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Carroll stories
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abstract
We study various aspects of the Carroll limit in which the speed of light is sent to zero. A large part of this paper is devoted to the quantization of Carroll field theories. We show that these exhibit infinite degeneracies in the spectrum and may suffer from non-normalizable ground states. As a consequence, partition functions of Carroll systems are ill-defined and do not lead to sensible thermodynamics. These seemingly pathological properties might actually be a virtue in the context of flat space holography. Better defined is the Carroll $\textit{regime}$, in which we consider the leading order term in an expansion around vanishing speed of light without taking the strict Carroll limit. Such an expansion may lead to sensible notions of Carroll thermodynamics. An interesting example is a gas of massless particles with an imaginary chemical potential conjugate to the momentum. In the Carroll regime we show that the partition function of such a gas leads to an equation of state with $w=-1$. As a separate story, we study aspects of Carroll gravity and couplings to Carrollian energy-momentum tensors. We discuss many examples of solutions to Carroll gravity, including wormholes, Maxwell fields, solutions with a cosmological constant, and discuss the structure of geodesics in a Carroll geometry. The coupling of matter to Carroll gravity also allows us to derive energy-momentum tensors for hypothetical Carroll fluids from expanding relativistic fluids as well as directly from hydrostatic partition functions.
Forward citations
Cited by 28 Pith papers
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The Energy-Momentum-News Complex near Future Null Infinity
A Carroll-covariant energy-momentum-news complex at future null infinity yields Ward identities that generalise the Bondi loss equations, with an anomalous Carroll boost.
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Missing Descendants in the Carrollian Conformal Family
Including the missing K0 descendant chain completes Carrollian conformal representations and produces C2>0 sectors and two-point correlators fixed only up to functions of Carrollian invariants.
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Carrollian limit of NS-NS and Heterotic Supergravity
Ultra-relativistic expansion plus dilaton scaling produces finite covariant Carrollian NS-NS and heterotic supergravity actions, with trivializable Green-Schwarz for the 1-form and finite leading Riem^{2} α' corrections.
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Stationary solutions in the small-$c$ expansion of GR
The NLO/NNLO small-c (Carroll) expansion of GR admits a rich stationary vacuum sector with rotating Lense-Thirring-type, C-metric-type, Hartle-Thorne-type, and higher-multipole solutions, going beyond the static magne...
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Scaling Symmetry and Carrollian Gravity
A single scaling-Carroll gauge-theory construction interpolates between dynamical Carroll gravity, Aristotelian gravity, and fracton gauge theories coupled to curved space.
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Tantum Gravity
A triple-scaling limit of quantum gravity keeps black hole thermodynamics finite and reproduces the Hawking temperature.
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Non-Lorentzian Supergravity and Kinematical Superalgebras
Supersymmetric extensions of extended kinematical algebras are classified via semigroup expansion, and non-degenerate Chern-Simons supergravity actions are constructed in three dimensions.
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Soft gravitons in three dimensions
Three-dimensional flat-space gravity, despite having no propagating gravitons, exhibits an infrared triangle: a soft graviton theorem, BMS3 asymptotic symmetries, and gravitational memory effects, all equivalent throu...
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Carroll fermions of arbitrary spin
Free massless fermions of arbitrary spin admit two inequivalent Carrollian (c→0) limits, electric and magnetic, derived from the Fang–Fronsdal actions, with the magnetic theory reducible to the projected relativistic ...
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A unified expansion of Einstein's gravity
A unified (s,n)-parametrized expansion of the Einstein-Hilbert action yields Galilean, Carroll, Lorentzian, and string Carroll gravity, and near-horizon black hole geometries satisfy the string Carroll equations.
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Carroll supergravities
Electric and magnetic Carrollian limits of N=1, D=4 supergravity are obtained by Hamiltonian contraction, yielding ultralocal electric and gradient-retaining magnetic theories with simplified constraint algebras.
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BMS$_3$ invariant field theories
New BMS3-invariant 2D scalar theories (electric, magnetic, canonical, coupled) with boundary analysis, flux laws, monodromy matching to 3D gravity, and complementary AdS3/dS3 flat limits.
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Infinite towers of 2d symmetry algebras from Carrollian limit of 3d CFT
The Carrollian limit of CFT3 operator products yields towers of sl(2,C) blocks that reproduce conformally soft photon and graviton theorems and the S and w1+∞ celestial symmetry algebras.
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Modular Hamiltonian and entanglement entropy in the BMS free fermion theory
In the BMS free fermion model, the two-interval modular Hamiltonian has local plus bi-local terms, and the vacuum entanglement entropy for n intervals is the chiral-CFT formula with c_L=1 and c_M=0.
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Anisotropic conformal Carroll field theories and their gravity duals
Plane wave spacetimes in three and four dimensions realize anisotropic conformal Carroll algebras as their (asymptotic) symmetry algebras, providing candidate holographic duals for z-anisotropic Carrollian CFTs.
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Notes on su$(1,2)\oplus$u$(1)$ Chern-Simons theory and Torsional Newton-Cartan gravity
The su(1,2)⊕u(1) Chern-Simons theory is torsional Newton-Cartan gravity whose 1/c expansion reproduces the extended z=2 Schrödinger gravity and whose asymptotic symmetry is the W_3^(2)⊕u(1) algebra.
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Postcarrollian gravity
New post-Carrollian gravity actions in 2d, 3d, and 4d are constructed by Lie algebra expansion, including the most general 2d dilaton gravity model and a 3d asymptotic symmetry algebra with central extensions.
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A finite Carrollian critical point
A double-scaled N to 0 limit of Carrollian vector models and Yang-Mills produces interacting Carrollian correlators with finite effective central charge and hyperscaling violation.
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Emergent Carroll symmetry at phase separation in one-dimensional lattice systems
Phase separation in one-dimensional Luttinger liquids is claimed to be governed by an emergent Carroll conformal field theory, with the density structure factor exponent jumping from 1 to 2.
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Carrollian superstring in the flipped vacuum
The Carrollian superstring in the flipped vacuum has a non-truncated spectrum with nonzero winding in the infinite-radius limit, and its three-point graviton amplitudes match tensile superstring results up to location...
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Tropical Branes
Quantizing open tropical strings with Dirichlet or Neumann boundary conditions gives a Hamiltonian of free, non-oscillating modes, named tropical branes, proposed to describe asymptotic on-shell string states.
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Foundations of Carrollian Geometry
A pedagogical review that establishes a unified intrinsic geometry for null hypersurfaces via Carrollian structures, adding new derivations of connection symbols and a null Gauss equation.
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Quantization of Carrollian fermions
A first interacting 4D Carrollian Yukawa theory is constructed, showing ultralocal fermion-scalar interactions and one-loop beta functions with mostly Gaussian fixed points.
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A time-like window into tensionless worldsheets
Kasner worldsheets near their null horizons reproduce the tensionless, Carrollian string physics previously found for Rindler worldsheets, with a Bogoliubov-map identification that depends on an arbitrary regularizati...
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Peierls substitution and Hall motion in exotic Carroll dynamics
Exotic Carroll particles with two-parameter central extension move by an anomalous Hall law, and their critical reduction reproduces the Dunne-Jackiw-Trugenberger model underlying the Peierls substitution.
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Carrollian Quantum Mechanics: Time-like, Space-like and Hybrid Sectors
A c→0 contraction of the Klein-Gordon equation yields three Carrollian quantum sectors, and the time-like sector shows temporal tunneling with |T|²=1+|R|².
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3D Carrollian gravity from 2D Euclidean symmetry
Post-Carroll-Newtonian Chern-Simons gravities are systematically obtained by semigroup-expanding 2D Euclidean B_k algebras, recovering known Carrollian models as subcases.
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Lectures on Carrollian Holography
Massless scattering amplitudes, including gravitons, can be recast as correlators of a carrollian conformal field theory on null infinity, but the non-perturbative bootstrap program remains incomplete.
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