Carroll covariant scalar fields in two dimensions

TL;DR

This paper explores three inequivalent free massless Carroll scalar field theories in two dimensions, revealing unique symmetry properties and potential applications to flat holography and tensionless strings.

Contribution

It introduces a new mixed-derivative Carroll scalar field action with distinct symmetry features, expanding the understanding of Carrollian field theories in 2D.

Findings

All three theories exhibit off-shell BMS invariance.

The mixed-derivative theory's on-shell symmetry reduces to a Virasoro algebra.

Potential relevance to tensionless strings and flat holography.

Abstract

Conformal Carroll symmetry generically arises on null manifolds and is important for holography of asymptotically flat spacetimes, generic black hole horizons and tensionless strings. In this paper, we focus on two dimensional (2d) null manifolds and hence on the 2d Conformal Carroll or equivalently the 3d Bondi-Metzner-Sachs (BMS) algebra. Using Carroll covariance, we write the most general free massless Carroll scalar field theory and discover three inequivalent actions. Of these, two viz. the time-like and space-like actions, have made their appearance in literature before. We uncover a third that we call the mixed-derivative theory. As expected, all three theories enjoy off-shell BMS invariance. Interestingly, we find that the on-shell symmetry of mixed derivative theory is a single Virasoro algebra instead of the full BMS. We discuss potential applications to tensionless strings and flat holography.