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arxiv: 2506.16164 · v3 · submitted 2025-06-19 · ✦ hep-th · cond-mat.str-el· gr-qc· math-ph· math.MP· nucl-th

The Carrollian Kaleidoscope

Arjun Bagchi , Aritra Banerjee , Prateksh Dhivakar , Saikat Mondal , Ashish Shukla This is my paper

Pith reviewed 2026-05-19 09:16 UTC · model grok-4.3

classification ✦ hep-th cond-mat.str-elgr-qcmath-phmath.MPnucl-th
keywords Carroll symmetriesconformal Carroll field theoriesasymptotically flat holographyCarroll hydrodynamicsfractonsLuttinger liquids
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0 comments X

The pith

Carroll symmetries from the zero speed of light limit appear in flat spacetime holography, hydrodynamics and condensed matter.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This review shows that the Carroll group, obtained by sending the speed of light to zero in the Poincare group, is no longer viewed only as a mathematical curiosity. Carroll and conformal Carroll symmetries now surface in many physical settings from condensed matter to quantum gravity. The paper first sets out the basic symmetry structures and constructs Carrollian and conformal Carroll field theories, then examines their use in building holographic duals for asymptotically flat spacetimes, in reconstructing hydrodynamics, and in describing fractons and flat bands.

Core claim

The Carroll group arises in the vanishing speed of light limit of the Poincare group. Recent developments have shown that Carroll and conformal Carroll symmetries are ubiquitous, appearing in condensed matter physics to quantum gravity. This review details the construction of Carrollian and Carrollian Conformal field theories and focuses on applications in AFS holography, Carroll hydrodynamics linked to ultrarelativistic flows, and condensed matter connections including fractons, flat bands and phase separation in Luttinger liquid models.

What carries the argument

The Carroll group and its conformal extensions that arise in the c to 0 limit and support constructions of CCFTs along with symmetry-based reconstructions of hydrodynamics.

If this is right

  • Co-dimension one dual CCFT descriptions for AFS3 and extensions to the dual of 4D AFS.
  • Symmetry-based reconstruction of Carroll hydrodynamics with concrete examples such as Bjorken and Gubser flows in the quark-gluon plasma.
  • Links to fractons, flat bands and phase separation in Luttinger liquid models.
  • Brief indications of further roles in string theory and black hole horizons.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Carrollian structures could supply a common language for null boundaries that appears in both gravitational and condensed matter settings.
  • Symmetry constraints from the c to 0 limit might generate new predictions for transport in flat-band materials that can be checked in tabletop experiments.
  • Extensions of these constructions to quantum gravity might clarify how information propagates along null surfaces.

Load-bearing premise

The vanishing speed of light limit of the Poincare group has physical relevance in holography, hydrodynamics and condensed matter rather than remaining a pure mathematical curiosity.

What would settle it

A direct calculation or measurement in an asymptotically flat spacetime dual or in a condensed matter system such as a Luttinger liquid that shows Carrollian symmetries do not emerge consistently in the c to 0 limit.

read the original abstract

The Carroll group arises in the vanishing speed of light limit of the Poincar\'{e} group and was initially discarded as just a mathematical curiosity. However, recent developments have proved otherwise. Carroll and conformal Carroll symmetries are now ubiquitous, appearing in diverse physical phenomena starting from condensed matter physics to quantum gravity. This review aims to provide the reader a gateway into this fast-developing field. After an introduction and setting the stage with basics of the symmetry in question, we detail the construction of Carrollian and Carrollian Conformal field theories (CCFT). We then focus on applications. By far the most popular of these applications is in the context of the construction of holography in asymptotically flat spacetimes (AFS) in terms of a co-dimension one dual CCFT. We review the early work on AFS$_3$ /CCFT$_2$ before delving into an in-depth analysis for the construction of the dual to 4D AFS. Two other important sets of applications are in hydrodynamics and in condensed matter physics, which we discuss in detail. Carroll hydrodynamics is introduced as the $c\to 0$ limit of relativistic hydrodynamics first and then reconstructed from a symmetry based approach. Relations to ultrarelativistic flows and connections to the quark-gluon plasma are discussed with concrete examples of the Bjorken and Gubser flow models. In condensed matter applications, we cover connections to fractons, flat bands, and phase separation in Luttinger liquid models. To conclude, we give very brief outlines of other topics of interest including string theory and black hole horizons.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

0 major / 3 minor

Summary. The manuscript is a review surveying Carrollian and conformal Carroll symmetries arising from the c→0 limit of the Poincaré group. After introducing the basics, it details constructions of Carrollian and conformal Carrollian field theories (CCFTs). Applications are reviewed in asymptotically flat holography (early AFS₃/CCFT₂ work and in-depth 4D AFS dual construction), Carroll hydrodynamics (both as the c→0 limit of relativistic hydrodynamics and via symmetry-based reconstruction, with relations to ultrarelativistic flows and concrete Bjorken/Gubser flow examples tied to the quark-gluon plasma), and condensed matter (fractons, flat bands, phase separation in Luttinger liquids). Brief outlines cover string theory and black hole horizons. The central claim is that recent developments have established these symmetries as physically relevant and ubiquitous across condensed matter, hydrodynamics, and quantum gravity rather than mere mathematical curiosities.

Significance. If the survey of constructions and applications is accurate and balanced, the review would provide a useful gateway into this developing area by organizing literature on CCFTs, AFS holography, symmetry-based hydrodynamics, and condensed-matter links such as fractons. The explicit treatment of concrete examples (Bjorken and Gubser flows) and the dual reconstruction of Carroll hydrodynamics from symmetries are strengths that could help readers connect the symmetry structures to physical regimes. The paper's scope aligns with the growing interest in Carrollian limits in high-energy theory and adjacent fields.

minor comments (3)
  1. In the hydrodynamics discussion, the transition from the c→0 limit to the symmetry-based reconstruction would benefit from an explicit statement of which hydrodynamic equations are preserved or modified under the Carrollian contraction (e.g., a short comparison table or key equation reference).
  2. The condensed-matter section on Luttinger liquids and phase separation would be clearer if a brief remark were added on how the Carrollian limit differs from the standard relativistic treatment in the same models.
  3. Throughout the review, ensure that all acronyms (AFS, CCFT, etc.) are expanded on first use in each major section, even if defined in the abstract, to aid readers who consult individual sections.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive and accurate summary of the manuscript, as well as for the encouraging assessment of its potential utility as a gateway into Carrollian symmetries and their applications. We appreciate the recognition of specific strengths such as the treatment of Bjorken and Gubser flows and the symmetry-based reconstruction of Carroll hydrodynamics. The recommendation for minor revision is noted, and we will incorporate improvements to clarity and balance in the revised version.

Circularity Check

0 steps flagged

No significant circularity: review of external literature

full rationale

This is a review paper that surveys existing constructions of Carrollian and conformal Carrollian field theories along with applications in asymptotically flat holography, hydrodynamics, and condensed matter. No original derivation chain is presented that reduces by construction to fitted inputs, self-definitions, or load-bearing self-citations. All central claims are framed as summaries of external developments, with the paper explicitly positioned as providing a gateway to the literature rather than deriving new results from its own premises. The analysis remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

No original free parameters, axioms, or invented entities are introduced because this is a review paper; all technical content is drawn from previously published works.

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Forward citations

Cited by 22 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Carrollian quantum states and flat space holography

    hep-th 2026-04 unverdicted novelty 7.0

    Carrollian QFTs from scalar limits admit regular invariant vacua and KMS states only in the massive electric sector; a factorizing quasifree state is constructed for flat-space holography isolating nonseparable zero modes.

  2. A Twisted Origin for Magnetic Carroll Supersymmetry

    hep-th 2026-03 unverdicted novelty 7.0

    Magnetic Carroll supersymmetry descends from a twisted relativistic parent rather than naive contraction, realized in 3D N=2 with vector multiplet action whose conformal extension matches global super-BMS4.

  3. On $\sqrt{T\overline{T}}$ deformed pathways: CFT to CCFT

    hep-th 2026-01 unverdicted novelty 7.0

    The marginal √(T T-bar) deformation of 2D massless scalars provides a dynamical map from relativistic CFT to Carrollian CCFT symmetries, recovering the electric Carroll theory and a novel magnetic counterpart in the e...

  4. Kerroll black holes

    hep-th 2026-05 unverdicted novelty 6.0

    Rotating black holes are constructed in Carroll gravity via connection freedom and an odd-power GR expansion, yielding an intrinsically Carrollian rotating solution and the Kerroll black hole analog.

  5. Carroll fermions from null reduction: A case of good and bad fermions

    hep-th 2026-05 unverdicted novelty 6.0

    Carrollian fermionic actions for electric and magnetic sectors are derived from a single Bargmann Dirac action by null reduction, with good and bad fermions as dynamical and constrained modes valid in any dimension.

  6. Stationary solutions in the small-$c$ expansion of GR

    gr-qc 2026-04 unverdicted novelty 6.0

    Exact Lense-Thirring-type, C-metric-type, and Hartle-Thorne-type stationary vacuum solutions are constructed in the NLO and NNLO small-c expansion of GR, revealing a richer sector than magnetic Carroll gravity.

  7. Carrollian ABJM: Fermions and Supersymmetry

    hep-th 2026-04 unverdicted novelty 6.0

    The c to zero limit of ABJM theory produces a Carrollian superconformal theory with extended BMS4 symmetry using Carrollian Dirac matrices.

  8. Carroll fermions, expansions and the lightcone

    hep-th 2026-04 unverdicted novelty 6.0

    Carrollian fermion actions are obtained from relativistic Dirac theory via c-expansion and connected to light-cone dynamics through co-dimension one Carroll subalgebras in the Poincaré algebra.

  9. On Carrollian Loop Amplitudes for Gauge Theory and Gravity

    hep-th 2026-04 unverdicted novelty 6.0

    Loop-level Carrollian amplitudes in N=4 SYM and N=8 supergravity are differential operators on tree-level versions, with logarithmic eikonal behavior and IR-safe factorization via natural splitting.

  10. The gravitational S-matrix from the path integral: asymptotic symmetries and soft theorems

    hep-th 2026-03 unverdicted novelty 6.0

    A path integral with asymptotic boundary conditions produces the gravitational S-matrix and derives soft graviton theorems from extended BMS symmetry Ward identities.

  11. Area Scaling of Dynamical Degrees of Freedom in Regularised Scalar Field Theory

    hep-th 2026-02 unverdicted novelty 6.0

    The minimal number of dynamical degrees of freedom in regularised scalar field theory scales with area, governed by the count of distinct normal-mode frequencies below the ultraviolet cutoff.

  12. Carroll hydrodynamics with spin

    hep-th 2026-01 unverdicted novelty 6.0

    Carroll hydrodynamics with spin is obtained as the c→0 limit of relativistic hydrodynamics with spin, extending the description of boost-invariant flows.

  13. From Asymptotically Flat Gravity to Finite Causal Diamonds

    hep-th 2025-12 unverdicted novelty 6.0

    The soft sector phase space of asymptotically flat gravity equals the phase space of radial size fluctuations of a finite causal diamond in flat spacetime.

  14. Conformal Blocks in 2d Carrollian/Galilean CFTs and Excited State Entanglement Entropy

    hep-th 2025-10 unverdicted novelty 6.0

    Derives heavy-light conformal blocks in 2d C/G CFTs and computes excited-state entanglement entropy via replica trick, finding thermal form that reproduces holographic EE and establishes dictionary between boundary we...

  15. Strings near BTZ black holes: A Carrollian Chronicle

    hep-th 2025-10 unverdicted novelty 6.0

    The paper classifies families of closed bosonic string solutions in the near-horizon non-extremal BTZ spacetime and identifies novel features via string-Carroll expansion.

  16. Radiation in Fluid/Gravity and the Flat Limit

    hep-th 2025-08 unverdicted novelty 6.0

    Establishes a holographic link between bulk gravitational radiation and dissipative corrections plus entropy production in boundary fluids, then constructs Carrollian analogues and celestial observables in the flat limit.

  17. On bulk reconstruction in Lorentzian AdS and its flat space limit

    hep-th 2026-05 unverdicted novelty 5.0

    Constructs bulk scalar field representations in Lorentzian AdS4 from boundary primaries via time-ordered propagators and derives their flat-space limits to plane-wave or Carrollian bases.

  18. On the Consistency of Null Strings Literature: The Tale of an Overlooked Symmetry

    hep-th 2026-05 unverdicted novelty 5.0

    Null strings possess an overlooked local symmetry that reduces their physical degrees of freedom to D-3 rather than the D-2 reported in prior literature.

  19. Generalized Entanglement Wedges and the Connected Wedge Theorem

    hep-th 2026-04 unverdicted novelty 5.0

    Generalized entanglement wedges rephrase the connected wedge theorem in bulk entropy terms, yielding mutual information bounds and a scattering-to-connected-wedge implication that extends to flat spacetimes.

  20. On Carrollian Loop Amplitudes for Gauge Theory and Gravity

    hep-th 2026-04 unverdicted novelty 5.0

    Loop-level Carrollian amplitudes in gauge theory and gravity preserve tree-level structures, show logarithmic dependence in the eikonal regime, and factorize to yield an IR-safe definition.

  21. More on Bulk Local State Reconstruction in Flat/Carr CFT

    hep-th 2026-03 unverdicted novelty 5.0

    Bulk local states are built in flat holography via induced representations, with a dual basis resolving 3D bra-ket scaling issues and a tilde basis enabling explicit constructions in higher dimensions that recover the...

  22. Aspects of Non-Relativistic Supersymmetric Theories

    hep-th 2026-04 unverdicted novelty 2.0

    Discusses features of non-relativistic supersymmetric field theories from Galilean and Carrollian points of view to aid construction of electric and magnetic variants.

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