Carroll covariant scalar fields in two dimensions

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.

v1: 49 pages, 1 figure; v2: 51 pages, 1 figure, added more discussion on Carroll geometry in section 2, added related discussions on Carroll geometry and Carroll symmetries at few other places, typos corrected, matches version to be published

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• Symmetry group at future null infinity I: Scalar theory
• Hydro & Thermo Dynamics at Causal Boundaries, Examples in 3d Gravity
• A BMS-invariant free fermion model
• Horizon Strings as 3d Black Hole Microstates
• Symmetry group at future null infinity II: Vector theory
• Carrollian Yang-Mills Theory
• Quantization of Carrollian conformal scalar theories
• Towards Carrollian quantization: renormalization of Carrollian electrodynamics
• Classification of Conformal Carroll Algebras
• Tropological Sigma Models
• Unique Carrollian manifolds emerging from Einstein spacetimes
• Sourced Carrollian Fluids Dual to Black Hole Horizons
• On $\sqrt{T\overline{T}}$ deformed pathways: CFT to CCFT