| Project Detail |
In this project, I will develop modern theoretical tools for non-Lorentzian geometry to advance our understanding of gravity and holography. Einsteins theory of general relativity describes gravity in terms of the curvature of a Lorentzian spacetime geometry. A similar geometric description of non-relativistic Newtonian gravity has been known for a long time. However, we have only recently figured out how the dynamics of such Newton-Cartan geometry can be extracted from a systematic expansion of general relativity. This gives a new and exciting approach to extracting predictions from general relativity using a geometric interpolation.
I have done fundamental work on such geometric expansions of general relativity, both in the Newton-Cartan and in the opposite Carroll limit, which similarly leads to solvable subsectors. In this project, I will develop an initial-value formulation for the resulting actions and I will show that the associated initial-value problem is well-posed, opening a path to numerical simulations. Using similar limits in string theory, I will establish new solvable sectors of string theory on negatively curved spacetime that are relevant to top-down models of the holographic correspondence.
On the other hand, in the astrophysically relevant setting of approximately flat spacetime, holography is much less understood, in part because of the null structure on its boundary. The supervisor (Prof. Marios Petropoulos) and myself have developed complementary approaches to constructing Carroll field theories on such null boundaries. Building on this, I will construct concrete dual field theory models, which will allow me to make contact with the celestial holography program of which Prof. Puhm is a world expert. The Centre de Physique Théorique at École Polytechnique is therefore the perfect place for me to unify these approaches to flat space holography and to work towards explicit constructions of top-down string theory models. |
