 of 10

    Only the sinusoidal quiver α(z)=A sin(ωz) in the new massive type IIA AdS5 family shows no chaotic signatures, providing suggestive evidence for its classical integrability.

  4. Brane Symmetries Revisited: Symmetries of Tensile and Tensionless Branes in Possibly Degenerate Metrics and their Manifestations

    hep-th 2025-12 conditional novelty 5.0 of 10

    Tensionless p-branes and branes in degenerate-metric spacetimes admit symmetry transformations built from Killing tensors of arbitrary rank, extending string W-symmetries to all brane dimensions.

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