Dynamics of Carroll Strings

TL;DR

The paper analyzes Carrollian limits of relativistic extended objects by deriving the canonical Carroll string action $S_{C_s}$ through an ultrarelativistic limit, and by studying its Killing symmetries which form an infinite-dimensional algebra. It shows that the free Carroll string and Carroll $p$-branes exhibit trivial dynamics (e.g., transverse coordinates are static in convenient gauges) but possess a rich symmetry structure, including longitudinal conformal invariance and, in certain cases, infinite-dimensional transverse conformal symmetry, encoded in constraints such as $H_{hat} = -E^2 + (P^1)^2 + T^2 Xprime_i^2$ and $T_{hat} = P \,ullet\, Xprime$. The work further analyzes tensionless limits and extends the Carroll construction to $p$-branes, highlighting the universal triviality of free Carroll dynamics while outlining avenues to induce nontrivial behavior via coupling to Carroll gravity or background fields. Overall, these results provide a clear framework for Carrollian dynamics of strings and branes and establish groundwork for Carroll holography and non-AdS bulk theories, with directions toward interacting and supersymmetric Carroll objects.

Abstract

We construct the canonical action of a Carroll string doing the Carroll limit of a canonical relativistic string. We also study the Killing symmetries of the Carroll string, which close under an infinite dimensional algebra. The tensionless limit and the Carroll $p$-brane action are also discussed.