Carrollian Gravity from the Polyakov Action

Abstract

This Master's Thesis project originates from the expectation that the equations of motion of Carroll gravity at leading order could emerge from the context of string theory, by applying the Carroll limit to the Polyakov action and imposing scale invariance. In our primary approach, we employ vielbein formalism to expand the curvature tensor in powers of the speed of light, and isolate the leading-order contribution of the Polyakov action in Riemann normal coordinates. We show that, by demanding the vanishing of the one-loop beta function, one of the three equations of the electric theory is recovered. We further discuss a possible secondary procedure, where the Carrollian analogue of normal coordinates is presented. The work opens with a pedagogical introduction to the basics of Carroll transformations and the Carroll algebra, followed by an overview of Carroll geometry and Carroll gravity.