Conformal Carroll Scalars with Boosts

Abstract

We construct two distinct actions for scalar fields that are invariant under local Carroll boosts and Weyl transformations. Conformal Carroll field theories were recently argued to be related to the celestial holography description of asymptotically flat spacetimes. However, only few explicit examples of such theories are known, and they lack local Carroll boost symmetry on a generic curved background. We derive two types of conformal Carroll scalar actions with boost symmetry on a curved background in any dimension and compute their energy-momentum tensors, which are traceless. In the first type of theories, time derivatives dominate and spatial derivatives are suppressed. In the second type, spatial derivatives dominate, and constraints are present to ensure local boost invariance. By integrating out these constraints, we show that the spatial conformal Carroll theories can be reduced to lower-dimensional Euclidean CFTs, which is reminiscent of the embedding space construction.

arXiv comment29+6 pages, two figures; v2: minor changes, added references, v3: expanded discussion of dimensional reduction, minor changes, one reference added

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• Ehlers, Carroll, Charges and Dual Charges
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• Quantization of Carrollian conformal scalar theories
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• Chern-Simons action and the Carrollian Cotton tensors
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• Setting the connection free in the Galilei and Carroll expansions of gravity
• Carroll-Schrödinger Equation
• Fracton and Non-Lorentzian Particle Duality: Gauge Field Couplings and Geometric Implications
• Anisotropic conformal Carroll field theories and their gravity duals
• Sourced Carrollian Fluids Dual to Black Hole Horizons
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• Unique Carrollian manifolds emerging from Einstein spacetimes
• Universal sectors of two-dimensional Carrollian CFTs
• Free-field construction of Carrollian $W_N$-algebras
• Null reduction and dynamical realization of Carrollian conformal symmetries