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

Authors

Oleg Lunin, Department of Physics, University at AlbanyFollow
Yuri Chervonyi, University at Albany, State University of New YorkFollow

Document Type

Article

Publication Date

Winter 2014

DOI

10.1007/JHEP02(2014)061

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 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.

Recommended Citation

Lunin, Oleg and Chervonyi, Yuri, "(Non)-Integrability of Geodesics in D-brane Backgrounds" (2014). Physics Faculty Scholarship. 12.
https://scholarsarchive.library.albany.edu/physics_fac_scholar/12