Carroll Geometry in Gravity, Holography and Strings

Compared to the usual non-relativistic large speed of light limit, taking the speed of light to be small may seem like a pretty obscure thing to consider. However, such an 'ultra-local' limit turns out to have a surprising amount of applications, which can be described using Carroll geometry. After briefly introducing this non-Lorentzian notion of geometry, I will apply it to gravity. There, Carroll geometry naturally appears in an ultra-local expansion of the Einstein—Hilbert action, which is related to the BLK approximation at leading order. I will also outline applications in the context of flat holography, where Carroll field theories provide an alternative approach to celestial holography. Finally, time permitting, I will briefly mention their relation to decoupling limits of string theory.