Anisotropic conformal Carroll field theories and their gravity duals

Dima Fontaine; Emilie Despontin; Stephane Detournay; Sudipta Dutta

REVIEW 3 major objections 4 minor 2 cited by

Anisotropic conformal Carroll field theories and their gravity duals

T0 review · 3 major / 4 minor · reviewed 2026-08-07 · deepseek-v4-flash

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

Pith's one-line read A four-dimensional plane wave realizes the full infinite-dimensional z=0 conformal Carroll algebra as its asymptotic symmetry algebra, giving an explicit holographic dual for anisotropic Carrollian field theories.

desk verdict A real but overstated flaw: the determinant gauge kills the transverse fluctuations, but the A_a,B_a sector still supports the asymptotic algebra, so this is a fixable gap rather than an empty phase space. read the letter →

arxiv 2505.23755 v1 pith:XX32VRPA submitted 2025-05-29 hep-th

Emilie Despontin , Stephane Detournay , Sudipta Dutta , Dima Fontaine This is my paper

classification hep-th PACS 04.20.Ha11.25.Tq

keywords asymptoticsymmetriesCarrollianholographicdualitiesplanewavesconformalfieldtheoryanisotropicscalingsupertranslationssuperrotations

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

The paper argues that anisotropic Carrollian conformal field theories, whose symmetries allow independent scaling of space and time, have concrete gravity duals built from plane-wave spacetimes. On the field theory side, it constructs the Carrollian stress tensor for z=0 in two and three dimensions, derives its transformation laws, and computes two-point functions in two inequivalent vacua: an SL(2,R)xSL(2,R)xU(1)-invariant vacuum gives power-law correlators, while a Carroll-invariant vacuum gives either zero-energy power laws or an ultra-local delta function for nonzero energy. On the gravity side, the paper identifies the four-dimensional metric $ds^2=2dudv+e^u(dx^2+dy^2)$ as a vacuum whose seven isometries form the type-D z=0 conformal Carroll algebra, and claims that a gauge-fixed family of metrics around it has residual diffeomorphisms reproducing the full infinite-dimensional algebra. The construction extends to arbitrary z through the metrics $ds^2=2dudv+u^k(dx^2+dy^2)$ with $k=2/z$, and to d=2 by dropping one spatial direction. If the proposal holds, it supplies a concrete starting point for matching correlation functions across a null boundary in this anisotropic Carrollian setting.

What carries the argument

The central object is the z=0 conformal Carroll algebra with mode generators $L_n$, $\bar L_n$, $M_{r,s}$, together with the seven-generator type-D subalgebra that contains the Carroll translations, boosts, Hamiltonian, and a spatial dilation. The mechanism that carries the argument is the identification of these generators with vector fields on plane-wave spacetimes: for the vacuum metric the Killing vectors are exactly the type-D algebra, while for the gauge-fixed family the residual diffeomorphisms expand into the full algebra. The gauge conditions $g_{uu}=g_{vv}=0$, $g_{uv}=1$, and $\partial_u\det(e^{-u}h_{ab})=0$, together with the fall-off choices in (4.21)-(4.22), are what promote a finite isometry statement into an asymptotic-symmetry statement; for general z, the same structure is repeated with $e^u$ replaced by $u^k$ with $k=2/z$.

What would settle it

Evaluate the gauge condition $\partial_u\det(e^{-u}h_{ab})=0$ on the phase-space metric (4.21)-(4.22). Substituting $h_{zz}=h_{zz}(z,\bar z)$, $h_{\bar z\bar z}=h_{\bar z\bar z}(z,\bar z)$, and $h_{z\bar z}=e^u/2+h(z,\bar z)$ gives $\partial_u\det(e^{-u}h_{ab})=-2e^{-2u}(h_{zz}h_{\bar z\bar z}-h^2)+e^{-u}h$, which vanishes for all u only when $h=0$ and $h_{zz}=h_{\bar z\bar z}=0$. Checking this determinant directly settles whether the phase space contains any metric other than the vacuum $ds^2=2dudv+e^u(dx^2+dy^2)$.

Watch

Extended reading notes

Core claim

The paper's central claim is an explicit holographic match between anisotropic conformal Carroll algebras and the symmetries of plane-wave spacetimes. The vacuum metric $ds^2=2dudv+e^u(dx^2+dy^2)$ has exactly seven Killing vectors, closing on the type-D z=0 conformal Carroll algebra spanned by $\{L_0,\bar L_0,L_{-1},\bar L_{-1},M_{0,0},M_{1,0},M_{0,1}\}$; as $u\to+\infty$ these vector fields reduce to the generators of the boundary field theory. The paper then defines the phase space (4.19)-(4.22) and shows that the diffeomorphisms preserving it are $\xi=-(\partial_z f^z+\partial_{\bar z}f^{\bar z})\partial_u+\alpha(z,\bar z)\partial_v+f^z\partial_z+f^{\bar z}\partial_{\bar z}$, whose modes $L_n=(n+1)z^n\partial_u-z^{n+1}\partial_z$, $\bar L_n=(n+1)\bar z^n\partial_u-\bar z^{n+1}\partial_{\bar z}$, and $M_{r,s}=z^r\bar z^s\partial_v$ satisfy the full infinite-dimensional d=3, z=0 conformal Carroll algebra. On the field theory side, the stress-tensor components $M$, $T_z$, and $T_{\bar z}$ transform as primaries with weights $(1,1)$, $(2,1)$, and $(1,2)$, and the two-point functions split into a zero-energy power-law branch and a nonzero-energy ultra-local branch depending on the vacuum. The same gauge-fixing and mode-expansion procedure is carried out for $0<z<+\infty$ with $u^k$ in place of $e^u$, and in d=2 by omitting one transverse spatial coordinate.

Load-bearing premise

The claimed infinite symmetry algebra rests on the assumption that the gauge conditions define a whole family of spacetimes around the plane wave, rather than just the plane wave itself, since if every metric in the family is forced back to that same vacuum there is no space of allowed metrics left for the symmetry computation to act on.

Editorial extensions

If this is right

The plane wave $ds^2=2dudv+e^u(dx^2+dy^2)$ provides an explicit vacuum on which the z=0 boundary theory can be defined, with the null hypersurface $u\to+\infty$ carrying the Carroll structure.
The asymptotic symmetry group of the proposed gauge-fixed family is the full infinite-dimensional z=0 conformal Carroll algebra, so a gravitational theory admitting this phase space has charges that obey exactly the algebra used to define the boundary CFT.
For every finite z in $0<z<+\infty$, the metric family $ds^2=2dudv+u^k(dx^2+dy^2)$ with $k=2/z$ yields the corresponding conformal Carroll algebra, giving each such theory a candidate holographic dual.
The flat-space cases k=0 and k=2 recover Minkowski space, and for k=2 the boundary conditions reduce to Bondi-like ones with the z=1 algebra being BMS4, so standard flat-holography boundary conditions appear as a special case.
The causal-boundary analysis confirms $u\to+\infty$ as the correct boundary for z=0, while showing that for k<1 and k=1 the hypersurface selected by projecting isometries is not the conformal boundary, so the bulk-boundary dictionary cannot be the ordinary conformal one in those cases.

Reading between the lines

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

Computing the central charges of the asymptotic algebras $L_n,\bar L_n$ for these phase spaces, a step the paper leaves open, would provide quantum-level data to match against the correlation functions derived in Section 3.
The ultra-local branch of the Carrollian correlators suggests that scalar two-point functions in the plane-wave background should contain contact terms in the transverse directions; this is testable once a bulk-to-boundary propagator is defined for the first-order-in-u wave equation.
Because the paper notes that the type-K conformal Carroll algebra arises from the Nappi-Witten metric, a parallel phase-space construction for that background would give a bulk dual for the other seven-generator conformal Carroll vacuum.
The reflection $k\leftrightarrow 2-k$ identifies isometry algebras at different z values; if the full asymptotic algebras are also isomorphic, this would produce a family of dualities between anisotropic Carrollian CFTs with different scaling exponents.

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.

Desk Editor's Note

read the letter

Quick take: this is a serious contribution to Carrollian holography. The field-theory half—stress tensor, transformation laws, two-vacuum correlators—is careful and extends known results cleanly. The bulk identification of the z=0 plane wave (1.2) with the seven-generator type-D algebra is new, and the Killing computation checks out. The general-z phase spaces are a natural extension. This deserves a real referee.

On the stress-test: the claim that the phase space is empty does not hold up. The determinant condition (4.19) does force h_zz=h_zbarzbar=h=0, so the transverse metric is exactly the vacuum. But the phase space also contains A_a and B_a, left free by the gauge, which give a non-trivial family of asymptotically plane-wave metrics. The residual diffeos (4.35) preserve that family; the Lie derivatives of the transverse metric vanish on the restricted class, so the determinant condition is preserved. The algebra derivation does not rest on an empty set.

There is still a real gap. The paper advertises the phase space as containing general transverse metric fluctuations, but the gauge condition forbids them. The residual-diffeomorphism calculation is run on the larger ansatz without explicitly enforcing the determinant condition, so it is unclear whether the algebra is for the intended class. The fix is straightforward: restrict (4.22) to the actual phase space and redo the calculation, or make the gauge condition asymptotic and state falloffs. The same issue affects the z≠0 phase space (4.42) for k≠1. This is a Section 4.2/4.3 revision, not a conceptual collapse.

Minor soft spots: the causal-boundary discussion is honest but leaves z<1 and k=1 in tension with the chosen holographic hypersurface; the authors acknowledge it. The field-theory section could state normal-ordering conventions more explicitly, but the correlators are consistent with the vacua.

This is for anyone in Carrollian or flat holography, near-horizon symmetries, or anisotropic CFTs. Section 3 stands alone. My recommendation: send to peer review, with a requirement to fix the phase-space characterization under the determinant gauge.

Referee Report

3 major / 4 minor

Summary. The paper develops both field-theoretic and gravitational aspects of anisotropic conformal Carroll symmetries with scaling exponent z. On the field theory side, it constructs the Carrollian stress tensor for d=2 and d=3, derives transformation laws, and solves Ward identities for two-point functions under two different vacuum choices, obtaining power-law and ultra-local branches. On the gravity side, it identifies four-dimensional plane wave metrics whose isometry algebra is the seven-generator type-D z=0 conformal Carroll algebra, and defines phase spaces of asymptotically plane wave metrics whose residual diffeomorphisms are claimed to realize the infinite-dimensional d=3 conformal Carroll algebra for general z, with a d=2 analogue. The paper also discusses the conformal boundary of these plane waves and their relation to warped CFTs and BMS symmetries.

Significance. If the bulk phase space construction worked, the paper would provide a concrete bottom-up framework for anisotropic Carrollian holography, complementing existing warped-flat and near-horizon constructions. The global isometry match between the plane wave metrics (4.5)/(4.6) and the seven-generator type-D algebra is a useful, explicit result, and the field-theory correlator analysis appears internally consistent and parameter-free: the Ward identities are solved directly, and the delta-function branch correctly yields the scaling-dimension constraints (e.g., Δ1+Δ2=2 in d=3). The paper is also candid about overlap with prior work [47,57,83]. However, the bulk phase space as defined has an internal inconsistency that affects the central asymptotic-symmetry claim, so the gravitational half of the paper needs substantive revision.

major comments (3)

[§4.2, Eqs. (4.19)–(4.22)] The determinant gauge condition is incompatible with the intended family of phase-space metrics. Substituting the ansatz (4.22) into ∂_u det(e^{-u} h_ab)=0 gives ∂_u det(e^{-u}h_ab) = -2e^{-2u}(h_zz h_zbarzbar - h^2) + e^{-u}h. Since e^{-2u} and e^{-u} are linearly independent, the condition for all u forces h=0 and h_zz h_zbarzbar=0, hence h_zz=h_zbarzbar=0 for a real metric. The phase space is therefore not the advertised family with fluctuating transverse metric: only A_a and B_a remain arbitrary, while the transverse metric is fixed to that of the vacuum (4.5). The statement that (4.21)–(4.22) defines a phase space of asymptotically plane wave spacetimes with non-trivial transverse fluctuations is thus not correct as written.
[§4.2, Eqs. (4.32)–(4.37)] The derivation of the residual diffeomorphism algebra breaks down once the determinant gauge is enforced. With h_zz=h_zbarzbar=0, preservation of g_zz=0 for all metrics in the phase space requires, in addition to ∂_z ξ^zbar=0, that ∂_z ξ^u=0 for generic A_a,B_a; the antiholomorphic component similarly gives ∂_zbar ξ^z=0 and ∂_zbar ξ^u=0. These conditions force ξ^z=az+b and ξ^zbar=czbar+d, with ξ^u constant. Consequently the modes L_n in (4.37) with |n|>1 do not preserve the phase space, and the algebra generated by (4.35)–(4.37) is not the residual symmetry algebra of (4.21)–(4.22). The step (4.34), which uses the variation of the diagonal spatial metric components to conclude ξ^z=f^z(z) with arbitrary f^z, assumes those components are free functions; that assumption is invalid once (4.19) forces them to vanish. The same obstruction applies to the z≠0 phase space (4.42) under the gauge (4.41) for k≠1.
[§2, Eqs. (2.8)–(2.9)] The mode expansion (2.8) and the claimed commutator (2.9) are inconsistent. For z=0 (k→∞), (2.8) gives L_n=-z^{n+1}∂_z and M_{r,s}=z^r zbar^s∂_t, hence [L_n,M_{r,s}]=-r M_{n+r,s}; (2.9) instead gives (1/2-r) M_{n+r,s}. For generic z, a direct computation from (2.8) yields [L_n,M_{r,s}]=-(r+z(n+1))M_{n+r,s}, not the expression in (2.9). Since the field-theory transformation laws in §3.1 and Table 2 rely on these brackets, this discrepancy should be resolved; if a different convention for M_{r,s} is intended, it should be stated explicitly.

minor comments (4)

[§4.2, around Eq. (4.18)] The isometry generators in (4.18) use a sign convention for L_0 that differs from the asymptotic modes in (4.37); for example L_0 in (4.18) is -∂_u+z∂_z, whereas the n=0 mode in (4.37) is ∂_u-z∂_z. The isomorphism between the two is only up to an overall sign on L_0, and this should be stated explicitly to avoid confusion.
[§3.1 and throughout] There are several typographical issues: 'T able' and 'T ransformation' in Section 3.1, 'realised' for 'realized' in places, and the matrix in (4.50) uses '×' without defining the symmetric entries. These should be fixed in a final version.
[§3.2, Eqs. (3.34) and (3.51)] The delta functions in the two-point functions are written with inconsistent notation, e.g., δ_{Q1+Q2} versus δ(Q1+Q2) or δ_{Q1+Q2,0}. Please standardize this notation.
[§4.5] The conformal-boundary analysis for the family (4.6) is interesting, but the text should state explicitly which notion of boundary (causal, conformal, or Penrose) is being used when comparing the hypersurfaces u→+∞ and u=0; this would clarify the discussion around Eqs. (4.63)–(4.69).

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: isometries, residual diffeomorphisms, and correlators are obtained by direct computation rather than by fitting or self-referential definition.

full rationale

The central claims are derived by explicit calculation rather than by construction from the target result. The isometry algebras of the plane-wave metrics (4.5) and (4.6) are computed from the Killing equations, and the residual diffeomorphism algebra in Section 4.2 is obtained by imposing the gauge conditions (4.19) and solving the Lie-derivative constraints; the resulting vector fields (4.35) and modes (4.37) are then recognized as the d=3 z=0 conformal Carroll algebra. This is a constructive bottom-up match, not a case where the target algebra was inserted as an ansatz or fitted parameter. Similarly, the Carrollian stress-tensor transformations and correlators follow from the assumed symmetry algebra and Ward identities, with no parameter fitted to the final correlators. Prior results from the literature, such as [47] for Carroll isometries of plane waves and [57] for conformal Carroll algebras, are invoked as external inputs and are not replaced by unverified self-citations; self-citations to [64,72,75] are contextual discussions of Warped backgrounds and do not carry the load of the new derivation. The phase-space ansatz in (4.21)-(4.22) is designed so that the residual diffeomorphisms reproduce the desired algebra, but the algebra itself is not presupposed in the calculation; it is the output of solving the preservation conditions. A separate concern has been raised that (4.22) may fail to satisfy the determinant gauge (4.19) except for the vacuum metric, but that would be an internal consistency or correctness issue, not a circularity in which the conclusion is equivalent to the input by definition. Under the standards of this pass, no step reduces to its own inputs, so the circularity score is 0.

Assumptions & free parameters 0 free parameters · 5 assumptions · 0 invented entities

The paper introduces no fitted numerical parameters; the scaling exponent z (or k) labels the family of theories and is not determined by data. The main axioms are the Carrollian geometric definitions (degenerate metric, kernel vector, conformal isometry equations), the vacuum choices, the Ward identity machinery, and the identification of plane wave spacetimes as bulk duals. The weakest unstated premise is the consistency of the phase space (4.21)-(4.22) with the gauge condition (4.19), which fails except at the vacuum. No new particles, forces, or fundamental entities are postulated.

assumptions (5)

domain assumption The anisotropic conformal Carroll symmetry algebra is defined by solving (2.4) with level k, giving the infinite-dimensional algebra (2.9).
This is the working definition of the symmetry group; the paper imports the framework from [42,54,101] and solves the conformal Killing equations (§2).
domain assumption The boundary of the plane wave spacetime is a codimension-one null hypersurface, e.g., u=constant, whose induced geometry is Carrollian with kernel ∂_v.
Projection of bulk isometries onto this hypersurface generates the field theory algebra (§4.2-4.4).
domain assumption Ward identities determine the correlation functions, assuming the existence of the two vacua (3.28) and (3.46).
Standard CFT machinery; the vacuum choices are the point of distinction between WCFT and Carrollian theories (§3.2).
domain assumption Plane waves are exact string backgrounds, so they are legitimate gravitational duals.
Used to justify the bulk side of the proposed duality, citing [91,92] (§4.1).
standard math Distribution identities for the delta function, such as (z∂z+z̄∂z̄)δ^{(2)}(z,z̄)=-2δ^{(2)} and xδ'(x)=-δ(x).
Used in the Ward identity derivations in §3.2.

how reviews work

0 comments

Cite this review

Pith. "Pith review of Anisotropic conformal Carroll field theories and their gravity duals." pith.science (2026). https://pith.science/paper/XX32VRPA

@misc{pith2026250523755,
  author       = {Pith},
  title        = {Pith review of: Anisotropic conformal Carroll field theories and their gravity duals},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/XX32VRPA}},
  note         = {Machine review of arXiv:2505.23755}
}

abstract

We investigate anisotropic conformal Carroll field theories and their holographic duals. On the field theory side, we focus on the case with scaling exponent $z=0$ in two and three spacetime dimensions. These theories exhibit infinite-dimensional symmetry algebras, including supertranslations and superrotations, and are closely related to, but distinct from, Warped Conformal Field Theories. We construct the associated Carrollian stress tensor, derive its transformation properties, and analyse the structure of correlation functions under different choices of vacua. On the gravity side, we identify three and four-dimensional plane wave geometries whose isometry algebras realise the two- and three-dimensional Carroll algebra and anisotropic scale transformations. We propose, for each scaling exponent, a phase space of asymptotically-plane wave spacetimes and show that the residual diffeomorphisms reproduce the expected conformal Carroll field theory algebra, establishing a framework for anisotropic Carrollian holography.

Discussion (0). Sign in to comment.

Forward citations

Cited by 2 Pith papers

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

Scaling Symmetry and Carrollian Gravity
hep-th 2025-12 conditional novelty 7.0 of 10

A single scaling-Carroll gauge-theory construction interpolates between dynamical Carroll gravity, Aristotelian gravity, and fracton gauge theories coupled to curved space.
Lectures on Carrollian Holography
hep-th 2025-11 conditional novelty 3.0 of 10

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.

Reference graph

Works this paper leans on

101 extracted references · 11 canonical work pages · cited by 2 Pith papers

[1]

’t Hooft,Dimensional reduction in quantum gravity,Conf

G. ’t Hooft,Dimensional reduction in quantum gravity,Conf. Proc.C930308(1993) 284–296, [gr-qc/9310026]

arXiv 1993
[2]

Susskind,The World as a hologram,J

L. Susskind,The World as a hologram,J. Math. Phys.36(1995) 6377–6396, [hep-th/9409089]

arXiv 1995
[3]

J. M. Maldacena,The Large N limit of superconformal field theories and supergravity,Adv. Theor. Math. Phys.2(1998) 231–252, [hep-th/9711200]

arXiv 1998
[4]

Witten,Anti-de Sitter space and holography,Adv

E. Witten,Anti-de Sitter space and holography,Adv. Theor. Math. Phys.2(1998) 253–291, [hep-th/9802150]

arXiv 1998
[5]

S. S. Gubser, I. R. Klebanov and A. M. Polyakov,Gauge theory correlators from noncritical string theory,Phys. Lett.B428(1998) 105–114, [hep-th/9802109]

arXiv 1998
[6]

Leblond,Une nouvelle limite non-relativiste du group de Poincar´ e,Annales Poincare Phys.Theor.3(1965)

L. Leblond,Une nouvelle limite non-relativiste du group de Poincar´ e,Annales Poincare Phys.Theor.3(1965)

1965
[7]

N. D. Sen Gupta,On an analogue of the Galilei group,Nuovo Cim. A44(1966) 512–517

1966
[8]

Barnich and C

G. Barnich and C. Troessaert,Symmetries of asymptotically flat 4 dimensional spacetimes at null infinity revisited,Phys. Rev. Lett.105(2010) 111103, [0909.2617]

arXiv 2010

Show all 101 references

[9]

Barnich and C

G. Barnich and C. Troessaert,Aspects of the BMS/CFT correspondence,JHEP05(2010) 062, [1001.1541]

2010 arXiv
[10]

Duval, G

C. Duval, G. W. Gibbons and P. A. Horvathy,Conformal carroll groups and bms symmetry, Classical and Quantum Gravity31(Apr., 2014) 092001

2014
[11]

Bagchi,Correspondence between Asymptotically Flat Spacetimes and Nonrelativistic Conformal Field Theories,Phys

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

2010 arXiv
[12]

Bagchi and R

A. Bagchi and R. Fareghbal,BMS/GCA Redux: Towards Flatspace Holography from Non-Relativistic Symmetries,JHEP10(2012) 092, [1203.5795]

2012 arXiv
[13]

Barnich,Entropy of three-dimensional asymptotically flat cosmological solutions,JHEP 10(2012) 095, [1208.4371]

G. Barnich,Entropy of three-dimensional asymptotically flat cosmological solutions,JHEP 10(2012) 095, [1208.4371]

2012 arXiv
[14]

Bagchi, S

A. Bagchi, S. Detournay, R. Fareghbal and J. Sim´ on,Holography of 3D Flat Cosmological Horizons,Phys. Rev. Lett.110(2013) 141302, [1208.4372]

2013 arXiv
[15]

Barnich, A

G. Barnich, A. Gomberoff and H. A. Gonz´ alez,Three-dimensional Bondi-Metzner-Sachs invariant two-dimensional field theories as the flat limit of Liouville theory,Phys. Rev.D87 (2013) 124032, [1210.0731]

2013 arXiv
[16]

Barnich and H

G. Barnich and H. A. Gonzalez,Dual dynamics of three dimensional asymptotically flat Einstein gravity at null infinity,JHEP05(2013) 016, [1303.1075]

2013 arXiv
[17]

Bagchi, R

A. Bagchi, R. Basu, D. Grumiller and M. Riegler,Entanglement entropy in Galilean conformal field theories and flat holography,Phys. Rev. Lett.114(2015) 111602, [1410.4089]

2015 arXiv
[18]

Hartong,Holographic Reconstruction of 3D Flat Space-Time,JHEP10(2016) 104, [1511.01387]

J. Hartong,Holographic Reconstruction of 3D Flat Space-Time,JHEP10(2016) 104, [1511.01387]. – 32 –

2016 arXiv
[19]

Jiang, W

H. Jiang, W. Song and Q. Wen,Entanglement Entropy in Flat Holography,JHEP07 (2017) 142, [1706.07552]

2017 arXiv
[20]

Bagchi, R

A. Bagchi, R. Basu, A. Kakkar and A. Mehra,Flat Holography: Aspects of the dual field theory,JHEP12(2016) 147, [1609.06203]

2016 arXiv
[21]

Ciambelli, C

L. Ciambelli, C. Marteau, A. C. Petkou, P. M. Petropoulos and K. Siampos,Flat holography and Carrollian fluids,JHEP07(2018) 165, [1802.06809]

2018 arXiv
[22]

Donnay, A

L. Donnay, A. Fiorucci, Y. Herfray and R. Ruzziconi,A Carrollian Perspective on Celestial Holography,2202.04702

arXiv
[23]

Bagchi, S

A. Bagchi, S. Banerjee, R. Basu and S. Dutta,Scattering Amplitudes: Celestial and Carrollian,Phys. Rev. Lett.128(2022) 241601, [2202.08438]

2022 arXiv
[24]

Donnay, A

L. Donnay, A. Fiorucci, Y. Herfray and R. Ruzziconi,Bridging Carrollian and Celestial Holography,2212.12553

arXiv
[25]

Bagchi, P

A. Bagchi, P. Dhivakar and S. Dutta,AdS Witten diagrams to Carrollian correlators,JHEP 04(2023) 135, [2303.07388]

2023 arXiv
[26]

Nguyen and P

K. Nguyen and P. West,Carrollian conformal fields and flat holography,2305.02884

arXiv
[27]

Mason, R

L. Mason, R. Ruzziconi and A. Yelleshpur Srikant,Carrollian amplitudes and celestial symmetries,JHEP05(2024) 012, [2312.10138]

2024 arXiv
[28]

L. F. Alday, M. Nocchi, R. Ruzziconi and A. Yelleshpur Srikant,Carrollian Amplitudes from Holographic Correlators,2406.19343

arXiv
[29]

Kraus and R

P. Kraus and R. M. Myers,Carrollian Partition Functions and the Flat Limit of AdS, 2407.13668

arXiv
[30]

P.-X. Hao, K. Shinmyo, Y.-k. Suzuki, S. Takahashi and T. Takayanagi,Bulk Reconstruction of Scalar Excitations in Flat 3/CCFT2 and the Flat Limit from (A)dS 3/CFT2,2505.20084
[31]

Bagchi, A

A. Bagchi, A. Banerjee, R. Basu, M. Islam and S. Mondal,Magic Fermions: Carroll and Flat Bands,2211.11640

arXiv
[32]

Bidussi, J

L. Bidussi, J. Hartong, E. Have, J. Musaeus and S. Prohazka,Fractons, dipole symmetries and curved spacetime,SciPost Phys.12(2022) 205, [2111.03668]

2022 arXiv
[33]

Kasikci, M

O. Kasikci, M. Ozkan, Y. Pang and U. Zorba,Carrollian supersymmetry and SYK-like models,Phys. Rev. D110(2024) L021702, [2311.00039]

2024 arXiv
[34]

Figueroa-O’Farrill, A

J. Figueroa-O’Farrill, A. P´ erez and S. Prohazka,Carroll/fracton particles and their correspondence,JHEP06(2023) 207, [2305.06730]

2023 arXiv
[35]

Figueroa-O’Farrill, A

J. Figueroa-O’Farrill, A. P´ erez and S. Prohazka,Quantum Carroll/fracton particles, 2307.05674

arXiv
[36]

de Boer, J

J. de Boer, J. Hartong, N. A. Obers, W. Sybesma and S. Vandoren,Carroll Symmetry, Dark Energy and Inflation,Front. in Phys.10(2022) 810405, [2110.02319]

2022 arXiv
[37]

de Boer, J

J. de Boer, J. Hartong, N. A. Obers, W. Sybesma and S. Vandoren,Carroll stories, 2307.06827

arXiv
[38]

Bagchi,Tensionless Strings and Galilean Conformal Algebra,JHEP05(2013) 141, [1303.0291]

A. Bagchi,Tensionless Strings and Galilean Conformal Algebra,JHEP05(2013) 141, [1303.0291]

2013 arXiv
[39]

Bagchi, S

A. Bagchi, S. Chakrabortty and P. Parekh,Tensionless Strings from Worldsheet Symmetries,JHEP01(2016) 158, [1507.04361]. – 33 –

2016 arXiv
[40]

Bagchi, A

A. Bagchi, A. Banerjee, S. Chakrabortty and R. Chatterjee,A Rindler road to Carrollian worldsheets,JHEP04(2022) 082, [2111.01172]

2022 arXiv
[41]

Kachru, X

S. Kachru, X. Liu and M. Mulligan,Gravity duals of Lifshitz-like fixed points,Phys. Rev. D 78(2008) 106005, [0808.1725]

2008 arXiv
[42]

Bekaert, A

X. Bekaert, A. Campoleoni and S. Pekar,Holographic Carrollian conformal scalars,JHEP 05(2024) 242, [2404.02533]

2024 arXiv
[43]

D. T. Son,Toward an AdS/cold atoms correspondence: A Geometric realization of the Schrodinger symmetry,Phys. Rev. D78(2008) 046003, [0804.3972]

2008 arXiv
[44]

Balasubramanian and J

K. Balasubramanian and J. McGreevy,Gravity duals for nonrelativistic conformal field theories,Physical Review Letters101(Aug., 2008)

2008
[45]

Taylor,Non-relativistic holography,0812.0530

M. Taylor,Non-relativistic holography,0812.0530

arXiv
[46]

X. Dong, S. Harrison, S. Kachru, G. Torroba and H. Wang,Aspects of holography for theories with hyperscaling violation,JHEP06(2012) 041, [1201.1905]

2012 arXiv
[47]

Duval, G

C. Duval, G. W. Gibbons, P. A. Horvathy and P. M. Zhang,Carroll symmetry of plane gravitational waves,Class. Quant. Grav.34(2017) 175003, [1702.08284]

2017 arXiv
[48]

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
[49]

D. E. Berenstein, J. M. Maldacena and H. S. Nastase,Strings in flat space and pp waves from N=4 superYang-Mills,JHEP04(2002) 013, [hep-th/0202021]

2002 arXiv
[50]

Marolf and S

D. Marolf and S. F. Ross,Plane waves: to infinity and beyond!,Classical and Quantum Gravity19(Nov., 2002) 6289–6302

2002
[51]

V. E. Hubeny and M. Rangamani,Causal structures of pp-waves,Journal of High Energy Physics2002(Dec., 2002) 043–043

2002
[52]

Henneaux,Geometry of Zero Signature Space-times,Bull

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

1979
[53]

Hartong,Gauging the Carroll Algebra and Ultra-Relativistic Gravity,JHEP08(2015) 069, [1505.05011]

J. Hartong,Gauging the Carroll Algebra and Ultra-Relativistic Gravity,JHEP08(2015) 069, [1505.05011]

2015 arXiv
[54]

Duval, G

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
[55]

Farahmand Parsa, H

A. Farahmand Parsa, H. R. Safari and M. M. Sheikh-Jabbari,On rigidity of 3d asymptotic symmetry algebras,Journal of High Energy Physics2019(Mar., 2019)

2019
[56]

Chen, P.-X

B. Chen, P.-X. Hao and Z.-F. Yu,2d Galilean Field Theories with Anisotropic Scaling, Phys. Rev. D101(2020) 066029, [1906.03102]

2020 arXiv
[57]

Afshar, X

H. Afshar, X. Bekaert and M. Najafizadeh,Classification of Conformal Carroll Algebras, 2409.19953

arXiv
[58]

Compere and S

G. Compere and S. Detournay,Boundary conditions for spacelike and timelike warpedAdS 3 spaces in topologically massive gravity,JHEP08(2009) 092, [0906.1243]

2009 arXiv
[59]

Compere and S

G. Compere and S. Detournay,Centrally extended symmetry algebra of asymptotically Godel spacetimes,JHEP03(2007) 098, [hep-th/0701039]

2007 arXiv
[60]

Compere and S

G. Compere and S. Detournay,Semi-classical central charge in topologically massive gravity,Class. Quant. Grav.26(2009) 012001, [0808.1911]. – 34 –

2009 arXiv
[61]

Blagojevic and B

M. Blagojevic and B. Cvetkovic,Asymptotic structure of topologically massive gravity in spacelike stretched AdS sector,JHEP09(2009) 006, [0907.0950]

2009 arXiv
[62]

Henneaux, C

M. Henneaux, C. Martinez and R. Troncoso,Asymptotically warped anti-de Sitter spacetimes in topologically massive gravity,Phys. Rev. D84(2011) 124016, [1108.2841]

2011 arXiv
[63]

Anninos, G

D. Anninos, G. Compere, S. de Buyl, S. Detournay and M. Guica,The Curious Case of Null Warped Space,JHEP11(2010) 119, [1005.4072]

2010 arXiv
[64]

Detournay, W

S. Detournay, W. Merbis, G. S. Ng and R. Wutte,Warped Flatland,JHEP11(2020) 061, [2001.00020]

2020 arXiv
[65]

Anninos, W

D. Anninos, W. Li, M. Padi, W. Song and A. Strominger,Warped AdS(3) Black Holes, JHEP03(2009) 130, [0807.3040]

2009 arXiv
[66]

Isra¨ el, C

D. Isra¨ el, C. Kounnas, D. Orlando and P. Marios Petropoulos,Electric/magnetic deformations of s3 and ads3, and geometric cosets,Fortschritte der Physik53(Dec., 2004) 73–104

2004
[67]

Rooman and P

M. Rooman and P. Spindel,G¨ odel metric as a squashed anti-de sitter geometry,Classical and Quantum Gravity15(Oct., 1998) 3241–3249

1998
[68]

Bouchareb and G

A. Bouchareb and G. Cl´ ement,Black hole mass and angular momentum in topologically massive gravity,Classical and Quantum Gravity24(Nov., 2007) 5581–5594

2007
[69]

Nutku,Exact solutions of topologically massive gravity with a cosmological constant, Classical and Quantum Gravity10(dec, 1993) 2657

Y. Nutku,Exact solutions of topologically massive gravity with a cosmological constant, Classical and Quantum Gravity10(dec, 1993) 2657

1993
[70]

G¨ urses,Perfect Fluid Sources in 2+1 Dimensions,Class

M. G¨ urses,Perfect Fluid Sources in 2+1 Dimensions,Class. Quant. Grav.11(1994) 2585

1994
[71]

D. M. Hofman and A. Strominger,Chiral Scale and Conformal Invariance in 2D Quantum Field Theory,Phys. Rev. Lett.107(2011) 161601, [1107.2917]

2011 arXiv
[72]

Detournay, T

S. Detournay, T. Hartman and D. M. Hofman,Warped Conformal Field Theory,Phys. Rev. D86(2012) 124018, [1210.0539]

2012 arXiv
[73]

Donnay, G

L. Donnay, G. Giribet, H. A. Gonzalez and M. Pino,Supertranslations and Superrotations at the Black Hole Horizon,Phys. Rev. Lett.116(2016) 091101, [1511.08687]

2016 arXiv
[74]

Grumiller, A

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) 041601, [1908.09833]

2020 arXiv
[75]

Afshar, S

H. Afshar, S. Detournay, D. Grumiller, W. Merbis, A. Perez, D. Tempo et al.,Soft Heisenberg hair on black holes in three dimensions,Phys. Rev. D93(2016) 101503, [1603.04824]

2016 arXiv
[76]

D. M. Hofman and B. Rollier,Warped conformal field theory as lower spin gravity,Nuclear Physics B897(2015) 1–38

2015
[77]

G. S. Hall,Symmetries and curvature structure in general relativity, vol. 46. world scientific, 2004

2004
[78]

Baiguera, G

S. Baiguera, G. Oling, W. Sybesma and B. T. Søgaard,Conformal Carroll Scalars with Boosts,2207.03468

arXiv
[79]

Dutta,Stress tensors of 3d Carroll CFTs,Phys

S. Dutta,Stress tensors of 3d Carroll CFTs,Phys. Lett. B853(2024) 138672, [2212.11002]

2024 arXiv
[80]

J. R. Klauder,Beyond conventional quantization. Cambridge University Press, 12, 2005. – 35 –

2005
[81]

Henneaux and P

M. Henneaux and P. Salgado-Rebolledo,Carroll contractions of Lorentz-invariant theories, JHEP11(2021) 180, [2109.06708]

2021 arXiv
[82]

Banerjee, R

K. Banerjee, R. Basu, A. Mehra, A. Mohan and A. Sharma,Interacting Conformal Carrollian Theories: Cues from Electrodynamics,Phys. Rev. D103(2021) 105001, [2008.02829]

2021 arXiv
[83]

Song and J

W. Song and J. Xu,Correlation Functions of Warped CFT,JHEP04(2018) 067, [1706.07621]

2018 arXiv
[84]

Blau,Plane waves and penrose limits,Lecture notes for the ICTP school on mathematics in string and field theory (June 2-13 2003)(2011)

M. Blau,Plane waves and penrose limits,Lecture notes for the ICTP school on mathematics in string and field theory (June 2-13 2003)(2011)

2011
[85]

Blau and M

M. Blau and M. O’Loughlin,Homogeneous plane waves,Nucl. Phys. B654(2003) 135–176, [hep-th/0212135]

2003 arXiv
[86]

Penrose,Any space-time has a plane wave as a limit,Differential geometry and relativity (1976) 271–275

R. Penrose,Any space-time has a plane wave as a limit,Differential geometry and relativity (1976) 271–275

1976
[87]

Singh,de-Sitter space, (D)pp-waves and star-matrix model,Journal of High Energy Physics2005(June, 2005) 061–061

H. Singh,de-Sitter space, (D)pp-waves and star-matrix model,Journal of High Energy Physics2005(June, 2005) 061–061

2005
[88]

M. Blau, M. Borunda, M. O’Loughlin and G. Papadpoulos,The universality of penrose limits near space-time singularities,Journal of High Energy Physics2004(July, 2004) 068–068

2004
[89]

M. Blau, J. Figueroa-O Farrill and G. Papadopoulos,Penrose limits, supergravity and brane dynamics,Classical and Quantum Gravity19(Sept., 2002) 4753–4805

2002
[90]

H. Fuji, K. Ito and Y. Sekino,Penrose limit and string theories on various brane backgrounds,Journal of High Energy Physics2002(Nov., 2002) 005–005

2002
[91]

Amati and C

D. Amati and C. Klimcik,Nonperturbative Computation of the Weyl Anomaly for a Class of Nontrivial Backgrounds,Phys. Lett. B219(1989) 443–447

1989
[92]

G. T. Horowitz and A. R. Steif,Strings in Strong Gravitational Fields,Phys. Rev. D42 (1990) 1950–1959

1990
[93]

Berenstein and H

D. Berenstein and H. Nastase,On lightcone string field theory from super yang-mills and holography, 2002

2002
[94]

Papadopoulos, J

G. Papadopoulos, J. G. Russo and A. A. Tseytlin,Solvable model of strings in a time-dependent plane-wave background,Classical and Quantum Gravity20(Feb., 2003) 969–1016

2003
[95]

Fransen,Quasinormal modes from Penrose limits,Class

K. Fransen,Quasinormal modes from Penrose limits,Class. Quant. Grav.40(2023) 205004, [2301.06999]

2023 arXiv
[96]

Sadri and M

D. Sadri and M. M. Sheikh-Jabbari,The Plane wave / superYang-Mills duality,Rev. Mod. Phys.76(2004) 853, [hep-th/0310119]

2004 arXiv
[97]

Compere, S

G. Compere, S. de Buyl, S. Detournay and K. Yoshida,Asymptotic symmetries of Schr¨ odinger spacetimes,JHEP10(2009) 032, [0908.1402]

2009 arXiv
[98]

Deser, R

S. Deser, R. Jackiw and S. Templeton,Topologically Massive Gauge Theories,Annals Phys. 140(1982) 372–411

1982
[99]

Deser, R

S. Deser, R. Jackiw and S. Templeton,Three-Dimensional Massive Gauge Theories,Phys. Rev. Lett.48(1982) 975–978. – 36 –

1982
[100]

Grumiller, A

D. Grumiller, A. P´ erez, M. M. Sheikh-Jabbari, R. Troncoso and C. Zwikel,Spacetime structure near generic horizons and soft hair,Physical Review Letters124(Jan., 2020)

2020
[101]

H. R. Safari and M. M. Sheikh-Jabbari,Bms4 algebra, its stability and deformations, Journal of High Energy Physics2019(Apr., 2019) . – 37 –

2019

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.

[1] [1]

’t Hooft,Dimensional reduction in quantum gravity,Conf

G. ’t Hooft,Dimensional reduction in quantum gravity,Conf. Proc.C930308(1993) 284–296, [gr-qc/9310026]

arXiv 1993

[2] [2]

Susskind,The World as a hologram,J

L. Susskind,The World as a hologram,J. Math. Phys.36(1995) 6377–6396, [hep-th/9409089]

arXiv 1995

[3] [3]

J. M. Maldacena,The Large N limit of superconformal field theories and supergravity,Adv. Theor. Math. Phys.2(1998) 231–252, [hep-th/9711200]

arXiv 1998

[4] [4]

Witten,Anti-de Sitter space and holography,Adv

E. Witten,Anti-de Sitter space and holography,Adv. Theor. Math. Phys.2(1998) 253–291, [hep-th/9802150]

arXiv 1998

[5] [5]

S. S. Gubser, I. R. Klebanov and A. M. Polyakov,Gauge theory correlators from noncritical string theory,Phys. Lett.B428(1998) 105–114, [hep-th/9802109]

arXiv 1998

[6] [6]

Leblond,Une nouvelle limite non-relativiste du group de Poincar´ e,Annales Poincare Phys.Theor.3(1965)

L. Leblond,Une nouvelle limite non-relativiste du group de Poincar´ e,Annales Poincare Phys.Theor.3(1965)

1965

[7] [7]

N. D. Sen Gupta,On an analogue of the Galilei group,Nuovo Cim. A44(1966) 512–517

1966

[8] [8]

Barnich and C

G. Barnich and C. Troessaert,Symmetries of asymptotically flat 4 dimensional spacetimes at null infinity revisited,Phys. Rev. Lett.105(2010) 111103, [0909.2617]

arXiv 2010