Speaker
Niels Obers
(NBI)
Description
Newton-Cartan geometry was introduced more than 90 years
ago in order to find a geometric formulation of Newtonian
gravity. I recent years, this geometry (including a novel
generalisation that includes torsion) has made its appearance
in holography for systems with non-relativistic symmetry and
been studied in parallel directly in a non-relativistic field
theory context. I will give an introduction to Newton-Cartan
(NC) geometry and its torsional version (TNC), and show how
this appears as a boundary geometry in the context of
holography for bulk Lifshitz spacetimes. The coupling of field
theories to TNC geometry will be discussed and I will exhibit
how dynamical NC geometry leads to a covariant formulation
of the known versions of Horava-Lifshitz gravity. The latter
may also be used as bulk theories in a holographic context,
which will be illustrated via a novel formulation of 3D Horava-
Lifsthiz gravity, providing a new way to implement a non-
relativistic gravity/field theory correspondence. Finally,
I will
outline a connection with flat space holography, which
features Carollian geometry
on the boundary. To conclude, I will summarize some open
problems and mention progress in related directions.
