Carroll covariant scalar fields in two dimensions

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.

Automated summary

This paper focuses on the 2d Conformal Carroll symmetry and the 3d Bondi-Metzner-Sachs (BMS) algebra. Three different massless Carroll scalar field theories are discovered, including a newly found mixed-derivative theory. All three theories exhibit BMS invariance on-shell, but the mixed-derivative theory only has a single Virasoro algebra as its on-shell symmetry. Potential applications to tensionless strings and flat holography are discussed.