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

Understand

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.