  In this thesis, we study some aspects of a possible holographic
correspondence in two different systems: three dimensional Chern-Simons theory
and asymptotically flat space-times. In the former we use simplicial techniques
to study CS/WZW correspondence and in particular we construct the discretized
WZW partition function for SU(2) group at level 1. In the latter we outline the
main characteristics of a field theory living at null infinity invariant under
the action of the asymptotic symmetry group: the BMS group. In particular,
using fibre bundle techniques, we derive the covariant wave equations for
fields carrying BMS representations in order to investigate the nature of
boundary degrees of freedom.
