Chern-Simons Holography: Boundary Conditions, Contractions and Double Extensions for a Journey Beyond Anti-de Sitter

Abstract

In this thesis Chern-Simons theories based on Lie algebras with invariant metric are constructed. It is discussed how contractions lead systematically to (higher spin) kinematical algebras of, e.g., Poincar\'e, Galilei and Carroll type and how they can be extended to permit an invariant metric. A new generalization of the In\"on\"u-Wigner contractions explains why the invariant metric stays nondegenerate in the ultra-relativistic limes to the Carroll algebras. Since asymptotic symmetries give a first glance of possible dual theories consistent boundary conditions for Lifshitz and null-warped higher spins and Carroll gravity are provided. Finally, selected higher spin generalizations will be examined on the linear level.