Pith. sign in

REVIEW 3 major objections 4 minor 1 cited by

3D Carrollian gravity from 2D Euclidean symmetry

T0 review · 3 major / 4 minor · reviewed 2026-08-10 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read Expanding 2D Euclidean algebras yields 3D Carrollian gravity actions

desk verdict The known Carrollian constructions check out, but the new post-Carroll-Newtonian master action is internally inconsistent and does not reduce to the claimed m=1 and m=2 cases. read the letter →

arxiv 2501.00205 v1 pith:MHUVD7SY submitted 2024-12-31 hep-th gr-qc

Patrick Concha , Evelyn Rodríguez , Sebastián Salgado This is my paper · ORCID
classification hep-thgr-qc
keywords CarrollsymmetryChern-SimonsgravityLiealgebraexpansionS-expansionAdS-CarrollCarroll-GalileiPost-Carroll-NewtonianB_kalgebras
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper claims that three-dimensional Carrollian gravity theories, which describe physics at the ultra-relativistic limit where the speed of light goes to zero, can be systematically obtained by applying a semigroup expansion to two-dimensional Euclidean symmetry algebras. Expanding the 2D Euclidean AdS algebra produces the AdS-Carroll algebra, and expanding its flat version produces the Carroll-Galilei algebra, with the corresponding Chern-Simons gravity actions constructed in each case. The paper observes that the vanishing-cosmological-constant limit taken on the 2D Euclidean side becomes a non-relativistic (speed of light going to infinity) limit after the expansion to three dimensions. It also shows that starting from a central-extension variant, the 2D Euclidean Maxwell algebra, cures the degeneracy that otherwise prevents well-defined equations of motion, and that expanding a family of 2D Euclidean B_k algebras generates a new family of post-Carroll-Newtonian algebras. A sympathetic reader would care because this gives one algebraic mechanism that organizes known Carrollian gravity models and produces new ones with non-degenerate invariant tensors.

What carries the argument

The central mechanism is the abelian semigroup expansion (S-expansion) of a Lie algebra. Starting from a 2D Euclidean algebra, one introduces the semigroup S_E^(1) = {λ0, λ1, λ2} with multiplication rule λ_α λ_β = λ_{α+β} if α+β ≤ 1 and λ2 otherwise, then forms new generators as λ0 and λ1 multiples of the original generators, and finally extracts the 0_S-reduced algebra by discarding the λ2 layer. This expansion determines both the new commutators and the invariant bilinear tensor, which is the input for the Chern-Simons action. The flat limit on the seed algebra is implemented as an Inönü-Wigner contraction with a parameter ε identified with the speed of light, so that the 2D flat limit becomes a non-relativistic limit in the expanded 3D algebra.

What would settle it

A concrete test is to take the post-Carroll-Newtonian algebra pcn_m for an odd value such as m = 3 and attempt to solve the invariance equations for a symmetric bilinear form; if a non-degenerate one exists despite the paper's even-m degeneracy claim, the central result would be refuted. Another check is to compute the expanded algebra without the 0_S-reduction step and see whether the resulting algebra is still isomorphic to the Carroll-Galilei algebra, since the derivation depends on that reduction.

Watch

Extended reading notes

Core claim

The paper's central claim is that the S-expansion method, applied to the 2D Euclidean AdS algebra and its flat version, reproduces the 3D AdS-Carroll and Carroll-Galilei algebras together with their Chern-Simons gravity actions. Using the semigroup S_E^(1) with zero element, the expansion generates the 3D generators as semigroup multiples of the 2D generators, and the same expansion transports the invariant tensor needed for the Chern-Simons action. The remarkable observation is that the flat limit on the 2D Euclidean side, which sends the cosmological constant to zero, acts as a non-relativistic limit on the 3D side because the contraction parameter can be identified with the speed of light. The paper further demonstrates that the degeneracy of the Carroll-Galilei invariant tensor is resolved by expanding the 2D Euclidean Maxwell algebra, yielding an extended Carroll-Galilei algebra with a non-degenerate bilinear trace. Finally, expanding the 2D Euclidean B_k algebra family gives post-Carroll-Newtonian algebras, with non-degeneracy available only for even values of the parameter m, and the most general post-Carroll-Newtonian Chern-Simons action decomposes into a sum of Carroll-Galilei, extended Carroll-Galilei, and higher post-Carroll-Newtonian terms.

Load-bearing premise

The load-bearing premise is that the contraction parameter ε introduced on the 2D Euclidean side can legitimately be identified with the speed of light c, so that the vanishing-cosmological-constant limit of the 2D algebra becomes a genuine non-relativistic limit of the expanded 3D theory; if that identification is rejected, the headline interpretation loses its force even though the algebraic constructions remain valid.

Editorial extensions

If this is right

  • The known 3D AdS-Carroll and Carroll-Galilei Chern-Simons gravity actions can be derived from a common 2D Euclidean seed, so the 2D Euclidean algebras serve as a unified starting point for Carrollian gravity.
  • The vanishing cosmological constant limit on the 2D Euclidean AdS algebra corresponds to a non-relativistic limit on the 3D Carrollian side, mirroring the known duality between the 2D conformal Galilei algebra and the asymptotic symmetry algebra bms3 of 3D flat gravity.
  • Adding a central charge to the 2D Euclidean Poincaré algebra, forming the 2D Euclidean Maxwell algebra, resolves the degeneracy problem and yields an extended Carroll-Galilei algebra with a non-degenerate invariant tensor and well-defined Chern-Simons field equations.
  • Expanding the 2D Euclidean B_k algebras produces a family of post-Carroll-Newtonian algebras pcn_m with m = k-2, recovering Carroll-Galilei for m = 1 and extended Carroll-Galilei for m = 2, and these algebras admit non-degenerate invariant tensors only for even m.
  • The most general post-Carroll-Newtonian Chern-Simons action is a direct sum of Carroll-Galilei, extended Carroll-Galilei, and higher post-Carroll-Newtonian Chern-Simons terms, each invariant under its corresponding pcn_n algebra.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Editorial inference: if the 2D-to-3D expansion works as claimed, the same mechanism can likely be iterated with other semigroups or applied to supersymmetric extensions to construct novel Carrollian supergravity actions, though the paper does not establish those constructions.
  • Editorial inference: the even-m restriction suggests that the family of well-defined post-Carroll-Newtonian Chern-Simons gravities is a discrete zoo labeled by even integers, and one could test whether their asymptotic symmetry algebras form a known sequence such as bms3-type algebras.
  • Editorial inference: the identification of the flat limit with a non-relativistic limit is algebraic rather than physical, so a natural test is whether local observables computed in the expanded 3D theory, such as conserved charges, actually match those of a genuine non-relativistic limit of a relativistic 3D theory.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 4 minor

Summary. The paper applies abelian semigroup (S-)expansion to 2D Euclidean AdS, Poincaré, Maxwell, and B_k algebras in order to construct 3D Carrollian Chern-Simons gravity actions. It reproduces the AdS-Carroll, Carroll-Galilei, and extended Carroll-Galilei algebras and actions from the 2D seed algebras, and proposes a new family of post-Carroll-Newtonian (pcnm) algebras together with a master CS action (4.24), claiming that the m=1 and m=2 members reduce to the known Carroll-Galilei and extended Carroll-Galilei actions. The paper also emphasizes an interpretation in which the flat (vanishing cosmological constant) contraction on the 2D Euclidean side becomes a non-relativistic limit in the expanded 3D sector.

Significance. If correct, the paper provides a systematic S-expansion route from 2D Euclidean symmetry algebras to 3D Carrollian Chern-Simons gravities, and its recovery of the known AdS-Carroll and Carroll-Galilei actions in Sections 3 and 4.1 is a genuine internal consistency check. The treatment of degeneracy through the 2D Euclidean Maxwell algebra is correct and clearly explained, and the paper explicitly identifies the non-degeneracy condition γ1 ≠ 0. The proposed post-Carroll-Newtonian family is the main novel contribution, and the paper makes a concrete, checkable claim that m=1 and m=2 reproduce previously known actions. However, the master action (4.24) in Section 4.2 is not established, and the claimed reductions fail as written; because this is the central new result, the paper cannot be accepted in its present form.

major comments (3)
  1. [§4.2, Eq. (4.24)] For m=1 the sum in (4.24) runs over n=1 to 2m-2=0 and is therefore empty, yet the next paragraph states that the Carroll-Galilei action (3.16) is recovered with β0=µ1. This is internally inconsistent: the empty sum contains no β0 term, and the µ0 ω dω term in (3.16) belongs to the α-sector that the text says was intentionally omitted. The m=1 reduction therefore fails as written.
  2. [§4.2, Eq. (4.24) versus Eqs. (4.13)-(4.14)] The claimed m=2 reproduction of the extended Carroll-Galilei action (4.13) also fails. The α-terms omitted from (4.24) include the entire γ0 sector of (4.14), namely the components ⟨P_aP_b⟩=γ0δ_ab, ⟨JS⟩=-γ0, and related pieces of the invariant tensor (4.9), while the β0=µ1 part of the Carroll-Galilei term (3.16) is also absent from the n=1,...,2 sum. Thus (4.24) can at most describe a γ1-only subsector, not the action (4.13) that the text identifies as its m=2 target.
  3. [§4.2, Eqs. (4.25) and (4.24)] The curvatures in (4.25) are incomplete for the m=2 case: R^a(ω_b(p)) omits the -ετe^b contribution that appears in the extended Carroll-Galilei curvature R(ω_a) in (4.12), and R(ω(p))=dω(p) omits the -1/2 ε e e contribution that appears in R(s) in (4.12). The extra δ^{i+p+q}_n ε τ e e term in (4.24) is added separately without a derivation, and a term-by-term comparison with (4.14) shows that it does not reproduce the target action. Equation (4.24) should be rederived systematically from the invariant tensor (4.22) and the curvatures that follow from the commutation relations (4.20).
minor comments (4)
  1. [§4.2, Eq. (4.20)] The commutators in (4.20) are written for the full ranges of the indices even when the right-hand-side generator index lies outside the domain of J(i) or H(i); the authors should state explicitly that such brackets vanish. This also affects the interpretation of (4.22) for odd m.
  2. [§3.2, footnote 5] The identification of the contraction parameter ε with the speed of light c is presented as an interpretation, but no physical argument is given for it; the statement that the flat limit becomes a non-relativistic limit is an algebraic analogy based on known isomorphisms and should be flagged as such in the main text.
  3. [§4.2, Eq. (4.24)] The Kronecker-delta notation δ^n_{p+q}, δ^n_{2(i+j)}, and δ^n_{i+p+q} is not defined; please clarify that these select the combinations of generator indices for which the invariant tensors in (4.22) are nonvanishing.
  4. [Throughout] There are minor typographical inconsistencies, including 'Carrol-Galilei' in several places and a stray comma after 'rescaling' before (4.15); a careful proofread would improve readability.

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity: explicit S-expansions from stated seed algebras; self-citations are non-load-bearing; the Eq. (4.24) issue is a consistency bug, not a circular argument.

full rationale

The paper's derivation chain is not circular. The seed algebras (AdS_E2, iso(2), Maxwell_E2, and the 2D Euclidean B_k family) are stated as inputs with their own commutation relations and invariant tensors in Eqs. (2.1), (2.3), (2.9), (4.1), (4.2), (4.17), and (4.18). The S-expansion with the explicit semigroup S_E(1) is then applied transparently: the generator assignments in Eqs. (3.2), (4.7), and (4.19) and the resulting invariant tensors in Eqs. (3.4), (3.13), (4.9), and (4.22) are written out. The Chern-Simons actions are obtained by substituting these expanded invariant tensors and displayed connections into the general CS formula (2.4); for example, Eq. (3.16) follows from (3.13)-(3.15), and Eq. (4.13)-(4.14) follows from (4.9)-(4.12). Known results such as [33,34,52] are used as cross-checks or labels rather than as inputs that force the expanded actions. The main self-citations are to the S-expansion formalism [39]; that formalism is parameter-free, published, and independent of the present applications, so it is real evidence rather than load-bearing circularity. The interpretive identification of the Euclidean flat limit with a 3D non-relativistic limit (footnote 5) is a formal analogy based on known isomorphisms, not a circular derivation. Separately, Eq. (4.24) has a genuine internal-consistency problem: for m=1 its sum is empty, while the text claims it recovers the Carroll-Galilei action (3.16), and the intentional omission of the alpha-exotic terms removes pieces needed for the claimed reductions. That is a correctness flaw in the B_k generalization, not a circularity, because the construction of Eq. (4.24) does not reduce to its own input by definition.

Assumptions & free parameters 4 free parameters · 4 assumptions · 0 invented entities

The derivation rests on the standard S-expansion method, known invariant tensors of seed algebras, and the Medina-Revy non-degeneracy criterion. The free parameters are arbitrary coefficients in CS actions, not fitted to data. No new physical entities are postulated. The only notable ad-hoc assumption is the epsilon-as-c identification used to frame the flat/non-relativistic correspondence.

free parameters (4)
  • beta_0, beta_1
    Arbitrary coefficients in the AdS-Carroll invariant tensor and CS action (3.4), not determined by the derivation.
  • mu_0, mu_1
    Arbitrary coefficients in the Carroll-Galilei invariant tensor and CS action (3.13), not fixed by the method.
  • gamma_0, gamma_1 (and mu_0, mu_1)
    Coefficients in the extended Carroll-Galilei invariant tensor (4.9); gamma_1 is required nonzero for non-degeneracy, but its value is arbitrary.
  • alpha_n, beta_n
    Coefficients in the post-Carroll-Newtonian invariant tensor (4.22); the paper sets alpha_n = 0 for simplicity, which does not affect non-degeneracy.
assumptions (4)
  • domain assumption The S-expansion method of ref. [39] with the semigroup S_E^{(1)} and 0_S-reduction produces valid Lie algebras and invariant tensors.
    Used throughout Sections 3 and 4 without restating the proof; the method is assumed to preserve Lie bracket and invariant tensor structure in the way described.
  • domain assumption The non-degeneracy of the invariant bilinear trace is necessary and sufficient for a Chern-Simons action to have vanishing curvatures as equations of motion.
    Invoked in Sections 2, 3, and 4, following the Medina-Revy theorem and refs. [53,54]; this underpins the construction of well-defined CS actions.
  • domain assumption The known invariant tensors for the 2D Euclidean AdS, Poincaré, Maxwell, and B_k algebras are correctly taken from prior literature.
    The paper uses invariant tensors from refs. [60,72,73] and related work without re-deriving them; if any of these are incorrect, the expanded actions would inherit errors.
  • ad hoc to paper Identifying the expansion parameter epsilon with the speed of light c in the contraction of AdS-Carroll to Carroll-Galilei.
    Introduced in Section 3.2, footnote 5, to support the interpretation that the flat limit on the 2D side becomes a non-relativistic limit in 3D; this is a formal analogy rather than a derived physical relation.

how reviews work

0 comments
Cite this review

Pith. "Pith review of 3D Carrollian gravity from 2D Euclidean symmetry." pith.science (2026). https://pith.science/paper/MHUVD7SY

@misc{pith2026250100205,
  author       = {Pith},
  title        = {Pith review of: 3D Carrollian gravity from 2D Euclidean symmetry},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/MHUVD7SY}},
  note         = {Machine review of arXiv:2501.00205}
}
read the original abstract

Carroll symmetry arises from Poincar\'e symmetry when the speed of light is sent to zero. In this work, we apply the Lie algebra expansion method to find the Carroll versions of different gravity models in three space-time dimensions. Our starting point is the 2D Euclidean AdS algebra along with its flat version. Novel and already known Carrollian algebras, such as the AdS-Carroll and Carroll-Galilei ones are found, and the Chern--Simons gravity theories based on them are constructed. Remarkably, after the expansion, the vanishing cosmological constant limit applied to the 2D Euclidean AdS algebra converts into a non-relativistic limit in three space-time dimensions. We extend our results to Post-Carroll-Newtonian algebras which can be found by expanding a family of 2D Euclidean algebras.

Figures

Figures reproduced from arXiv: 2501.00205 by the authors.

Figure 1
Figure 1. Diagram summarizing the S-expansion, flat limit and non-relativistic limit. [PITH_FULL_IMAGE:figures/full_fig_p008_1.png] view at source ↗

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

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

  1. Carrollian superstring in the flipped vacuum

    hep-th 2025-01 conditional novelty 6.0 of 10

    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...

Reference graph

Works this paper leans on

100 extracted references · 28 canonical work pages · cited by 1 Pith paper

  1. [1]

    Une nouvelle limite non-relativiste du groupe de poincar´ e,

    J. L´ evy-Leblond, “Une nouvelle limite non-relativiste du groupe de poincar´ e,”Annales de l’institut Henri Poincar´ e (A) Physique th´ eorique3 (1965) 1–12. 12

    1965

  2. [2]

    Possible kinematics,

    H. Bacry and J. Levy-Leblond, “Possible kinematics,” J. Math. Phys. 9 (1968) 1605–1614

    1968

  3. [3]

    Tachyon condensates, Carrollian contraction of Lorentz group, and fundamental strings,

    G. Gibbons, K. Hashimoto, and P. Yi, “Tachyon condensates, Carrollian contraction of Lorentz group, and fundamental strings,” JHEP 09 (2002) 061, hep-th/0209034

    arXiv 2002

  4. [4]

    Warped Conformal Field Theory as Lower Spin Gravity,

    D. M. Hofman and B. Rollier, “Warped Conformal Field Theory as Lower Spin Gravity,” Nucl. Phys. B 897 (2015) 1–38, 1411.0672

    arXiv 2015

  5. [5]

    Tensionless Strings and Galilean Conformal Algebra,

    A. Bagchi, “Tensionless Strings and Galilean Conformal Algebra,” JHEP 05 (2013) 141, 1303.0291

    arXiv 2013

  6. [6]

    Exotic Origins of Tensionless Superstrings,

    A. Bagchi, A. Banerjee, S. Chakrabortty, and P. Parekh, “Exotic Origins of Tensionless Superstrings,” Phys. Lett. B 801 (2020) 135139, 1811.10877

    arXiv 2020

  7. [7]

    Asymptotic symmetries in Carrollian theories of gravity,

    A. P´ erez, “Asymptotic symmetries in Carrollian theories of gravity,” JHEP 12 (2021) 173, 2110.15834

    arXiv 2021

  8. [8]

    Asymptotic symmetries in Carrollian theories of gravity with a negative cosmological constant,

    A. P´ erez, “Asymptotic symmetries in Carrollian theories of gravity with a negative cosmological constant,” JHEP 09 (2022) 044, 2202.08768

    arXiv 2022

Show all 100 references
  1. [9]

    Asymptotic structure of Carrollian limits of Einstein-Yang-Mills theory in four spacetime dimensions,

    O. Fuentealba, M. Henneaux, P. Salgado-Rebolledo, and J. Salzer, “Asymptotic structure of Carrollian limits of Einstein-Yang-Mills theory in four spacetime dimensions,” Phys. Rev. D 106 (2022), no. 10, 104047, 2207.11359

    2022 arXiv

  2. [10]

    Conformal Carroll groups and BMS symmetry,

    C. Duval, G. W. Gibbons, and P. A. Horvathy, “Conformal Carroll groups and BMS symmetry,” Class. Quant. Grav. 31 (2014) 092001, 1402.5894

    2014 arXiv

  3. [11]

    Gauging the Carroll Algebra and Ultra-Relativistic Gravity,

    J. Hartong, “Gauging the Carroll Algebra and Ultra-Relativistic Gravity,” JHEP 08 (2015) 069, 1505.05011

    2015 arXiv

  4. [12]

    Holographic Reconstruction of 3D Flat Space-Time,

    J. Hartong, “Holographic Reconstruction of 3D Flat Space-Time,” JHEP 10 (2016) 104, 1511.01387

    2016 arXiv

  5. [13]

    Flat Holography: Aspects of the dual field theory,

    A. Bagchi, R. Basu, A. Kakkar, and A. Mehra, “Flat Holography: Aspects of the dual field theory,” JHEP 12 (2016) 147, 1609.06203

    2016 arXiv

  6. [14]

    Carrollian Perspective on Celestial Holography,

    L. Donnay, A. Fiorucci, Y. Herfray, and R. Ruzziconi, “Carrollian Perspective on Celestial Holography,” Phys. Rev. Lett. 129 (2022), no. 7, 071602, 2202.04702

    2022 arXiv

  7. [15]

    Intrinsic approach to 1 + 1D Carrollian Conformal Field Theory,

    A. Saha, “Intrinsic approach to 1 + 1D Carrollian Conformal Field Theory,” JHEP 12 (2022) 133, 2207.11684

    2022 arXiv

  8. [16]

    Carrollian approach to 1 + 3D flat holography,

    A. Saha, “Carrollian approach to 1 + 3D flat holography,” JHEP 06 (2023) 051, 2304.02696

    2023 arXiv

  9. [17]

    Carrollian Conformal Fields and Flat Holography,

    K. Nguyen and P. West, “Carrollian Conformal Fields and Flat Holography,” Universe 9 (2023), no. 9, 385, 2305.02884

    2023 arXiv

  10. [18]

    Holography in flat spacetimes: the case for Carroll,

    A. Bagchi, P. Dhivakar, and S. Dutta, “Holography in flat spacetimes: the case for Carroll,” JHEP 08 (2024) 144, 2311.11246. 13

    2024 arXiv

  11. [19]

    Celestial holography: An asymptotic symmetry perspective,

    L. Donnay, “Celestial holography: An asymptotic symmetry perspective,” Phys. Rept. 1073 (2024) 1–41, 2310.12922

    2024 arXiv

  12. [20]

    Carrollian Physics at the Black Hole Horizon,

    L. Donnay and C. Marteau, “Carrollian Physics at the Black Hole Horizon,” Class. Quant. Grav. 36 (2019), no. 16, 165002, 1903.09654

    2019 arXiv

  13. [21]

    Carroll Structures, Null Geometry and Conformal Isometries,

    L. Ciambelli, R. G. Leigh, C. Marteau, and P. M. Petropoulos, “Carroll Structures, Null Geometry and Conformal Isometries,” Phys. Rev. D 100 (2019), no. 4, 046010, 1905.02221

    2019 arXiv

  14. [22]

    Spacetime structure near generic horizons and soft hair,

    D. Grumiller, A. P´ erez, M. M. Sheikh-Jabbari, R. Troncoso, and C. Zwikel, “Spacetime structure near generic horizons and soft hair,” Phys. Rev. Lett. 124 (2020), no. 4, 041601, 1908.09833

    2020 arXiv

  15. [23]

    Carroll stories,

    J. de Boer, J. Hartong, N. A. Obers, W. Sybesma, and S. Vandoren, “Carroll stories,” JHEP 09 (2023) 148, 2307.06827

    2023 arXiv

  16. [24]

    Carroll black holes,

    F. Ecker, D. Grumiller, J. Hartong, A. P´ erez, S. Prohazka, and R. Troncoso, “Carroll black holes,” SciPost Phys. 15 (2023), no. 6, 245, 2308.10947

    2023

  17. [25]

    Geometry of Zero Signature Space-times,

    M. Henneaux, “Geometry of Zero Signature Space-times,” Bull. Soc. Math. Belg. 31 (1979) 47–63

    1979

  18. [26]

    Cartan-like formulation of electric Carrollian gravity,

    S. Pekar, A. P´ erez, and P. Salgado-Rebolledo, “Cartan-like formulation of electric Carrollian gravity,” JHEP 09 (2024) 059, 2406.01665

    2024 arXiv

  19. [27]

    Carroll versus Galilei Gravity,

    E. Bergshoeff, J. Gomis, B. Rollier, J. Rosseel, and T. ter Veldhuis, “Carroll versus Galilei Gravity,” JHEP 03 (2017) 165, 1701.06156

    2017 arXiv

  20. [28]

    Carroll contractions of Lorentz-invariant theories,

    M. Henneaux and P. Salgado-Rebolledo, “Carroll contractions of Lorentz-invariant theories,” JHEP 11 (2021) 180, 2109.06708

    2021 arXiv

  21. [29]

    Magnetic Carrollian gravity from the Carroll algebra,

    A. Campoleoni, M. Henneaux, S. Pekar, A. P´ erez, and P. Salgado-Rebolledo, “Magnetic Carrollian gravity from the Carroll algebra,” JHEP 09 (2022) 127, 2207.14167

    2022 arXiv

  22. [30]

    Carroll Expansion of General Relativity,

    D. Hansen, N. A. Obers, G. Oling, and B. T. Søgaard, “Carroll Expansion of General Relativity,” SciPost Phys. 13 (2022), no. 3, 055, 2112.12684

    2022 arXiv

  23. [31]

    Conformal Carroll scalars with boosts,

    S. Baiguera, G. Oling, W. Sybesma, and B. T. Søgaard, “Conformal Carroll scalars with boosts,” SciPost Phys. 14 (2023), no. 4, 086, 2207.03468

    2023 arXiv

  24. [32]

    A Conformal Approach to Carroll Gravity,

    E. A. Bergshoeff, P. Concha, O. Fierro, E. Rodr ´ ıguez, and J. Rosseel, “A Conformal Approach to Carroll Gravity,” 2412.17752

    arXiv

  25. [33]

    Limits of three-dimensional gravity and metric kinematical Lie algebras in any dimension,

    J. Matulich, S. Prohazka, and J. Salzer, “Limits of three-dimensional gravity and metric kinematical Lie algebras in any dimension,” JHEP 07 (2019) 118, 1903.09165

    2019 arXiv

  26. [34]

    AdS Carroll Chern-Simons supergravity in 2 + 1 dimensions and its flat limit,

    L. Ravera, “AdS Carroll Chern-Simons supergravity in 2 + 1 dimensions and its flat limit,” Phys. Lett. B 795 (2019) 331–338, 1905.00766

    2019 arXiv

  27. [35]

    N -extended Chern-Simons Carrollian supergravities in 2 + 1 spacetime dimensions,

    F. Ali and L. Ravera, “ N -extended Chern-Simons Carrollian supergravities in 2 + 1 spacetime dimensions,” JHEP 02 (2020) 128, 1912.04172. 14

    2020 arXiv

  28. [36]

    Newton-Hooke/Carrollian expansions of (A)dS and Chern-Simons gravity,

    J. Gomis, A. Kleinschmidt, J. Palmkvist, and P. Salgado-Rebolledo, “Newton-Hooke/Carrollian expansions of (A)dS and Chern-Simons gravity,” JHEP 02 (2020) 009, 1912.07564

    2020 arXiv

  29. [37]

    Three-dimensional Maxwellian Carroll gravity theory and the cosmological constant,

    P. Concha, D. Pe˜ nafiel, L. Ravera, and E. Rodr ´ ıguez, “Three-dimensional Maxwellian Carroll gravity theory and the cosmological constant,” Phys. Lett. B 823 (2021) 136735, 2107.05716

    2021 arXiv

  30. [38]

    Non-Lorentzian Supergravity and Kinematical Superalgebras,

    P. Concha and L. Ravera, “Non-Lorentzian Supergravity and Kinematical Superalgebras,” 2412.07665

    arXiv

  31. [39]

    Expanding Lie (super)algebras through Abelian semigroups,

    F. Izaurieta, E. Rodriguez, and P. Salgado, “Expanding Lie (super)algebras through Abelian semigroups,” J. Math. Phys. 47 (2006) 123512, hep-th/0606215

    2006 arXiv

  32. [40]

    ExtendedD = 3 Bargmann supergravity from a Lie algebra expansion,

    J. A. de Azc´ arraga, D. G´ utiez, and J. M. Izquierdo, “ExtendedD = 3 Bargmann supergravity from a Lie algebra expansion,” 1904.12786

    1904 arXiv

  33. [41]

    Lie Algebra Expansions and Actions for Non-Relativistic Gravity,

    E. Bergshoeff, J. M. Izquierdo, T. Ort ´ ın, and L. Romano, “Lie Algebra Expansions and Actions for Non-Relativistic Gravity,” JHEP 08 (2019) 048, 1904.08304

    2019 arXiv

  34. [42]

    Non-Relativistic Gravity Theory based on an Enlargement of the Extended Bargmann Algebra,

    P. Concha and E. Rodr ´ ıguez, “Non-Relativistic Gravity Theory based on an Enlargement of the Extended Bargmann Algebra,” JHEP 07 (2019) 085, 1906.00086

    2019 arXiv

  35. [43]

    Non-relativistic symmetries in three space-time dimensions and the Nappi-Witten algebra,

    D. M. Pe˜ nafiel and P. Salgado-Rebolledo, “Non-relativistic symmetries in three space-time dimensions and the Nappi-Witten algebra,” Phys. Lett. B 798 (2019) 135005, 1906.02161

    2019 arXiv

  36. [44]

    Non-Relativistic Four Dimensional p-Brane Supersymmetric Theories and Lie Algebra Expansion,

    L. Romano, “Non-Relativistic Four Dimensional p-Brane Supersymmetric Theories and Lie Algebra Expansion,” Class. Quant. Grav. 37 (2020), no. 14, 145016, 1906.08220

    2020 arXiv

  37. [45]

    Non-relativistic limits and three-dimensional coadjoint Poincare gravity,

    E. Bergshoeff, J. Gomis, and P. Salgado-Rebolledo, “Non-relativistic limits and three-dimensional coadjoint Poincare gravity,” Proc. Roy. Soc. Lond. A 476 (2020), no. 2240, 20200106, 2001.11790

    2020 arXiv

  38. [46]

    Three-dimensional higher-order Schr¨ odinger algebras and Lie algebra expansions,

    O. Kasikci, N. Ozdemir, M. Ozkan, and U. Zorba, “Three-dimensional higher-order Schr¨ odinger algebras and Lie algebra expansions,”JHEP 04 (2020) 067, 2002.03558

    2020 arXiv

  39. [47]

    Lie Algebra Expansion and Integrability in Superstring Sigma-Models,

    A. Fontanella and L. Romano, “Lie Algebra Expansion and Integrability in Superstring Sigma-Models,” JHEP 20 (2020) 083, 2005.01736

    2020 arXiv

  40. [48]

    Non-relativistic and ultra-relativistic expansions of three-dimensional spin-3 gravity theories,

    P. Concha, C. Henr ´ ıquez-B´ aez, and E. Rodr ´ ıguez, “Non-relativistic and ultra-relativistic expansions of three-dimensional spin-3 gravity theories,” JHEP 10 (2022) 155, 2208.01013

    2022 arXiv

  41. [49]

    Nonrelativistic spin-3 symmetries in 2+1 dimensions from expanded and extended Nappi-Witten algebras,

    R. Caroca, D. M. Pe˜ nafiel, and P. Salgado-Rebolledo, “Nonrelativistic spin-3 symmetries in 2+1 dimensions from expanded and extended Nappi-Witten algebras,” Phys. Rev. D 107 (2023), no. 6, 064034, 2208.00602

    2023 arXiv

  42. [50]

    Three-dimensional Newtonian gravity with cosmological constant and torsion,

    P. Concha, E. Rodr ´ ıguez, G. Rubio, and P. Ya˜ nez, “Three-dimensional Newtonian gravity with cosmological constant and torsion,” Eur. Phys. J. C 83 (2023), no. 1, 47, 2204.11763

    2023 arXiv

  43. [51]

    Non-relativistic gravity theories in four spacetime dimensions,

    P. Concha, E. Rodr ´ ıguez, and G. Rubio, “Non-relativistic gravity theories in four spacetime dimensions,” JHEP 02 (2023) 191, 2210.04101. 15

    2023 arXiv

  44. [52]

    Extended kinematical 3D gravity theories,

    P. Concha, D. Pino, L. Ravera, and E. Rodr ´ ıguez, “Extended kinematical 3D gravity theories,” JHEP 01 (2024) 040, 2310.01335

    2024 arXiv

  45. [53]

    Alg` ebres de Lie et produit scalaire invariant,

    A. Medina and P. Revoy, “Alg` ebres de Lie et produit scalaire invariant,”Annales scientifiques de l’ ´Ecole Normale Sup´ erieure4e s´ erie, 18(1985), no. 3, 553–561

    1985

  46. [54]

    On the structure of symmetric selfdual Lie algebras,

    J. M. Figueroa-O’Farrill and S. Stanciu, “On the structure of symmetric selfdual Lie algebras,” J. Math. Phys. 37 (1996) 4121–4134, hep-th/9506152

    1996 arXiv

  47. [55]

    Group-theoretical analysis of elementary particles in an external electromagnetic field. 1. the relativistic particle in a constant and uniform field,

    H. Bacry, P. Combe, and J. Richard, “Group-theoretical analysis of elementary particles in an external electromagnetic field. 1. the relativistic particle in a constant and uniform field,” Nuovo Cim. A 67 (1970) 267–299

    1970

  48. [56]

    Group-theoretical analysis of elementary particles in an external electromagnetic field. 2. the nonrelativistic particle in a constant and uniform field,

    H. Bacry, P. Combe, and J. L. Richard, “Group-theoretical analysis of elementary particles in an external electromagnetic field. 2. the nonrelativistic particle in a constant and uniform field,” Nuovo Cim. A 70 (1970) 289–312

    1970

  49. [57]

    The maxwell group and the quantum theory of particles in classical homogeneous electromagnetic fields,

    R. Schrader, “The maxwell group and the quantum theory of particles in classical homogeneous electromagnetic fields,” Fortsch. Phys. 20 (1972) 701–734

    1972

  50. [58]

    On free Lie algebras and particles in electro-magnetic fields,

    J. Gomis and A. Kleinschmidt, “On free Lie algebras and particles in electro-magnetic fields,” JHEP 07 (2017) 085, 1705.05854

    2017 arXiv

  51. [59]

    Generalized cosmological term from Maxwell symmetries,

    J. A. de Azcarraga, K. Kamimura, and J. Lukierski, “Generalized cosmological term from Maxwell symmetries,” Phys. Rev. D 83 (2011) 124036, 1012.4402

    2011 arXiv

  52. [60]

    Topological gravity and transgression holography,

    P. Salgado, R. J. Szabo, and O. Valdivia, “Topological gravity and transgression holography,” Phys. Rev. D 89 (2014), no. 8, 084077, 1401.3653

    2014 arXiv

  53. [61]

    (2+1)-dimensional gravity from Maxwell and semisimple extension of the Poincar´ e gauge symmetric models,

    S. Hoseinzadeh and A. Rezaei-Aghdam, “(2+1)-dimensional gravity from Maxwell and semisimple extension of the Poincar´ e gauge symmetric models,”Phys. Rev. D 90 (2014), no. 8, 084008, 1402.0320

    2014 arXiv

  54. [62]

    Maxwell Superalgebras and Abelian Semigroup Expansion,

    P. Concha and E. Rodr ´ ıguez, “Maxwell Superalgebras and Abelian Semigroup Expansion,” Nucl. Phys. B 886 (2014) 1128–1152, 1405.1334

    2014 arXiv

  55. [63]

    N = 1 Supergravity and Maxwell superalgebras,

    P. Concha and E. Rodr ´ ıguez, “N = 1 Supergravity and Maxwell superalgebras,”JHEP 09 (2014) 090, 1407.4635

    2014 arXiv

  56. [64]

    On the Hidden Maxwell Superalgebra underlying D=4 Supergravity,

    D. M. Pe˜ nafiel and L. Ravera, “On the Hidden Maxwell Superalgebra underlying D=4 Supergravity,” Fortsch. Phys. 65 (2017), no. 9, 1700005, 1701.04234

    2017 arXiv

  57. [65]

    Hidden role of Maxwell superalgebras in the free differential algebras of D = 4 and D = 11 supergravity,

    L. Ravera, “Hidden role of Maxwell superalgebras in the free differential algebras of D = 4 and D = 11 supergravity,” Eur. Phys. J. C 78 (2018), no. 3, 211, 1801.08860

    2018 arXiv

  58. [66]

    Asymptotic symmetries of three-dimensional Chern-Simons gravity for the Maxwell algebra,

    P. Concha, N. Merino, O. Miskovic, E. Rodr ´ ıguez, P. Salgado-Rebolledo, and O. Valdivia, “Asymptotic symmetries of three-dimensional Chern-Simons gravity for the Maxwell algebra,” JHEP 10 (2018) 079, 1805.08834

    2018 arXiv

  59. [67]

    On the Maxwell supergravity and flat limit in 2 + 1 dimensions,

    P. Concha, D. M. Pe˜ nafiel, and E. Rodr ´ ıguez, “On the Maxwell supergravity and flat limit in 2 + 1 dimensions,” Phys. Lett. B 785 (2018) 247–253, 1807.00194. 16

    2018 arXiv

  60. [68]

    Spontaneously broken 3 d Hietarinta/Maxwell Chern–Simons theory and minimal massive gravity,

    D. Chernyavsky, N. S. Deger, and D. Sorokin, “Spontaneously broken 3 d Hietarinta/Maxwell Chern–Simons theory and minimal massive gravity,” Eur. Phys. J. C 80 (2020), no. 6, 556, 2002.07592

    2020 arXiv

  61. [69]

    Gauge theory of the Maxwell and semi-simple extended (anti) de Sitter algebra,

    S. Kibaro˘ glu and O. Cebecio˘ glu, “Gauge theory of the Maxwell and semi-simple extended (anti) de Sitter algebra,” Int. J. Mod. Phys. D 30 (2021), no. 10, 2150075, 2007.14795

    2021 arXiv

  62. [70]

    Hypersymmetric extensions of Maxwell-Chern-Simons gravity in 2+1 dimensions,

    R. Caroca, P. Concha, J. Matulich, E. Rodr ´ ıguez, and D. Tempo, “Hypersymmetric extensions of Maxwell-Chern-Simons gravity in 2+1 dimensions,” Phys. Rev. D 104 (2021), no. 6, 064011, 2105.12243

    2021 arXiv

  63. [71]

    Enlarged super-bms3 algebra and its flat limit,

    J. Matulich and E. Rodr ´ ıguez, “Enlarged super-bms3 algebra and its flat limit,”Phys. Rev. D 110 (2024), no. 6, 064064, 2310.16614

    2024 arXiv

  64. [72]

    Lie-algebra expansions, Chern-Simons theories and the Einstein-Hilbert Lagrangian,

    J. D. Edelstein, M. Hassaine, R. Troncoso, and J. Zanelli, “Lie-algebra expansions, Chern-Simons theories and the Einstein-Hilbert Lagrangian,” Phys. Lett. B 640 (2006) 278–284, hep-th/0605174

    2006 arXiv

  65. [73]

    Standard General Relativity from Chern-Simons Gravity,

    F. Izaurieta, E. Rodriguez, P. Minning, P. Salgado, and A. Perez, “Standard General Relativity from Chern-Simons Gravity,” Phys. Lett. B 678 (2009) 213–217, 0905.2187

    2009 arXiv

  66. [74]

    Even-dimensional General Relativity from Born-Infeld gravity,

    P. Concha, D. Pe˜ nafiel, E. Rodr ´ ıguez, and P. Salgado, “Even-dimensional General Relativity from Born-Infeld gravity,” Phys. Lett. B 725 (2013) 419–424, 1309.0062

    2013 arXiv

  67. [75]

    Generalized Poincar´ e algebras and Lovelock–Cartan gravity theory,

    P. Concha, D. Pe˜ nafiel, E. Rodr ´ ıguez, and P. Salgado, “Generalized Poincar´ e algebras and Lovelock–Cartan gravity theory,” Phys. Lett. B 742 (2015) 310–316, 1405.7078

    2015 arXiv

  68. [76]

    (2+1)-Dimensional Gravity as an Exactly Soluble System,

    E. Witten, “(2+1)-Dimensional Gravity as an Exactly Soluble System,” Nucl. Phys. B 311 (1988) 46

    1988

  69. [77]

    Lecture notes on Chern-Simons (super-)gravities. Second edition (February 2008),

    J. Zanelli, “Lecture notes on Chern-Simons (super-)gravities. Second edition (February 2008),” in 7th Mexican Workshop on Particles and Fields . 2, 2005. hep-th/0502193

    2008 arXiv

  70. [78]

    AdS Carroll Structures from Poincar´ e Isomorphism: Asymptotic Symmetry Analysis,

    L. Avil´ es, J. Gomis, D. Hidalgo, and O. Valdivia, “AdS Carroll Structures from Poincar´ e Isomorphism: Asymptotic Symmetry Analysis,” 2407.14457

    arXiv

  71. [79]

    Galilean Conformal Algebras and AdS/CFT,

    A. Bagchi and R. Gopakumar, “Galilean Conformal Algebras and AdS/CFT,” JHEP 07 (2009) 037, 0902.1385

    2009 arXiv

  72. [80]

    GCA in 2d,

    A. Bagchi, R. Gopakumar, I. Mandal, and A. Miwa, “GCA in 2d,” JHEP 08 (2010) 004, 0912.1090

    2010 arXiv

  73. [81]

    Classical central extension for asymptotic symmetries at null infinity in three spacetime dimensions,

    G. Barnich and G. Compere, “Classical central extension for asymptotic symmetries at null infinity in three spacetime dimensions,” Class. Quant. Grav. 24 (2007) F15–F23, gr-qc/0610130

    2007 arXiv

  74. [82]

    Aspects of the BMS/CFT correspondence,

    G. Barnich and C. Troessaert, “Aspects of the BMS/CFT correspondence,” JHEP 05 (2010) 062, 1001.1541

    2010 arXiv

  75. [83]

    The Flat limit of three dimensional asymptotically anti-de Sitter spacetimes,

    G. Barnich, A. Gomberoff, and H. A. Gonzalez, “The Flat limit of three dimensional asymptotically anti-de Sitter spacetimes,” Phys. Rev. D 86 (2012) 024020, 1204.3288. 17

    2012 arXiv

  76. [84]

    Correspondence between Asymptotically Flat Spacetimes and Nonrelativistic Conformal Field Theories,

    A. Bagchi, “Correspondence between Asymptotically Flat Spacetimes and Nonrelativistic Conformal Field Theories,” Phys. Rev. Lett. 105 (2010) 171601, 1006.3354

    2010 arXiv

  77. [85]

    Tensor extension of the Poincare’ algebra,

    D. V. Soroka and V. A. Soroka, “Tensor extension of the Poincare’ algebra,” Phys. Lett. B 607 (2005) 302–305, hep-th/0410012

    2005 arXiv

  78. [86]

    Non-relativistic three-dimensional supergravity theories and semigroup expansion method,

    P. Concha, M. Ipinza, L. Ravera, and E. Rodr ´ ıguez, “Non-relativistic three-dimensional supergravity theories and semigroup expansion method,” JHEP 02 (2021) 094, 2010.01216

    2021 arXiv

  79. [87]

    Flat space holography and the complex Sachdev-Ye-Kitaev model,

    H. Afshar, H. A. Gonz´ alez, D. Grumiller, and D. Vassilevich, “Flat space holography and the complex Sachdev-Ye-Kitaev model,” Phys. Rev. D 101 (2020), no. 8, 086024, 1911.05739

    2020 arXiv

  80. [88]

    Extended Nappi-Witten Geometry for the Fractional Quantum Hall Effect,

    P. Salgado-Rebolledo and G. Palumbo, “Extended Nappi-Witten Geometry for the Fractional Quantum Hall Effect,” Phys. Rev. D 103 (2021) 125006, 2102.03886

    2021 arXiv

  81. [89]

    A WZW model based on a nonsemisimple group,

    C. R. Nappi and E. Witten, “A WZW model based on a nonsemisimple group,” Phys. Rev. Lett. 71 (1993) 3751–3753, hep-th/9310112

    1993 arXiv

  82. [90]

    More D-branes in the Nappi-Witten background,

    J. M. Figueroa-O’Farrill and S. Stanciu, “More D-branes in the Nappi-Witten background,” JHEP 01 (2000) 024, hep-th/9909164

    2000 arXiv

  83. [91]

    A Chern-Simons approach to Galilean quantum gravity in 2+1 dimensions,

    G. Papageorgiou and B. J. Schroers, “A Chern-Simons approach to Galilean quantum gravity in 2+1 dimensions,” JHEP 11 (2009) 009, 0907.2880

    2009 arXiv

  84. [92]

    Three-Dimensional Extended Bargmann Supergravity,

    E. A. Bergshoeff and J. Rosseel, “Three-Dimensional Extended Bargmann Supergravity,” Phys. Rev. Lett. 116 (2016), no. 25, 251601, 1604.08042

    2016 arXiv

  85. [93]

    Symmetries of post-Galilean expansions,

    J. Gomis, A. Kleinschmidt, J. Palmkvist, and P. Salgado-Rebolledo, “Symmetries of post-Galilean expansions,” Phys. Rev. Lett. 124 (2020), no. 8, 081602, 1910.13560

    2020 arXiv

  86. [94]

    Three-dimensional Spin-3 Theories Based on General Kinematical Algebras,

    E. Bergshoeff, D. Grumiller, S. Prohazka, and J. Rosseel, “Three-dimensional Spin-3 Theories Based on General Kinematical Algebras,” JHEP 01 (2017) 114, 1612.02277

    2017 arXiv

  87. [95]

    Hypersymmetry in D = 3 of Coupled Gravity Massless Spin 5/2 System,

    C. Aragone and S. Deser, “Hypersymmetry in D = 3 of Coupled Gravity Massless Spin 5/2 System,” Class. Quant. Grav. 1 (1984) L9

    1984

  88. [96]

    Hypergravity in AdS 3,

    Yu. M. Zinoviev, “Hypergravity in AdS 3,” Phys. Lett. B739 (2014) 106–109, 1408.2912

    2014 arXiv

  89. [97]

    Extended anti-de Sitter Hypergravity in 2 + 1 Dimensions and Hypersymmetry Bounds,

    M. Henneaux, A. P´ erez, D. Tempo, and R. Troncoso, “Extended anti-de Sitter Hypergravity in 2 + 1 Dimensions and Hypersymmetry Bounds,” in International Workshop on Higher Spin Gauge Theories. 12, 2015. 1512.08603

    2015 arXiv

  90. [98]

    Hypersymmetry bounds and three-dimensional higher-spin black holes,

    M. Henneaux, A. Perez, D. Tempo, and R. Troncoso, “Hypersymmetry bounds and three-dimensional higher-spin black holes,” JHEP 08 (2015) 021, 1506.01847

    2015 arXiv

  91. [99]

    Extension of the Poincar´ e group with half-integer spin generators: hypergravity and beyond,

    O. Fuentealba, J. Matulich, and R. Troncoso, “Extension of the Poincar´ e group with half-integer spin generators: hypergravity and beyond,” JHEP 09 (2015) 003, 1505.06173

    2015 arXiv

  92. [100]

    Asymptotically flat structure of hypergravity in three spacetime dimensions,

    O. Fuentealba, J. Matulich, and R. Troncoso, “Asymptotically flat structure of hypergravity in three spacetime dimensions,” JHEP 10 (2015) 009, 1508.04663. 18

    2015 arXiv

Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.