The study of physics beyond Lorentz invariance and without Lorentz (or Poincaré) symmetry and the geometry underlying these Non-Lorentzian structures have become very fashionable of late. This is primarily due to the discovery of uses of non-Lorentzian structures in various branches of physics, including condensed matter physics, hydrodynamics, cosmology and quantum gravity. A prominent example of a non-Lorentzian symmetry structure is Carrollian symmetry. This was first introduced by taking a contraction from the Poincaré group; the contraction being equivalent to taking the speed of light going to zero limit. Interestingly, any null hypersurface is a Carroll manifold. The spacetime metric becomes degenerate and because of that the best way to understand Carroll manifold is through a fibre-bundle structure where there are two distinct metrics on the base and the fibre instead of a single non-degenerate metric for the entire spacetime. Two of the most important examples of null hypersurfaces are null boundary of asymptotically flat spacetimes and the event horizon of generic black holes. 

Our proposed project is aimed at understanding large-N techniques in the context of Carrollian quantum field theories in a bid to build a specific putative dual theory to a specific theory of quantum gravity in asymptotically flat spacetimes. Following our work on fermions on Carroll background, we wish to particularly look at specific examples like Gross-Neveu model and also for Yang-Mills theory by examining the large N limit in conjunction with the Carroll limit. We will consider general Feynman diagrams labelled with vertices, edges and loops and also take into account that the Carrollian limit requires us to scale momenta in a particular way. Preliminary investigations lead us to believe that this analysis would result in the generalisation of the original large N expansion, given that we have another handle, ‘c’, in our analysis.