What is Classical Null String Theory?

H. Yavartanoo; M.M. Sheikh-Jabbari

REVIEW

What is Classical Null String Theory?

M.M. Sheikh-Jabbari, H. Yavartanoo

High Energy Physics - Theory · Submitted 4 Sep 2026 · 26 references

Pith's verdict: A clear, honest companion paper that demotes the ILST action to a partially gauged sigma-model and adds a third first-class constraint, but the central claim rests on a stated definitional criterion rather than a theorem, and the full analysis lives in the authors' own companion papers.

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arXiv ID2609.04844 (version 1)

Pith IDTWMOUJ5M, Pith's permanent record of this paper and its review

CitationH. Yavartanoo, M.M. Sheikh-Jabbari. "What is Classical Null String Theory?." arXiv:2609.04844 (2026). https://pith.science/paper/TWMOUJ5M

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Claim paper

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Editor's note

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You should know two things. First, the central result is not new here: the Carroll-Weyl gauged action and the constraint P·X=0 come from the authors' companion papers [15,17], and the paper says so. Second, the claim that ILST is not a null string theory is conditional on a definitional criterion they state in Section 2.2: every local change of representative of the intrinsic Carrollian geometry must be gauged. If you accept that, the rest follows cleanly. If you don't, there is no contradiction in ILST that forces C3.

What the paper does well: it cleanly separates a consistent sigma-model from a gauge-complete string theory, and it fixes a sensible logical order — necessity from representational redundancy, admissibility from the zero-tension Poisson algebra. Appendix B gives the explicit constraint algebra for C1, P·X', and P·X, and it looks right; the algebra closes as first-class at zero tension. The finite-tension obstruction in (2.15) is a plausible reason why this extra symmetry cannot be gauged for tensile strings. Section 3 is the freshest part: treating the null string as a congruence of null geodesics, where preserving the constraint surface under the combined diffeo + Carroll-Weyl transformation forces P·Q=0 for arbitrary α(σ). That is a neat, self-contained argument, and the D−3 degree-of-freedom count follows consistently.

Soft spots, in proportion. The load-bearing criterion is asserted, not derived. The paper does not show that ILST overcounts in a way that produces wrong physics; it says the theory is consistent but gauge-incomplete under this criterion. A reader with a more permissive definition — ILST plus its own gauge symmetries is the null string — can reject the conclusion, and the paper gives no argument that would move that reader. Second, the full classical analysis of the gauged action is deferred to self-cited companions; you cannot check the W_a equation-of-motion derivation from this preprint alone. Third, the authors are honest that translation symmetry is not manifest in the gauged action, and that is a real open point.

On balance, the argument holds if the criterion is accepted, and the weak spot is exactly where the stress-test puts it. The paper is clearly written, credits [15,17] properly, and does not oversell. I would send it to a serious referee — the conceptual distinction matters and the companion chain deserves scrutiny — but I would ask the authors to state the criterion as a postulate rather than a consequence, and to either include the W_a derivation or make the deferral explicit. The audience is people working on tensionless strings, Carrollian holography, and null string quantization.

Referee report

Significance

If correct, the paper sharpens the classical definition of the null string: the ILST action would be a consistent but gauge-incomplete Carrollian sigma-model, and the genuine null string would include a third first-class constraint C3 and its gauge quotient, reducing local degrees of freedom from D-2 to D-3. This distinction matters for the growing literature on tensionless strings, Carrollian geometry, and near-horizon/null hypersurface physics. The paper also provides a physically transparent target-space interpretation in terms of null geodesic congruences, extends the BMS3/χ-symmetry story, and usefully separates the question of why C3 should be imposed (necessity from Carrollian representative redundancy) from whether it can be imposed (admissibility from the first-class algebra). The explicit constraint algebra in Appendix B is a concrete, checkable asset, as is the explicit obstruction formula in Eq. (2.15). Stated caveats (flat target, classical level, translation non-invariance of the minimal gauged action) are acknowledged.

Major objections (5)

[Sec. 2.2, first paragraph and Eq. (2.8)] The central claim that ILST is not a physical null string theory rests on the asserted criterion that a physical string theory must gauge every local change of worldsheet representative. This criterion is stated as a postulate and is not derived from any standard definition, action principle, or demonstrated physical inconsistency (e.g. overcounting of states, unitarity violation, or contradictory predictions). A reader who defines the null string directly by the ILST action and its manifest gauge symmetries (diffeomorphisms plus Weyl) will not be forced to accept the conclusion. The manuscript would be substantially strengthened by showing an observable consequence that distinguishes the partially gauged system from the fully gauged one—for instance, a concrete two-point function, a partition function, or a classical phase-space counting argument that shows the D-2 system genuinely overcounts—rather than relying on the asserted necessity. As written this is the load-bearing premise and it is not established by the paper's own dynamics.
[Sec. 2.3, Eqs. (2.9)-(2.11)] The minimal gauged action assigns Carroll-Weyl weight +1 to X^mu and introduces a connection W_a. This is presented as 'the minimal realization' and hence as a uniqueness claim, but no uniqueness theorem is proved: one could imagine other minimal completions that gauge the relative rescaling with different field content, different weights, or non-minimal couplings, and the paper does not show that the physical content (C3=0 plus the quotient) is independent of such choices. Since Secs. 2.3 and 4 draw conclusions about the 'physical null string theory' from this specific completion, the construction choice should be framed as such, or complemented by an argument that all admissible minimal completions yield the same constraint and quotient.
[Sec. 3, Eq. (3.5b) and the derivation of C3] The geodesic-congruence argument derives C3=P·Q=0 by demanding that the constraint surface C1=C2=0 be preserved under the combined transformation (3.4). This is a consistency argument for the gauged system, but it does not establish the necessity premise: the partially gauged ILST system with only C1 and C2 has perfectly consistent configurations with P·Q != 0, and the paper itself notes in Sec. 4 that the ILST χ(σ) symmetry organizes solutions into sectors labelled by C3(σ). The argument therefore converts the definitional criterion of Sec. 2.2 into a preservation condition; it does not independently demonstrate physical distinctness of the C3 sectors. The text should be explicit that (3.5b) is a consequence of imposing the Carroll-Weyl gauge equivalence, not evidence that the equivalence itself is mandatory.
[Sec. 2.3 and Appendix B, Eq. (2.15)] The admissibility of C3 at zero tension is supported by the first-class algebra in Appendix B, but the Poisson brackets are computed only for the smeared constraints on the ILST phase space after temporal gauge fixing. Since the paper's conclusion concerns the fully gauged action (2.9), the reader cannot fully verify within this preprint that the Hamiltonian analysis of (2.9) before gauge fixing yields exactly the same first-class system with C3 as the Gauss law; the details are deferred to refs. [15,17]. This deferral is acceptable for a companion-paper chain, but the manuscript should at least state the assumptions used in [15,17] (e.g. the treatment of W_a as an independent field vs. auxiliary) so that the constraint algebra claim is checkable in principle.
[Sec. 4, last paragraph and Sec. C] The paper honestly notes that the minimal gauged action (2.9) breaks the rigid target-space translation symmetry (4.1) that the ILST action enjoys. Since global translations are part of the Poincare symmetry of the Minkowski background and of the standard string spectrum (zero modes), a proposed definition of the classical null string should either preserve translations or explain why the loss is acceptable (e.g. as a feature of the gauge-fixed representative rather than of the quotient). As written, the translation issue is flagged as beyond scope, but it is directly relevant to whether (2.9) can serve as the fundamental definition of the null string on flat space; the paper should clarify whether the full theory (with quotient) retains a non-manifest translation symmetry or genuinely loses it.

Minor objections (5)

[Abstract and Sec. 2.3] The abstract and Sec. 2.3 use 'P·X=0 physicality constraint' and later 'C3:=P·Q=0' without always distinguishing the gauge-invariant statement P·X=0 from its temporal-gauge form P·Q=0. Since P·X = tau P^2 + P·Q, the distinction matters on the constraint surface; a short notational remark would prevent confusion.
[Sec. 3, Eqs. (3.1)-(3.5)] The notation for transformed objects (P_tilde, Q_tilde, C_tilde) is clear, but Eq. (3.5b) contains a somewhat dense combination of parameters; writing the infinitesimal version or defining b/a ratio explicitly would improve readability.
[Sec. 2.1 and Eq. (2.3)] The review of the ILST action is brief; in particular the derivation that V^a equations of motion give P^2=0 and P·X'=0 is only implicit. A one-sentence derivation or a reference to the specific equation in [15] would help the reader who wants to check the starting point.
[References] Several key references are to companion papers [15,16,17] and [20]; the paper would benefit from stating explicitly which results are established there and which are established here. In particular, the full classical analysis of (2.9) and the phase-space count 2(D-3) are cited to [15-17] and not shown in this preprint.
[Appendix A, Eq. (A.8)] The variation of the bare kinetic term under χ is given, but the integration-by-parts details for the gauged action (2.9) are omitted. A short explicit check that (2.10) transforms as a covariant derivative would be useful for the reader.

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The paper

The paper claims

A physical null string theory must gauge Carroll-Weyl scaling, adding a third constraint that reduces local degrees of freedom from D-2 to D-3.

The reading

This paper argues that the standard action for null strings, the ILST action, is not a complete description of a physical string theory because it fails to gauge all worldsheet redundancies. Carrollian worldsheets admit two independent rescalings: the common Weyl rescaling (which is gauged in the ILST action) and the Carroll-Weyl rescaling (which is not). The authors show that gauging Carroll-Weyl symmetry forces a new first-class constraint, P·X = 0, and identifies configurations along its orbits. The resulting theory has 2(D−3) local phase-space degrees of freedom, whereas the ungauged ILST theory has 2(D−2). Clarifying this distinction is a prerequisite for quantization and for linking null strings to horizon physics.

What carries the argument

Carroll-Weyl scaling: the relative rescaling of the temporal and spatial representatives of a Carrollian worldsheet that leaves the volume form invariant. The paper gauges this symmetry by introducing a connection W_a and assigning X^μ Carroll-Weyl weight 1, resulting in a Gauss-law constraint P·X = 0 that distinguishes the null string from the partially gauged ILST $\sigma$-model.

Extended reading notes

Core claim

The core discovery is that classical null string theory is not the ILST action alone, but the ILST action supplemented with a Carroll-Weyl gauge symmetry and its associated Gauss-law constraint P·X = 0 (or in temporal gauge P·Q = 0). The paper demonstrates that a Carrollian worldsheet possesses two independent local scalings—common Weyl and Carroll-Weyl—and that both must be gauged for the $\sigma$-model to describe a physical string. By introducing a minimal Carroll-Weyl connection and assigning Carroll-Weyl weight 1 to X^μ, the authors construct a gauged action that reduces to the ILST form in a particular gauge but retains the extra constraint as a first-class constraint. This constraint, together with the ILST constraints, closes an extended BMS algebra and reduces the local configuration-space degrees of freedom from D−2 to D−3.

Load-bearing premise

The paper assumes that a physical string theory must gauge every local change of worldsheet representative, a criterion that is stated as necessary but not derived from any more fundamental principle or universally agreed definition.

Editorial extensions

If this is right

Null string quantization must include the third constraint P·X = 0, potentially altering the spectrum and anomaly structure compared to quantizations based solely on the ILST action.
The classical null string phase space has 2(D−3) local degrees of freedom, one fewer than previously assumed, which affects state counting in applications such as black hole entropy.
The extended BMS algebra generated by the three first-class constraints (P^2, P·X', P·X) provides the correct gauge algebra for null strings, analogous to Virasoro for tensile strings.
Generalizations to curved target spaces must incorporate the Carroll-Weyl connection in a background-covariant way, which may introduce additional geometric constraints.
The separation between tensionless limit and intrinsic Carrollian gauging clarifies that the null string cannot be obtained simply by taking T→0 of the tensile string; an extra symmetry principle is needed.

Reading between the lines

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

If the paper is correct, many previous works on null strings that used only the ILST action likely described a partially gauged sigma-model rather than a full string theory; their results (e.g., on symmetries, spectra, or holography) may need re-evaluation with the third constraint.
The necessity of Carroll-Weyl gauging suggests that null string theory is intrinsically a Carrollian conformal field theory, where the Caroll-Weyl connection plays a role similar to the spin connection in worldsheet gravity.
The third constraint reduces the local degrees of freedom, which may resolve or shift puzzles in the tensionless limit, such as the counting of physical states or the appearance of zero modes.
The distinction may have observable consequences for strings near black hole horizons (which are Carrollian), possibly affecting the entropy or scattering calculations in that context.

Original abstract

We revisit the classical definition of a null string in a D-dimensional Minkowski target space and distinguish a consistent partially-gauged Carrollian sigma-model from the null string theory. The Isberg-Lindstr\"om-Sundborg-Theodoridis (ILST) action gauges worldsheet diffeomorphisms and the common Weyl rescaling, but not the independent relative rescaling of the temporal and spatial representatives of the intrinsic Carrollian structure, Carroll-Weyl scaling. A physical string theory requires every local change of worldsheet representative to be gauged, therefore, the Carroll-Weyl symmetry should be gauged in a null string theory. In the minimal realization, the corresponding gauging is obstructed at finite tension, whereas at zero tension it yields an additional first-class constraint and the associated identification of physical configurations along its gauge orbits. The description of the null worldsheet as a congruence of null geodesics provides a complementary target-space interpretation of gauging of the Carroll-Weyl scaling. Our analysis thus provides the supplementary requirements that turns the ILST theory into the null string theory.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 5,074 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.44 · human participants 0.01 · controlled comparison 0.07 · randomized assignment 0.01 · states quantitative result 0.10 · compares with prior results 0.76 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; show every role.

We revisit the classical definition of a null string in a D-dimensional Minkowski target space and distinguish a consistent partially-gauged Carrollian sigma-model from the null string theory. The Isberg-Lindstr\"om-Sundborg-Theodoridis (ILST) action gauges worldsheet diffeomorphisms and the common Weyl rescaling, but not the independent relative rescaling of the temporal and spatial representatives of the intrinsic Carrollian structure, Carroll-Weyl scaling. A physical string theory requires every local change of worldsheet representative to be gauged, therefore, the Carroll-Weyl symmetry should be gauged in a null string theory. In the minimal realization, the corresponding gauging is obstructed at finite tension, whereas at zero tension it yields an additional first-class constraint and the associated identification of physical configurations along its gauge orbits. The description of the null worldsheet as a congruence of null geodesics provides a complementary target-space interpretation of gauging of the Carroll-Weyl scaling. Our analysis thus provides the supplementary requirements that turns the ILST theory into the null string theory.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We revisit the classical definition of a null string in a D-dimensional Minkowski target space and distinguish a consistent partially-gauged Carrollian sigma-model from the null string theory.	contribution 0.93	0.84	0.17	asserted 0.99
s1	The Isberg-Lindstr\"om-Sundborg-Theodoridis (ILST) action gauges worldsheet diffeomorphisms and the common Weyl rescaling, but not the independent relative rescaling of the temporal and spatial representatives of the intrinsic Carrollian structure, Carroll-Weyl scaling.	background 0.59	0.19	0.08	asserted 1.00
s2	A physical string theory requires every local change of worldsheet representative to be gauged, therefore, the Carroll-Weyl symmetry should be gauged in a null string theory.	interpretation 0.55	0.33	0.28	asserted 0.99
s3	In the minimal realization, the corresponding gauging is obstructed at finite tension, whereas at zero tension it yields an additional first-class constraint and the associated identification of physical configurations along its gauge orbits.	result 0.99	0.76	0.19	asserted 1.00
s4	The description of the null worldsheet as a congruence of null geodesics provides a complementary target-space interpretation of gauging of the Carroll-Weyl scaling.	interpretation 0.98	0.71	0.08	asserted 0.97
s5	Our analysis thus provides the supplementary requirements that turns the ILST theory into the null string theory.	result 0.62	0.88	0.72	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.97 · evidence from proof or derivation 0.83.

What was examined, and what was not

sources read

arXiv listing abstract v1

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

References

Works cited (26)

[1]

A. M. Polyakov, “Quantum geometry of bosonic strings,”Phys. Lett.B103(1981) 207–210

View on Pith 1981
[2]

M. B. Green, J. H. Schwarz, and E. Witten,Superstring Theory. Cambridge University Press, 1987. Vol. 1: Introduction

View on Pith 1987
[3]

J. Polchinski, “String theory. Vol. 2: Superstring theory and beyond,”. Cambridge, UK: Univ. Pr. (1998) 531 p

View on Pith 1998
[4]

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

View on Pith 1968
[5]

C. Duval, G. Gibbons, P. Horvathy, and P. Zhang, “Carroll versus Newton and Galilei: two dual non-Einsteinian concepts of time,”1402.0657

View on Pith Pith review arXiv
[6]

C. Duval, G. Gibbons, and P. Horvathy, “Conformal Carroll groups,”1403.4213

View on Pith Pith review arXiv
[7]

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

View on Pith Pith review arXiv 2015
[8]

L. Ciambelli, R. G. Leigh, C. Marteau, and P. M. Petropoulos, “Carroll Structures, Null Geometry and Conformal Isometries,”Phys. Rev. D100(2019), no. 4, 046010,1905.02221

View on Pith Pith review arXiv 2019
[9]

Y. Herfray, “Carrollian manifolds and null infinity: a view from Cartan geometry,”Class. Quant. Grav.39 (2022), no. 21, 215005,2112.09048

View on Pith Pith review arXiv 2022
[10]

L. Ciambelli and P. Jai-akson, “Foundations of Carrollian Geometry,”2510.21651

View on Pith Pith review arXiv
[11]

A. Schild, “Classical Null Strings,”Phys. Rev. D16(1977) 1722

View on Pith 1977
[12]

J. Isberg, U. Lindstrom, and B. Sundborg, “Space-time symmetries of quantized tensionless strings,”Phys. Lett. B293(1992) 321–326,hep-th/9207005

View on Pith Pith review arXiv 1992
[13]

J. Isberg, U. Lindstrom, B. Sundborg, and G. Theodoridis, “Classical and quantized tensionless strings,” Nucl. Phys. B411(1994) 122–156,hep-th/9307108

View on Pith Pith review arXiv 1994
[14]

A. Bagchi, A. Banerjee, R. Chatterjee, and P. Pandit, “The tensionless lives of null strings,”Phys. Rept. 1185(2026) 1–91,2601.20959

View on Pith arXiv 2026
[15]

M. M. Sheikh-Jabbari and H. Yavartanoo, “Null strings gauged and reloaded, I: Null strings have Carroll-Weyl gauge symmetry,”Phys. Lett. B880(2026) 140824,2605.25817

View on Pith Pith review arXiv 2026
[16]

M. M. Sheikh-Jabbari and H. Yavartanoo, “On the Consistency of Null Strings Literature: The Tale of an Overlooked Symmetry,”2605.12414

View on Pith Pith review arXiv
[17]

M. M. Sheikh-Jabbari and H. Yavartanoo, “Null strings gauged and reloaded, II: Consistent classical treatment of the null strings,”Phys. Lett. B880(2026) 140775,2605.26822. – 10 –

View on Pith Pith review arXiv 2026
[18]

H. Gustafsson, U. Lindstrom, P. Saltsidis, B. Sundborg, and R. van Unge, “Hamiltonian BRST quantization of the conformal string,”Nucl. Phys. B440(1995) 495–520,hep-th/9410143

View on Pith Pith review arXiv 1995
[19]

U. Lindström, “The conformal null string ind+ 2andddimensions,”2606.22498

View on Pith Pith review arXiv
[20]

I. M. Rasulian, M. M. Sheikh-Jabbari, and H. Yavartanoo, “Null-strings Gauged, Reloaded and Quantized, I: Canonical Quantization in the Light-Cone Gauge,”2607.02970

View on Pith Pith review arXiv
[21]

A. Bagchi, A. Banerjee, J. Hartong, E. Have, K. S. Kolekar, and M. Mandlik, “Strings near black holes are Carrollian,”Phys. Rev. D110(2024), no. 8, 086009,2312.14240

View on Pith Pith review arXiv 2024
[22]

A. Bagchi, A. Banerjee, J. Hartong, E. Have, and K. S. Kolekar, “Strings near black holes are Carrollian. Part II,”JHEP11(2024) 024,2407.12911

View on Pith Pith review arXiv 2024
[23]

A. Bagchi, A. Bhattacharya, S. Rajesh Iyer, and K. Narayan, “Blackhole near horizons through the looking glass,”JHEP08(2026) 088,2602.20267

View on Pith Pith review arXiv 2026
[24]

S. Duary and S. Maji, “Path integral quantization of null bosonic strings with Carroll-Weyl ghosts,” 2606.04999

View on Pith Pith review arXiv
[25]

S. Duary and S. Maji, “BRST quantization of Carroll-Weyl gauged null strings,”2608.02731

View on Pith Pith review arXiv
[26]

B. Chen and Z. Hu, “Quantum Anomalies of Tensionless Bosonic Strings,”2608.02987. – 11 –

View on Pith Pith review arXiv

Forward citations

Cited by 5 Pith papers

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

Null Strings Gauged, Reloaded and Quantized, II: Null Strings on Flat Backgorund Have Discrete Spectrum
hep-th 2026-11 conditional novelty 6.0 of 10

Within a regular separated Schrödinger sector, the paper derives a discrete, nonnegative mass-squared spectrum mu^2=m(m-1) for bosonic null strings on flat space, with no critical dimension and no tachyons.
Reflected constraint algebras of open Carroll--Weyl null strings
hep-th 2026-10 conditional novelty 6.0 of 10

Open Carroll-Weyl null strings have a reflected classical phase space whose boundary algebra is the boundary Carrollian conformal algebra extended by one weight-one current, with D-3 local embedding pairs.
Carrollian Worldsheets on Carrollian Targets, When does ILST describe a null string theory?
hep-th 2026-10 conditional novelty 6.0 of 10

On Carrollian target spaces with a homothetic kernel generator, the CW-gauged null string action equals the ILST action off shell, making the two theories classically equivalent.
Trinity of Carrollian Gravity: Dynamically Equivalent Formulations of Magnetic Carrollian Gravity
hep-th 2026-10 conditional novelty 6.0 of 10

Magnetic Carrollian gravity is recast into dynamically equivalent Electric Carrollian, fracton-like tensor gauge, Maxwell electric, and dilaton theories by trading curvature for torsion and non-metricity.
Null String Holography, Null Strings Probe Projective Boundary of Their Target Spaces
hep-th 2026-09 conditional novelty 6.0 of 10

Minimal null string theory on a background manifold is classically equivalent to the tensionless ILST string theory on the projective boundary of that manifold, giving concrete AdS, dS, and flat-space duals.

Discussion

Disagree with the review, or know something it missed? Leave a comment, highlight any passage above to comment on it, or challenge this review formally.

[1] [1]

A. M. Polyakov, “Quantum geometry of bosonic strings,”Phys. Lett.B103(1981) 207–210

View on Pith 1981

[2] [2]

M. B. Green, J. H. Schwarz, and E. Witten,Superstring Theory. Cambridge University Press, 1987. Vol. 1: Introduction

View on Pith 1987

[3] [3]

J. Polchinski, “String theory. Vol. 2: Superstring theory and beyond,”. Cambridge, UK: Univ. Pr. (1998) 531 p

View on Pith 1998

[4] [4]

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

View on Pith 1968

[5] [5]

C. Duval, G. Gibbons, P. Horvathy, and P. Zhang, “Carroll versus Newton and Galilei: two dual non-Einsteinian concepts of time,”1402.0657

View on Pith Pith review arXiv

[6] [6]

C. Duval, G. Gibbons, and P. Horvathy, “Conformal Carroll groups,”1403.4213

View on Pith Pith review arXiv

[7] [7]

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

View on Pith Pith review arXiv 2015

[8] [8]

L. Ciambelli, R. G. Leigh, C. Marteau, and P. M. Petropoulos, “Carroll Structures, Null Geometry and Conformal Isometries,”Phys. Rev. D100(2019), no. 4, 046010,1905.02221

View on Pith Pith review arXiv 2019

[9] [9]

Y. Herfray, “Carrollian manifolds and null infinity: a view from Cartan geometry,”Class. Quant. Grav.39 (2022), no. 21, 215005,2112.09048

View on Pith Pith review arXiv 2022

[10] [10]

L. Ciambelli and P. Jai-akson, “Foundations of Carrollian Geometry,”2510.21651

View on Pith Pith review arXiv

[11] [11]

A. Schild, “Classical Null Strings,”Phys. Rev. D16(1977) 1722

View on Pith 1977

[12] [12]

J. Isberg, U. Lindstrom, and B. Sundborg, “Space-time symmetries of quantized tensionless strings,”Phys. Lett. B293(1992) 321–326,hep-th/9207005

View on Pith Pith review arXiv 1992

[13] [13]

J. Isberg, U. Lindstrom, B. Sundborg, and G. Theodoridis, “Classical and quantized tensionless strings,” Nucl. Phys. B411(1994) 122–156,hep-th/9307108

View on Pith Pith review arXiv 1994

[14] [14]

A. Bagchi, A. Banerjee, R. Chatterjee, and P. Pandit, “The tensionless lives of null strings,”Phys. Rept. 1185(2026) 1–91,2601.20959

View on Pith arXiv 2026

[15] [15]

M. M. Sheikh-Jabbari and H. Yavartanoo, “Null strings gauged and reloaded, I: Null strings have Carroll-Weyl gauge symmetry,”Phys. Lett. B880(2026) 140824,2605.25817

View on Pith Pith review arXiv 2026

[16] [16]

M. M. Sheikh-Jabbari and H. Yavartanoo, “On the Consistency of Null Strings Literature: The Tale of an Overlooked Symmetry,”2605.12414

View on Pith Pith review arXiv

[17] [17]

M. M. Sheikh-Jabbari and H. Yavartanoo, “Null strings gauged and reloaded, II: Consistent classical treatment of the null strings,”Phys. Lett. B880(2026) 140775,2605.26822. – 10 –

View on Pith Pith review arXiv 2026

[18] [18]

H. Gustafsson, U. Lindstrom, P. Saltsidis, B. Sundborg, and R. van Unge, “Hamiltonian BRST quantization of the conformal string,”Nucl. Phys. B440(1995) 495–520,hep-th/9410143

View on Pith Pith review arXiv 1995

[19] [19]

U. Lindström, “The conformal null string ind+ 2andddimensions,”2606.22498

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