Motivated by the desire to understand the dynamics of light modes on various gravitational backgrounds, this talk summarizes recent results concerning properties of scalar, vector, and tensor excitations of black holes and integrable stringy geometries. For rotating black holes and for certain Wess-Zumino-Witten models, full separability of all dynamical equations is demonstrated, and symmetries underlying this property are uncovered. For other classes of integrable backgrounds, the energy spectra of various fields are evaluated, and the algebraic constructions of the corresponding eigenfunctions are presented. Join Zoom Meeting https://zoom.us/j/94137164225?pwd=ZTV3Z2c3aStOdk5sSFRRbkhQRUh5dz09 Meeting ID: 941 3716 4225 Passcode: 500873

Motivated by the search for new backgrounds with solvable string theories, the talk classifies the D-brane geometries leading to integrable geodesics. This analysis gives severe restrictions on the potential candidates for integrable string theories. It is demonstrated that the Hamilton-Jacobi equation for massless geodesics can only separate in elliptic or spherical coordinates, all known integrable backgrounds are covered by this separation, and new examples are constructed. The Killing and Killing-Yano tensors associated with such separation and their transformations under string dualities are also discussed.

The Tachyon-Dirac-Born-Infeld (TDBI) action captures some aspects of the dynamics of non-BPS D-branes in type II string theory. We show that it can also be used to study the classical interactions of BPS branes and antibranes. Our analysis sheds light on real time D-Dbar tachyon condensation, on the proposal that the tachyon field can be thought of as an extra spatial dimension whose role is similar to the radial direction in holography, and on Sen's open string completeness conjecture.