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Carroll covariant scalar fields in two dimensions

Arjun Bagchi, Aritra Banerjee, Sudipta Dutta, Kedar S. Kolekar, Punit Sharma

TL;DR

This paper investigates 2d Carrollian (Conformal Carroll) field theories living on null surfaces, showing three inequivalent Carroll-covariant free massless scalar actions—timelike, spacelike, and a novel mixed-derivative form. All three actions are off-shell invariant under the BMS3 algebra, while the mixed-derivative action exhibits an on-shell enhancement to a single Virasoro algebra, highlighting a chiral structure reminiscent of tensionless string theories. The authors develop Carroll covariant, zweibein-based formulations, analyze residual symmetries, compute stress tensors, and connect these results to flatspace holography and potential dualities with flat-space chiral gravity, as well as to ILST-type null-string formalisms. The work clarifies how gauge choices for unfixed background data like e^t_1 affect symmetries and suggests promising directions for higher-dimensional extensions, quantization, and holographic interpretations of Carrollian field theories.

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.

Carroll covariant scalar fields in two dimensions

TL;DR

This paper investigates 2d Carrollian (Conformal Carroll) field theories living on null surfaces, showing three inequivalent Carroll-covariant free massless scalar actions—timelike, spacelike, and a novel mixed-derivative form. All three actions are off-shell invariant under the BMS3 algebra, while the mixed-derivative action exhibits an on-shell enhancement to a single Virasoro algebra, highlighting a chiral structure reminiscent of tensionless string theories. The authors develop Carroll covariant, zweibein-based formulations, analyze residual symmetries, compute stress tensors, and connect these results to flatspace holography and potential dualities with flat-space chiral gravity, as well as to ILST-type null-string formalisms. The work clarifies how gauge choices for unfixed background data like e^t_1 affect symmetries and suggests promising directions for higher-dimensional extensions, quantization, and holographic interpretations of Carrollian field theories.

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.
Paper Structure (31 sections, 224 equations, 1 figure)

This paper contains 31 sections, 224 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Carroll and Asymptotically Flat Spacetime
  3. Flatspace Holography
  4. Horizons, Carroll strings and other things
  5. What is in this paper?
  6. Carroll spacetime in $(d+1)$ dimesions
  7. Flat Carroll spacetime in generic dimensions
  8. Carroll spacetime in two dimensions
  9. Flat Carroll manifold in $2d$
  10. BMS invariant actions for a $2d$ scalar field
  11. BMS invariance on flat Carroll background
  12. Invariance under tangent space transformations
  13. Comments on fixing $e^t_1$
  14. Stress tensors
  15. Warming up: Residual symmetries of the timelike action
  16. ...and 16 more sections

Figures (1)

  • Figure 1: Collapsing of the lightcone towards the Schwarzschild horizon.