Theoretical Physics Wednesday Seminar: Claire Zukowski

Kinematic Space and the Orbit Method

Coadjoint orbits are symplectic manifolds that are the classical analogues of a Lie group’s unitary irreducible representations. In this talk I will argue that the space of Ryu-Takayanagi surfaces in anti de Sitter spacetime, known as kinematic space, is a particular coadjoint orbit of the conformal group. In addition, I will show that the Crofton form on kinematic space, that was shown to compute the lengths of bulk curves, is equal to the standard Kirillov-Kostant symplectic form on the coadjoint orbit. Since kinematic space is Kähler in addition to symplectic, it can be quantized. The orbit method then translates geometrical properties of holographic auxiliary spaces like kinematic space into statements about the representation theory of the conformal group. This is a new application of the orbit method to holography that extends the kinematic space dictionary and suggests generalizations as well as obstructions for kinematic space.