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

TL;DR

This thesis explores Chern-Simons theories with Lie algebra contractions and extensions, analyzing boundary conditions and asymptotic symmetries for various spacetimes, advancing understanding of higher spin gravity beyond AdS.

Contribution

It introduces a new contraction method preserving the invariant metric and applies it to boundary conditions and asymptotic symmetries in higher spin theories beyond AdS.

Findings

Contractions lead to kinematical algebras like Poincaré, Galilei, Carroll.

Invariant metric remains nondegenerate in ultra-relativistic limits.

Asymptotic symmetries suggest dual theories for Lifshitz, null-warped, and Carroll spacetimes.

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.