Pith. sign in

REVIEW 4 major objections 3 minor 4 cited by

This paper claims that the non-relativistic limit of bosonic supergravity can be formulated purely in metric terms, using a torsionless affine connection with fixed non-metricities, and that this reproduces the vielbein string Newton–Cartan

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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

T0 review · deepseek-v4-flash

2026-08-03 12:18 UTC pith:FSFIZNO2

load-bearing objection Metric-only reformulation of NR bosonic supergravity that could save labor, but the non-metricity inputs are asserted and one equation has undefined frame fields, so the equivalence claim is not yet shown. the 4 major comments →

arxiv 2601.03342 v4 pith:FSFIZNO2 submitted 2026-01-06 hep-th gr-qc

Curvatures and Non-metricities in the Non-Relativistic Limit of Bosonic Supergravity

Eric Lescano This is my paper
classification hep-th gr-qc
keywords non-relativistic limitbosonic supergravitystring Newton-Cartan geometrynon-metricitytorsionless connectioncurvature decompositionalpha-prime correctionsmetric formulation
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

This paper claims that the non-relativistic (NR) limit of bosonic supergravity can be described entirely in terms of metric variables, using a torsionless affine connection together with a fixed set of non-metricity tensors. The non-metricities are determined by requiring compatibility with the relativistic metric before the c→∞ expansion, and they allow every term in the c-expansion of the Riemann tensor, Ricci tensor, and scalar curvature to be rewritten in a manifestly diffeomorphism-covariant form. If this is right, the finite two-derivative NR bosonic supergravity action can be written without vielbeins or spin connections, and higher-derivative α′ corrections can be organized order by order in c. The paper further claims the resulting metric Lagrangian is equivalent to the vielbein string Newton–Cartan formulation at the level of the action.

Core claim

The paper's central claim is that a torsionless affine connection built from the NR fields τ and h, together with non-metricity tensors Q that are fixed by the relativistic Levi-Civita compatibility conditions, provides a complete covariant decomposition of the relativistic curvature tensors in the non-relativistic limit. Concretely, the c^4, c^2, c^0, c^{-2}, and c^{-4} pieces of the relativistic Riemann tensor are each written as combinations of covariant derivatives of τ and h using Γ and the Q-tensors. The same is done for the Ricci tensor and scalar. This yields a manifestly diffeomorphism-covariant, pure-metric formula for the finite two-derivative bosonic supergravity Lagrangian in th

What carries the argument

The central objects are the torsionless connection Γ^ρ_{μν}(τ,h) = ½ h^{ρσ}(2∂_{(μ}h_{ν)σ} − ∂_σ h_{μν}) + ½ τ^{ρσ}(2∂_{(μ}τ_{ν)σ} − ∂_σ τ_{μν}) and the four non-metricity tensors Q^{(τ)}_{μνρ}, Q^{(τ^{-1})}_{μ}{}^{νρ}, Q^{(h)}_{μνρ}, Q^{(h^{-1})}_{μ}{}^{νρ} defined in Eqs. (21)–(24). These Q's encode the failure of the NR fields to be parallel under Γ; they are fixed by demanding compatibility with the relativistic metric. The method works by rewriting the partial derivatives appearing in the c-expansion of the relativistic Levi-Civita connection as covariant derivatives plus Q-terms, thereby making every order in c manifestly covariant under diffeomorphisms.

Load-bearing premise

The load-bearing premise is that the non-metricity tensors (21)–(24), fixed by relativistic metric compatibility, are both well-defined and uniquely determined; in particular Eq. (21) uses objects e_{ρa'} that are never defined, so the premise is currently unverifiable.

What would settle it

Compute the right-hand side of Eq. (21) in a simple coordinate system: since e_{ρa'} is undefined, the expression cannot be evaluated, so the construction as written lacks a well-defined check. Alternatively, expand a known relativistic background in c, compute the c^0 piece of the Riemann tensor directly, and compare with Eq. (32); any mismatch would falsify the decomposition.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • The finite two-derivative NR bosonic supergravity Lagrangian can be written in a manifestly covariant, pure-metric form, avoiding vielbeins and spin connections.
  • Every relativistic curvature invariant admits a covariant decomposition in powers of c, making the NR limit of higher-derivative α′ corrections a bookkeeping problem rather than a divergent-expansion problem.
  • The existence of the decomposition supports the view that the NR limit of bosonic supergravity is a non-metric geometry whose non-metricities carry the information normally carried by torsion in the vielbein string Newton–Cartan picture.
  • Choosing a different set of non-metricities (e.g., all zero) yields a family of f(R,Q) Newton–Cartan gravities, though the boost symmetry of the supergravity NR limit is then lost.

Where Pith is reading between the lines

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

  • One consequence the paper leaves implicit: if the decomposition is valid, the same metric mechanism should extend to heterotic and other supergravity NR limits, since it relies only on the gravitational sector.
  • The undefined e_{ρa'} in Eq. (21) suggests the advertised 'pure metric' construction is not yet self-contained; a reader cannot independently check the non-metricity definitions without an extra, unstated definition.
  • A concrete way to stress-test the paper: apply Eq. (32) to a known background and compare with the direct c-expansion of the Riemann tensor; the identity should hold order by order.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 3 minor

Summary. The paper proposes a metric-only, torsionless affine connection \Gamma (Eq. 10), taken as the c^0 part of the relativistic Levi-Civita connection, and uses it to define covariant derivatives of the non-relativistic fields \tau_{\mu\nu}, h_{\mu\nu}, \tau^{\mu\nu}, h^{\mu\nu}. The resulting non-metricities (17)-(20) are said to be fixed by requiring compatibility with the relativistic metric before taking c\to\infty. On this basis the paper claims a fully covariant decomposition of the relativistic Riemann, Ricci and scalar curvatures (Eqs. 25-43), a finite non-relativistic bosonic supergravity Lagrangian (Eq. 44), and an equivalence with the vielbein string Newton-Cartan formulation of [13] at the level of the action. Applications to finite \alpha' corrections and to f(R,Q) Newton-Cartan theories are also sketched.

Significance. If the central construction is correct, it would give a practical purely metric route to non-relativistic supergravity actions, avoiding spin connections and vielbeins, and would provide a systematic way to organize NR limits of higher-derivative invariants. The paper contains explicit candidate decompositions and an explicit finite two-derivative Lagrangian, and the proposed f(R,Q) extension is a potentially useful idea. However, the main result is conditional on several unproved steps: the fixed non-metricities are asserted rather than derived, one of them is written with undefined frame-like symbols, the replacement of partial derivatives by covariant derivatives is not justified, and the claimed equivalence to [13] is not demonstrated by a term-by-term mapping. These are load-bearing gaps, not presentation issues.

major comments (4)
  1. [§III, Eq. (21)] The expression for Q^{(\tau)}_{\mu\nu\rho} contains objects e^\alpha_{a'} and e_\rho^{a'} that are never defined and are not part of the advertised metric data (\tau_{\mu\nu}, h_{\mu\nu}, \tau^{\mu\nu}, h^{\mu\nu}). This contradicts the pure-metric claim and makes Eq. (21) unusable as it stands. Since the non-metricities (21)-(24) feed directly into the covariant curvature decompositions and the Lagrangian (44), the derivation must be supplied: expand \hat\nabla_\mu \hat g_{\nu\rho}=0 using (1)-(2), define all symbols, and show that the resulting Q's are uniquely fixed. If frame-like fields are genuinely needed, the 'metric only' framing must be revised.
  2. [§IV, Eqs. (26)-(32)] The passage from partial-derivative expressions such as (26) to covariant-derivative expressions such as (27) is asserted without proof. Because the connection (10) has nonzero non-metricities, \nabla_\mu\tau_{\nu\rho} and \nabla_\mu h_{\nu\rho} differ from the corresponding partial derivatives by connection terms. For example, the combination \nabla_\alpha\tau_{[\mu\sigma]} - \nabla_\sigma\tau_{[\mu\alpha]} is not identically equal to its partial-derivative counterpart unless the connection terms cancel or are absorbed into the fixed Q's. The paper gives no such computation. This is a direct load-bearing step for the claimed covariant decomposition of the relativistic Riemann tensor.
  3. [§V.A and §VI] The claimed action-level equivalence to the vielbein string Newton-Cartan formulation of [13] is not established. Equation (44) is presented as the finite NR bosonic supergravity Lagrangian, but no term-by-term identification with the SNC action is provided. The paper itself concedes that compatibility at the level of equations of motion is not guaranteed and that it is unclear whether the torsion constraint of [13] is required in the metric approach. If the two Lagrangians agree only after imposing a torsion constraint, they are not equivalent as actions on the same unconstrained field space. Either provide an explicit dictionary and a proof of equality, or substantially weaken the equivalence claim.
  4. [§V.B, Eq. (48) and Appendix A] The finite contributions from the Metsaev-Tseytlin Lagrangian are obtained by applying the curvature decompositions whose derivation is the unresolved issue in the preceding comments. The extremely long expressions in (48) and (A1)-(A3) are not independently checked or compared with any known limit. These application results should be presented as conditional on the covariant decomposition, or the missing derivation should be supplied first.
minor comments (3)
  1. [§III, after Eq. (21)] The text says 'the relativistic metric conditions (21)-(21)' but should refer to (21)-(24).
  2. [§V.A, Eq. (44)] The notation e^{-1} in the Lagrangian is not defined in this purely metric formalism; presumably it denotes the inverse volume density, but this should be stated explicitly.
  3. [§II, Eq. (10)] It would help to state explicitly that \Gamma is the c^0 part of the relativistic Levi-Civita connection and to show that this part indeed transforms as a connection; this is asserted but not demonstrated.

Circularity Check

0 steps flagged

No significant circularity: the non-metricities are fixed by relativistic metric compatibility, and the curvature decompositions are algebraic rewritings; the asserted equivalence with [13] is a support gap, not a circular reduction.

full rationale

The paper's core derivation is not circular under the rubric. The torsionless connection (10) is defined from the NR metric data, and the non-metricities (17)-(20) are claimed to be fixed by the stated compatibility conditions, \hat\nabla\hat g=0, rather than by the target Lagrangian (44). The curvature decompositions (26)-(43) are presented as algebraic rewritings of the relativistic Levi-Civita curvatures in terms of \nabla and the Q tensors; even if (21)-(24) are asserted rather than derived, and Eq. (21) uses undefined frame-like e's, nothing in those equations is fitted to (44) or renamed as a prediction. The claimed equivalence with [13] is not established term by term—the paper itself states in Sec. V.A that 'compatibility at the equations of motion is not guaranteed, since it is not clear that the torsion constraint found in [13] is required in the metric approach'—but an unverified equivalence claim is a correctness/completeness gap, not a circular reduction. The self-citations [41]-[42] are used only for the alpha-prime scaling in an application section and are not load-bearing for the central decomposition. No uniqueness theorem from the authors' prior work is invoked to force the choice of Q, and no fitted parameter is relabeled as a prediction. Therefore no specific circular step meets the evidentiary bar; the low score reflects minor support gaps rather than circularity.

Axiom & Free-Parameter Ledger

1 free parameters · 4 axioms · 0 invented entities

No new physical fields, particles, or dimensions are postulated. The non-metricity tensors are new mathematical bookkeeping, not independent entities. The main free parameters are the arbitrary coefficients a1, a2 in the speculative f(R,Q) extension; the central derivation has no fitted parameters.

free parameters (1)
  • a1, a2 (coefficients of the f(R,Q) Lagrangian when Q=0) = arbitrary
    Eq. (54) introduces the general Lagrangian L_NR|Q=0 = a1 R_{\mu\nu} h^{\mu\nu} + a2 R_{\mu\nu} \tau^{\mu\nu} with undetermined coefficients; these are ad hoc choices, not fitted to data, and belong to a speculative extension rather than the main derivation.
axioms (4)
  • domain assumption The c→\infty expansion (1)-(4) of the relativistic fields, together with the projection conditions (5)-(7), is the correct controlled NR limit.
    The whole construction uses the split ĝ = c^2 τ + h, ĝ^{-1} = c^{-2} τ^{μν} + h^{μν}, B̂ = -c^2 c + b, φ̂ = ln c + φ, inherited from [13]. If the scaling or the constraints are different, the decomposition changes.
  • ad hoc to paper The affine connection Γ in Eq. (10), the c^0 part of the relativistic Levi-Civita connection, is torsionless and is the right connection for covariantizing NR quantities.
    The paper chooses this connection to mimic the relativistic construction. No proof of uniqueness or of equivalence to the torsionful string Newton-Cartan connection is given; the equivalence is asserted only at the Lagrangian level.
  • domain assumption The non-metricities (21)-(24) are completely fixed by the relativistic metric compatibility conditions and need no additional input.
    The paper states these are 'the fixed values' following from ∇̂ĝ = 0 after expansion, but the derivation is not shown. Since they are central to covariantizing the curvatures, this is a load-bearing input.
  • domain assumption The cancellation that keeps the two-derivative action finite in the NR limit is inherited from the vielbein computation of [13].
    Section I invokes the non-trivial cancellation from [13]; the metric-only Lagrangian (44) is presented as using previous-section results, not as a self-contained derivation of finiteness.

pith-pipeline@v1.3.0-alltime-deepseek · 12743 in / 14401 out tokens · 133133 ms · 2026-08-03T12:18:39.082709+00:00 · methodology

0 comments
read the original abstract

We construct a metric-like formulation of the non-relativistic (NR) limit of bosonic supergravity at the Lagrangian level. This formulation is particularly useful for decomposing relativistic tensors, such as powers of the Riemann tensor, in a manifest covariant form with respect to infinitesimal diffeomorphisms. The construction is purely geometrical and is based on a torsionless connection, mimicking the construction of the relativistic theory. The formulation contains non-vanishing non-metricities, which are associated with the gravitational fields of the theory ($\tau_{\mu\nu}$, $h_{\mu\nu}$, $\tau^{\mu\nu}$, $h^{\mu\nu}$). The non-metricities are fixed by requiring compatibility with the relativistic metric, before taking the NR expansion. We provide a fully covariant decomposition of the relativistic Riemann tensor, Ricci tensor, and scalar curvature. Our results establish an equivalence between the vielbein approach of string Newton--Cartan geometry at the level of the Lagrangian and the proposed construction. We also discuss potential applications, including a pure metric rewriting of the two-derivative finite bosonic supergravity Lagrangian under the NR limit, a powerful simplification in deriving NR bosonic $\alpha'$-corrections and extensions to more general $f(R,Q)$ Newton--Cartan geometries.

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Forward citations

Cited by 4 Pith papers

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

  1. Carrollian limit of NS-NS and Heterotic Supergravity

    hep-th 2026-07 conditional novelty 7.0

    Ultra-relativistic expansion plus dilaton scaling produces finite covariant Carrollian NS-NS and heterotic supergravity actions, with trivializable Green-Schwarz for the 1-form and finite leading Riem^{2} α' corrections.

  2. Carrollian limit of NS-NS and Heterotic Supergravity

    hep-th 2026-07 conditional novelty 7.0

    A finite Carrollian limit of NS-NS and heterotic supergravity is constructed by field expansion, including a gauge sector, a Green-Schwarz mechanism analysis, and a finite leading α' correction.

  3. Carrollian bosonic supergravity at order $\alpha'$ and the universal cancellation of higher-curvature divergences

    hep-th 2026-07 conditional novelty 5.0

    Four-derivative and higher pure-gravitational α' corrections to bosonic supergravity admit a finite Carrollian limit, with an explicit action and a universal finiteness criterion for Riem^N terms.

  4. An Introduction to String Newton-Cartan Holography and Integrability

    hep-th 2026-03 accept novelty 3.0

    String Newton-Cartan holography, the non-relativistic limit of the AdS/CFT correspondence, is organized and reviewed around five consistency conditions, with its classical solutions, spectrum, and integrability structure.

Reference graph

Works this paper leans on

48 extracted references · 30 linked inside Pith · cited by 3 Pith papers

  1. [1]

    IIA/B, wound and wrapped,

    U. H. Danielsson, A. Guijosa, and M. Kruczenski, “IIA/B, wound and wrapped,” JHEP 10 (2000) 020, arXiv:hep- th/0009182

    arXiv 2000

  2. [2]

    Nonrelativistic closed string theory,

    J. Gomis and H. Ooguri, “Nonrelativistic closed string theory,” J. Math. Phys., vol. 42, pp. 3127–3151, 2001

    2001

  3. [3]

    Newtonian gravitons and D-brane collective coordinates in wound string theory,

    U. H. Danielsson, A. Guijosa, and M. Kruczenski, “Newtonian gravitons and D-brane collective coordinates in wound string theory,” JHEP 03 (2001) 041, arXiv:hep-th/0012183

    Pith/arXiv arXiv 2001

  4. [4]

    An Action for Extended String Newton-Cartan Gravity,

    E. A. Bergshoeff, K. T. Grosvenor, C. Simsek, and Z. Yan, “An Action for Extended String Newton-Cartan Gravity,” JHEP, vol. 01, p. 178, 2019

    2019

  5. [5]

    Relating non-relativistic string theories,

    T. Harmark, J. Hartong, L. Menculini, N. A. Obers, and G. Oling, “Relating non-relativistic string theories,” JHEP, vol. 11, p. 071, 2019

    2019

  6. [6]

    String Theory and String Newton-Cartan Geometry,

    E. A. Bergshoeff, J. Gomis, J. Rosseel, C. Simsek, and Z. Yan, “String Theory and String Newton-Cartan Geometry,” J. Phys. A, vol. 53, no. 1, p. 014001, 2020

    2020

  7. [7]

    Background Field Method for Nonlinear Sigma Models in Nonrelativistic String Theory,

    Z. Yan and M. Yu, “Background Field Method for Nonlinear Sigma Models in Nonrelativistic String Theory,” JHEP, vol. 03, p. 181, 2020

    2020

  8. [8]

    Null-killing vector dimensional reduction and galilean geometrodynamics,

    B. Julia and H. Nicolai, “Null-killing vector dimensional reduction and galilean geometrodynamics,” Nuclear Physics B, vol. 439, no. 1, pp. 291 – 323, 1995. 8

    1995

  9. [9]

    Nonrelativistic String Theory and T-Duality,

    E. Bergshoeff, J. Gomis, and Z. Yan, “Nonrelativistic String Theory and T-Duality,” JHEP, vol. 11, p. 133, 2018

    2018

  10. [10]

    Remark About Non-Relativistic String in Newton-Cartan Background and Null Reduction,

    J. Kluson, “Remark About Non-Relativistic String in Newton-Cartan Background and Null Reduction,” JHEP, vol. 05, p. 041, 2018

    2018

  11. [11]

    Nonrelativistic String Theory in Background Fields,

    J. Gomis, J. Oh, and Z. Yan, “Nonrelativistic String Theory in Background Fields,” JHEP 10 (2019) 101, arXiv:hep- th/1905.07315

    Pith/arXiv arXiv 2019

  12. [12]

    Torsional Newton Cartan gravity from non-relativistic strings,

    A. D. Gallegos, U. Gursoy, and N. Zinnato, “Torsional Newton Cartan gravity from non-relativistic strings,” JHEP 09 (2020) 172, arXiv:hep-th/1906.01607

    Pith/arXiv arXiv 2020

  13. [13]

    ,25 are space-time indices andc µν satisfiesc µρτ ρσcσν =τ µν

    by introducing an explicit expansion in powers ofc, ˆgµν =c 2τµν +h µν ,(1) ˆgµν = 1 c2 τ µν +h µν ,(2) ˆBµν =−c 2cµν +b µν ,(3) ˆϕ= ln(c) +φ ,(4) whereµ, ν= 0, . . . ,25 are space-time indices andc µν satisfiesc µρτ ρσcσν =τ µν. These variables satisfy the defining relations hµντνρ =h µνcνρ = 0,(5) hµντ νρ = 0,(6) hµνhνρ =δ ρ µ −τ µντ νρ ,(7) Although in...

    Pith/arXiv arXiv 2026

  14. [14]

    Bidussi, T

    L. Bidussi, T. Harmark, J. Hartong, N. A. Obers, and G. Oling, Torsional string Newton-Cartan geometry for non- relativistic strings, JHEP02(2022) 116, arXiv:hep-th/2107.00642

    Pith/arXiv arXiv 2022

  15. [15]

    E. A. Bergshoeff, J. Lahnsteiner, L. Romano, J. Rosseel and C.Simsek,´´A non-relativistic limit of NS-NS gravity´´, JHEP06(2021) 021, arXiv:hep-th/2102.06974

    Pith/arXiv arXiv 2021

  16. [16]

    The surprising structure of non-relativistic 11-dimensional supergravity,

    E. A. Bergshoeff, C. D. A. Blair, J. Lahnsteiner, and J. Rosseel, “The surprising structure of non-relativistic 11-dimensional supergravity,” JHEP 12 (2024) 010, arXiv:hep-th/2407.21648

    Pith/arXiv arXiv 2024

  17. [17]

    E. A. Bergshoeff, J. Lahnsteiner, L. Romano, J. Rosseel, and C. Simsek, ‘Non-relativistic ten-dimensional minimal super- gravity´, JHEP12(2021) 123, arXiv:hep-th/2107.14636

    Pith/arXiv arXiv 2021

  18. [18]

    Aspects of Nonrelativistic Strings,

    G. Oling and Z. Yan, “Aspects of Nonrelativistic Strings,” Front. in Phys. 10 (2022) 832271, arXiv:hep-th/2202.12698

    Pith/arXiv arXiv 2022

  19. [19]

    On the inclusion of statistical matter in the non-relativistic limit of NS-NS supergravity,

    E. Lescano, “On the inclusion of statistical matter in the non-relativistic limit of NS-NS supergravity,” Phys.Rev.D 110 (2024) 10, 106007, Phys.Rev.D 110 (2024) 106007

    2024

  20. [20]

    While the NR limit of NS-NS gravity has been deeply studied in [13], the authors have addressed the construc- tion in the vielbein formalism of NR theory

    and references therein). While the NR limit of NS-NS gravity has been deeply studied in [13], the authors have addressed the construc- tion in the vielbein formalism of NR theory. In this work we will reformulate this same setup, but using a fully met- ric approach, where the full Lorentz symmetry is man- ifest from the starting point. In other words, we ...

  21. [21]

    Review on Non-Relativistic Gravity

    J. Hartong, N. A. Obers, and G. Oling, “Review on Non-Relativistic Gravity”, arXiv:hep-th/2212.11309

    Pith/arXiv arXiv

  22. [22]

    Guijosa, “On the Underlying Nonrelativistic Nature of Relativistic Holography“, arXiv:hep-th/2502.03031

    A. Guijosa, “On the Underlying Nonrelativistic Nature of Relativistic Holography“, arXiv:hep-th/2502.03031

    Pith/arXiv arXiv

  23. [23]

    Order alpha-prime (Two Loop) Equivalence of the String Equations of Motion and the Sigma Model Weyl Invariance Conditions: Dependence on the Dilaton and the Antisymmetric Tensor,

    R. R. Metsaev and A. A. Tseytlin, “Order alpha-prime (Two Loop) Equivalence of the String Equations of Motion and the Sigma Model Weyl Invariance Conditions: Dependence on the Dilaton and the Antisymmetric Tensor,” Nucl. Phys. B 293(1987) 385

    1987

  24. [24]

    E. A. Bergshoeff and L. Romano, Non-relativistic heterotic string theory, JHEP 01 (2024) 146, arXiv:hep-th/2310.19716

    Pith/arXiv arXiv 2024

  25. [25]

    A Non-Relativistic Limit for Heterotic Supergravity and its Gauge Lagrangian

    E. Lescano, “A Non-Relativistic Limit for Heterotic Supergravity and its Gauge Lagrangian”, 2502.08711 [hep-th]

    Pith/arXiv arXiv

  26. [26]

    E. A. Bergshoeff, K. T. Grosvenor, L. Romano, Z. Yan, ”Heterotic string sigma models: discrete light cone quantization and its current-current deformation”, JHEP 09 (2025) 021, 2505.07458 [hep-th]

    Pith/arXiv arXiv 2025

  27. [27]

    Hull and B

    C. Hull and B. Zwiebach, ‘Double Field Theory”, JHEP0909(2009) 099, arXiv:hep-th/0904.4664]

    Pith/arXiv arXiv 2009

  28. [28]

    Generalized metric formulation of Double Field Theory

    O. Hohm, C. Hull and B. Zwiebach, “Generalized metric formulation of Double Field Theory”, JHEP1008(2010) 008, arXiv:hep-th/1006.4823

    Pith/arXiv arXiv 2010

  29. [29]

    Stringy differential geometry, beyond Riemann

    I. Jeon, K. Lee and J. H. Park, “Stringy differential geometry, beyond Riemann”, Phys. Rev. D84(2011) 044022, arXiv:hep-th/1105.6294

    Pith/arXiv arXiv 2011

  30. [30]

    Differential geometry with a projection: Application to Double Field Theory

    I. Jeon, K. Lee and J. H. Park, “Differential geometry with a projection: Application to Double Field Theory”, JHEP 1104(2011) 014, arXiv:hep-th/1011.1324

    Pith/arXiv arXiv 2011

  31. [31]

    Classification of non-Riemannian doubled-yet-gauged spacetime,

    K. Morand and J.-H. Park, “Classification of non-Riemannian doubled-yet-gauged spacetime,” Eur. Phys. J. C, vol.77, no. 10, p. 685, 2017. [Erratum: Eur.Phys.J.C 78, 901 (2018)]

    2017

  32. [32]

    A worldsheet supersymmetric Newton-Cartan string,

    C. D. A. Blair, “A worldsheet supersymmetric Newton-Cartan string,” JHEP, vol.10, p. 266, 2019, [arXiv:1908.00074]

    Pith/arXiv arXiv 2019

  33. [33]

    Remarks on the non-Riemannian sector in Double Field Theory

    K. Cho, J-H Park, “ Remarks on the non-Riemannian sector in Double Field Theory”, Eur.Phys.J.C80(2020) 2, 101, [arXiv:1909.10711]

    Pith/arXiv arXiv 2020

  34. [34]

    String Theory and non-Riemannian Geometry

    J.-H. Park, S. Sugimoto, “String Theory and non-Riemannian Geometry”, Phys.Rev.Lett.125(2020) 21, 211601, [arXiv:2008.03084]

    Pith/arXiv arXiv 2020

  35. [35]

    Non-Riemannian gravity actions from double field theory

    A.D. Gallegos, U. G¨ ursoy, S. Verma, N. Zinnato, “Non-Riemannian gravity actions from double field theory”, JHEP06 (2021) 173, [arXiv:2012.07765]

    Pith/arXiv arXiv 2021

  36. [36]

    Non-Riemannian isometries from double field theory

    C. D. A. Blair, G. Oling, and J.-H. Park, “Non-Riemannian isometries from double field theory”, JHEP04(2021) 072, [arXiv:2012.07766]

    Pith/arXiv arXiv 2021

  37. [37]

    N=1 supersymmetry and Non-Riemannian Double Field Theory

    E. Lescano, “N=1 supersymmetry and Non-Riemannian Double Field Theory”, [arXiv:2212.13853]

    Pith/arXiv arXiv

  38. [38]

    Identifying Riemannian Singularities with Regular Non-Riemannian Geometry,

    K. Morand, J. H. Park and M. Park, “Identifying Riemannian Singularities with Regular Non-Riemannian Geometry,” Phys. Rev. Lett. 128, no.4, 041602 (2022) doi:10.1103/PhysRevLett.128.041602 [arXiv:2106.01758 [hep-th]]

    Pith/arXiv arXiv 2022

  39. [39]

    Fractons, non-Riemannian geometry, and double field theory,

    S. Angus, M. Kim and J. H. Park, “Fractons, non-Riemannian geometry, and double field theory,” Phys. Rev. Res. 4, no.3, 033186 (2022) doi:10.1103/PhysRevResearch.4.033186 [arXiv:2111.07947 [hep-th]]

    Pith/arXiv arXiv 2022

  40. [40]

    Lescano and D

    E. Lescano and D. Osten, Non-relativistic limits of bosonic and heterotic Double Field Theory, JHEP 07 (2024) 286, arXiv:hep-th/2405.10362

    Pith/arXiv arXiv 2024

  41. [41]

    Lescano, ”The non-relativistic limit of HSZ Theory”, 2505.22707 [hep-th]

    E. Lescano, ”The non-relativistic limit of HSZ Theory”, 2505.22707 [hep-th]

    Pith/arXiv arXiv

  42. [42]

    Cardona and L

    B. Cardona and L. Romano, ”Higher-Order Newton-Cartan Gravity”, 2507.05489 [hep-th]

    Pith/arXiv arXiv

  43. [43]

    E.Lescano, ”Trivialization of the gravitational Green-Schwarz mechanism in the non-relativistic limit of string theory”, Phys.Rev.D 113 (2026) 4, L041902

    2026

  44. [44]

    Lescano, ”Gravitational four-derivative corrections in non-relativistic heterotic supergravity and theSO(8) Green- Schwarz mechanism”, 2508.09250 [hep-th]

    E. Lescano, ”Gravitational four-derivative corrections in non-relativistic heterotic supergravity and theSO(8) Green- Schwarz mechanism”, 2508.09250 [hep-th]

    arXiv

  45. [45]

    Bergshoeff, J

    E. Bergshoeff, J. Figueroa-O’Farrill, K. van Helden, J. Rosseel, I. Rotko, T. ter Veldhuis,”p-brane Galilean and Carrollian geometries and gravities”, J.Phys.A 57 (2024) 24, 245205

    2024

  46. [46]

    The Quartic Effective Action for the Heterotic String,

    D. J. Gross and J. H. Sloan, “The Quartic Effective Action for the Heterotic String,” Nucl. Phys. B291(1987), 41-89 doi:10.1016/0550-3213(87)90465-2

    doi:10.1016/0550-3213(87)90465-2 1987

  47. [47]

    Heterotic String Covariant Amplitudes and Low-energy Effective Action,

    Y. Cai and C. A. Nunez, “Heterotic String Covariant Amplitudes and Low-energy Effective Action,” Nucl. Phys. B287, 279 (1987). 9

    1987

  48. [48]

    Lescano,α’-corrections and their double formulation, J

    E. Lescano,α’-corrections and their double formulation, J. Phys. A 55 (2022), no. 5 053002, arXiv:hep-th/2108.12246

    Pith/arXiv arXiv 2022