From noncommutative Yang-Mills to noncommutative gravity through a classical double copy map

Eric Lescano; Larisa Jonke

REVIEW 2 major objections 5 minor 1 cited by

From noncommutative Yang-Mills to noncommutative gravity through a classical double copy map

T0 review · 2 major / 5 minor · reviewed 2026-08-09 · deepseek-v4-flash

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

Pith's one-line read This paper derives the first nontrivial noncommutative correction to the Einstein-Hilbert action from the double copy of noncommutative Yang-Mills: an explicit theta-squared Riemann-cubic action in the pure-gravity limit.

desk verdict A real but underdetermined computation: the θ² Riem³ correction from double-copying ncYM is a one-parameter family, and p=1 is a convention. read the letter →

arxiv 2502.03521 v1 pith:FLDEODKI submitted 2025-02-05 hep-th gr-qcmath-phmath.MP

Larisa Jonke , Eric Lescano This is my paper · ORCID

classification hep-thgr-qcmath-phmath.MP PACS 11.10.Nx11.15.-q

keywords classicaldoublecopynoncommutativeYang-MillsSeiberg-WittenmapMoyal-WeylstarproductfieldtheoryEinstein-HilbertactionRiemanncubiccorrectionsgravitationalwavedispersion

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper claims that the classical double copy map, which turns Yang-Mills theory into double field theory and then into gravity, can be extended to the noncommutative regime, and that the extension yields the first nontrivial noncommutative correction to the Einstein-Hilbert Lagrangian. Starting from noncommutative SU(N) Yang-Mills theory whose fields are expressed through the Seiberg-Witten map in terms of ordinary ones, kept to cubic order in fields and to order $\theta^2$ in the noncommutativity parameter, the authors construct the three-point vertex operators and square the theory as an ncYM × ncYM double copy. The target is a noncommutatively corrected cubic double field theory carrying two star products, with parameters $\theta$ and $\bar{\theta}$, mirroring the doubled coordinates of double field theory; solving the level matching condition $\bar{x} = x$ identifies the two products and produces $\theta^2$ corrections to the cubic action, while the quadratic part stays uncorrected. In $D=4$ with the transverse-traceless gauge and no $b$-field or dilaton, the pure gravity limit is Einstein-Hilbert plus the explicit $\theta^2$ Riemann-cubic action of Eq. (40). A sympathetic reader would care because gauge-theory noncommutativity then translates into specific higher-curvature corrections to gravity, with testable consequences for the gravitational wave dispersion relation.

What carries the argument

The load-bearing machinery is the set of three-point vertex operators of Seiberg-Witten expanded Moyal-Weyl noncommutative Yang-Mills theory: $\pi^{(0)}$, the commutative antisymmetric vertex carried by the structure constant $f_{abc}$; $\pi^{(1)}$, the $\theta$-linear symmetric vertex carried by $d_{abc}$; and $\pi^{(2)}$, the $\theta^2$ correction to the antisymmetric vertex. The double copy replaces colour structures by barred kinematic vertices, $f_{abc} \to \tfrac{i}{8}(\bar{\pi}^{(0)} + \bar{\pi}^{(2)})$ and $d_{abc} \to \tfrac{ip}{8}\bar{\pi}^{(1)}$, producing a doubled geometrical theory with two star products, $\theta$ and $\bar{\theta}$, that mirror the doubled coordinates of double field theory. The level matching condition $\bar{x} = x$ identifies the two products and converts the mixed $\theta\bar{\theta}$ terms of the doubled action into $\theta^2$ corrections to the cubic DFT action. The free parameter $p$, introduced by the map of the symmetric colour factor and not fixed by the double copy procedure itself, is set to $p=1$ by the rewriting of Eqs. (43)–(45), which assumes that symmetrisation kills the cross terms $f_{abc}\pi^{(1)}$, $d_{abc}\pi^{(0)}$, and $d_{abc}\pi^{(2)}$.

What would settle it

Compute the three-graviton on-shell amplitude at order $\theta^2$ directly from the Seiberg-Witten expanded noncommutative Yang-Mills three-point vertices by squaring the kinematic numerators in the standard amplitude double copy, and compare its coefficients with those following from Eq. (40): this fixes the parameter $p$ from amplitude data, and any mismatch in the Riemann-cubic structure would falsify the map $d_{abc} \to \tfrac{ip}{8}\bar{\pi}^{(1)}$. A second check: with $\theta$ restricted to spatial directions the equation of motion must keep the wave operator free of higher time derivatives; if higher time derivatives survive even for spatial $\theta$, the truncation is inconsistent.

Watch

Extended reading notes

Core claim

On the paper's own terms, the central result is that the first nontrivial noncommutative correction to the Einstein-Hilbert Lagrangian can be computed through the classical double copy of noncommutative Yang-Mills theory. The Seiberg-Witten expansion of the Moyal-Weyl gauge theory, kept to cubic order in fields and to order $\theta^2$, defines three-point vertex operators $\pi^{(0)}$ (commutative, antisymmetric), $\pi^{(1)}$ (linear in $\theta$, symmetric), and $\pi^{(2)}$ (order $\theta^2$, antisymmetric). Under the double copy the colour structures map to barred kinematic operators, $f_{abc} \to \tfrac{i}{8}(\bar{\pi}^{(0)} + \bar{\pi}^{(2)})$ and $d_{abc} \to \tfrac{ip}{8}\bar{\pi}^{(1)}$, with $p$ a free parameter of order one, and the doubled theory is a noncommutative deformation of the cubic DFT action (Eq. A1) carrying a pair of star products, $\theta$ and $\bar{\theta}$. Solving the level matching condition $\bar{x} = x$ identifies the two products, delivering $\theta^2$ corrections to the cubic DFT action. In the pure gravitational limit ($D=4$, transverse-traceless gauge with $\partial_\mu h^{\mu\nu}=0=h$, $b_{\mu\nu}=0$, $\varphi=0$) the action reduces to Einstein-Hilbert plus the explicit Riemann-cubic terms of Eq. (40), with equation-of-motion corrections $C_{\mu\nu}(\theta^2)$ containing three- and four-derivative parts; restricting $\theta$ to spatial directions removes higher time derivatives so that no unphysical degrees of freedom propagate.

Load-bearing premise

The paper's result rests on identifying the symmetric colour factor $d_{abc}$ of noncommutative Yang-Mills with the $\theta$-linear vertex $\pi^{(1)}$ of the double copy through a weight $p$ that the construction itself cannot fix, and on the symmetry argument of Eqs. (43)–(45) that sets $p = 1$; if that identification or that symmetry argument fails, the $\theta^2$ Riemann-cubic action of Eq. (40) is not uniquely determined by the noncommutative gauge theory.

Editorial extensions

If this is right

The quadratic part of the double-copied theory receives no noncommutative corrections; all $\theta^2$ effects enter at cubic order in fields, matching the absence of nontrivial corrections at quadratic level.
In the pure gravity limit ($D=4$, transverse-traceless gauge, $b_{\mu\nu}=0$, $\varphi=0$) gravity becomes Einstein-Hilbert plus the explicit $\theta^2$ Riemann-cubic action of Eq. (40), so the double copy yields a concrete higher-curvature gravitational theory whose coefficients are fixed up to the parameter $p$ by gauge-theory data.
The $\theta^2$ corrections alter the subleading dispersion relation of gravitational waves; when $\theta$ is restricted to spatial directions, no higher time derivatives appear and no unphysical degrees of freedom propagate.
Because the two star products are identified by the level matching condition, noncommutativity inherits the doubled-coordinate structure of double field theory, and the authors expect analogous $\theta^2$ corrections in the single and zeroth copy procedures and for Kerr-Schild-type solutions.

Reading between the lines

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

The freedom in $p$ means Eq. (40) really describes a one-parameter family of higher-curvature gravity actions; an independent physical input, such as requiring causal, unitary propagation of gravitational waves, would be needed to single out one member.
If the cubic-level map is consistent, the same colour-to-vertex identification should extend to quartic order, generating a tower of $\theta^2 R^4$ and higher terms that could be tested by algebraic construction and direct squaring of ncYM amplitudes.
Enforcing the twisted colour-kinematics duality of noncommutative U(N) gauge theory, which the authors note their $p=1$ rewriting resembles, could provide an independent derivation of that value and remove the ambiguity from the double copy input.

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

Colleague,

The thing to know: this paper does a concrete, previously missing computation—double-copying noncommutative Yang-Mills to cubic order and extracting the leading θ² correction to the Einstein-Hilbert Lagrangian as Riemann-cube terms. That part is real and worth knowing. The catch is that the final action (40) is not uniquely determined by the ncYM input; it depends on a free parameter p that the authors themselves say the double copy cannot fix, and their later 'rewriting' to set p=1 is just a convention, as the stress-test correctly shows.

What is genuinely new: the identification of the symmetric structure constant d_abc with the noncommutative vertex π^(1) (Eq. 30), the doubled star-product structure, and the explicit reduction to D=4 TT gauge yielding Eq. (40) and the equation-of-motion corrections (B1)-(B2). The lengthy appendix A is a real computation, done with CADABRA and presumably reproducible, which counts in its favor. The paper is honest about its own limitation: Section V admits p cannot be fixed by the classical double copy procedure.

Where it is soft: the p problem is not a minor aside. The stress-test argument shows that the rewriting (43)-(45) is one of a one-parameter family: for any λ, μ=1/λ, the same cross-term symmetry gives (f+λd)(π^(0)+μπ^(1)+π^(2)), and double-copying this yields θ² corrections scaling as μ². So Eq. (40) is not 'the' correction; it is a member of a family parameterized by p. The paper provides no external principle (e.g., twisted colour-kinematics duality from Ref. [20], unitarity with spatial θ, or causality) to single out μ=1. This is load-bearing because the central claim is precisely the specific Riem^3 action. In addition, the transition from the full (A1) to the compact (40) is not fully shown; a referee would need the intermediate steps or a script to verify. The generic-θ issue of higher time derivatives is acknowledged and partially addressed by restricting to spatial θ, which is a reasonable but incomplete answer.

Overall: the paper is a serious, honest computation with a real gap. It deserves a serious referee—not because it is correct as stated, but because the question is important and the computation is a useful starting point. If I were the editor, I would send it out with a request to either fix p by a physical principle or present the result as a one-parameter family and discuss the dependence. A referee should also ask for the CADABRA output or a detailed derivation of (40). I would bring it to a reading group as a case study in how double-copy prescriptions carry arbitrary parameters. I'd cite it with the caveat highlighted.

Referee Report

2 major / 5 minor

Summary. The paper claims to compute the first nontrivial noncommutative correction to the Einstein-Hilbert Lagrangian by applying the classical double copy map of Diaz-Jaramillo-Hohm-Plefka [24] to noncommutative SU(N) Yang-Mills theory with a Seiberg-Witten expansion. Starting from published noncommutative Yang-Mills actions [29,31,32], the authors define three-point vertex operators π(0), π(1), and π(2), and replace the color factors by barred kinematic tensors: d_abc → (i p/8) π̄(1) and f_abc → (i/8)(π̄(0)+π̄(2)). This yields a θ²-corrected cubic double field theory action, Eq. (A1). After solving the level matching condition as x = x̄, restricting to pure gravity with b = 0 and φ = 0 in D = 4, and imposing the transverse-traceless gauge, they reduce the action to Einstein-Hilbert plus Riemann-cubic corrections, Eq. (40), and give the corresponding linearized equations of motion in Appendix B. They also argue that for spatial θ there are no higher time derivatives and therefore no propagating unphysical degrees of freedom.

Significance. If the computation is correct, this is a concrete and novel realization of noncommutative gravitational corrections from a gauge-theory double copy, extending the double field theory double-copy program to Moyal-Weyl deformed gauge theories. The explicit Riem³ Lagrangian and the equations of motion are falsifiable predictions that can be compared with effective actions for deformed gravity, and the framework suggests a tower of higher-derivative corrections. The paper properly builds on independent published actions and the existing double-copy map rather than restating them, and the use of CADABRA for the long algebra is appropriate. The main caveat is that the final action is not uniquely determined from the noncommutative Yang-Mills input unless the free parameter p is fixed by a derivation rather than by an internal rewriting convention.

major comments (2)

[§V, Eqs. (30), (40), (43)–(45)] The free parameter p is load-bearing and is not fixed. The paper itself states in Section V that p 'cannot be fixed by the classical double copy procedure.' Eq. (40) depends on p, and the proposed p=1 rewriting is only a convention: for any λ with μ=1/λ, the same symmetrization argument used for Eq. (44) allows the cubic color factor to be rewritten as (f+λd)(π(0)+μπ(1)+π(2)). Double-copying this factor with the combined map f+λd → (i/8)(π̄(0)+μπ̄(1)+π̄(2)) gives a θ² correction proportional to μ² π̄(1)π(1), so the effective coefficient in Eq. (40) is μ² rather than 1. An additional physical input is needed to select μ=1; otherwise the claimed 'first nontrivial noncommutative correction' is one member of a one-parameter family. The same issue propagates into the equations of motion in Appendix B, whose coefficients depend on p.
[§IV, Eq. (44)] The rewriting of Eq. (43) as Eq. (44) is asserted 'due to different symmetrization', but the index symmetries that make f_abc π(1), d_abc π(0), and d_abc π(2) vanish after contraction with A^a_1 A^b_2 A^c_3 are not exhibited. This is exactly the step through which p=1 is introduced, so it cannot remain a bare assertion. Please show the contraction identities for each cross term, or state explicitly the symmetrization properties of π(0), π(1), and π(2) under the relevant exchanges.

minor comments (5)

[Abstract and §IV.A] There are typos: 'they produced θ²-corrections' should be 'they produce θ²-corrections', and 'Limiting nocommutativity to spacial direction' should be 'Limiting noncommutativity to spatial directions'.
[References] References [2] and [3] are duplicate entries of the same paper (Bern, Carrasco, Johansson, Phys. Rev. Lett. 105 (2010) 061602); please merge them.
[§III, Eqs. (27) and (33)] The notation S*_3 is used both for the θ-linear correction in Eq. (27) and for the θ² correction in Eq. (33), which is confusing; a notation such as S*_(3,1) and S*_(3,2) would clarify the order in θ.
[Appendix A] The expression (A1) is very hard to parse because of unbalanced parentheses and repeated η factors, e.g. in terms involving θ_{(μ|σ} θ̄_{(ar μ|ar σ} ... ∂_{ρ)} ∂̄_{ar ρ)}. Please rewrite it with a cleaner symmetrization convention or provide an ancillary file with the machine-readable expression.
[Appendix A and §IV.A] The CADABRA code is described as 'available upon request'; depositing it as ancillary material would improve reproducibility and allow readers to verify the reduction from (A1) to Eq. (40).

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the double-copy computation is self-contained, with the free parameter p being an acknowledged ambiguity rather than a circular reduction.

full rationale

The paper's derivation chain starts from published independent inputs: the Seiberg-Witten expanded noncommutative Yang-Mills cubic action from Refs. [29,31,32] and the classical double copy map from Ref. [24]. The gravitational Riem^3 action in Eq. (40) is obtained by explicit substitution of the ncYM vertex operators pi^(0), pi^(1), pi^(2) into the double copy prescription, followed by solving the level matching condition x = xbar and imposing the transverse-traceless gauge. This is a computation, not a restatement of the input: the output contains structures (Riemann-cubic invariants and theta^2 corrections to the DFT action) not present in the ncYM action itself. No fitted parameter is relabeled as a prediction; no uniqueness theorem from the authors' prior work is invoked; and the cited previous work by the authors ([25,26,28,41]) is used only for context or for related constructions, not as the load-bearing justification for the central result. The one notable weakness is the free parameter p introduced in Eq. (30) and later 'fixed' to p=1 via the rewriting in Eqs. (43)-(45). The paper explicitly concedes that p cannot be fixed by the classical double copy procedure, and the final action (40) depends on p. This is a genuine ambiguity or non-uniqueness in the derived correction, and a potential correctness risk, but it is not circularity: the derivation does not assume the Riem^3 result as an input, and p is not fitted to any target datum. The cross-term symmetrization argument in Eqs. (43)-(45) is an additional convention rather than a derivation of p, but choosing a convention is not equivalent to assuming the conclusion. Accordingly, no circular step is exhibited; the correct circularity score is 0, with the caveat that the p-dependence should be addressed in an improved version of the paper.

Assumptions & free parameters 1 free parameters · 5 assumptions · 0 invented entities

The derivation rests on the known Seiberg-Witten expanded noncommutative Yang-Mills actions, on the assumption that the classical double copy map extends to noncommutative gauge theories, and on the identification of the doubled star products after level matching. The most fragile input is the mapping of the symmetric color factor d_abc, which requires a free parameter p that is later fixed to 1 by an internal rewriting. No new particles or forces are introduced.

free parameters (1)

p = 1 (fixed by combined identification (45))
Introduced in Eq (30) as a free parameter of order 1 in the double copy identification d_abc -> (i p/8) pi^(1)_barmubar nubar rho. Section V states that p cannot be fixed by the classical double copy procedure. It is later set to 1 by the combined identification (45), and the coefficients in the final Riem^3 correction (40) depend on p, so this choice is load-bearing.

assumptions (5)

domain assumption The Seiberg-Witten map expansion of the noncommutative SU(N) Yang-Mills action up to theta^2 and cubic order in fields, as given in Refs [29,31,32], is complete and correct.
The starting actions (27) and (33) are taken from these references; any missing terms at this order would change the vertices (29) and (35) and hence the final gravitational action.
domain assumption The classical double copy prescription of [24] extends to noncommutative Yang-Mills by replacing f_abc and d_abc with barred kinematic vertices.
The map (8), (9), (16), (30), and (36) is assumed. For the symmetric d_abc factor there is no derivation from color-kinematics duality, and the paper introduces a free parameter p.
domain assumption Solving the level matching condition by identifying x = xbar identifies the two star products, theta = thetabar, so that only theta^2 terms survive after the double copy.
Section II and IV use this standard level-matching solution from [24], but for the noncommutative deformation it is an additional identification of deformation parameters.
domain assumption The transverse-traceless gauge is compatible with the De Donder gauge and makes R = 0 + O(h^2), allowing Ricci-containing cubic terms to be dropped or absorbed by field redefinitions.
Used in Section IV.A to obtain (39)-(40). If this gauge choice is not valid for the noncommutative corrections, the Riem^3 expression is not the full result.
ad hoc to paper The rewriting (44) is valid because symmetry forces f_abc pi^(1), d_abc pi^(0), and d_abc pi^(2) cross terms to vanish.
Used to fix p=1. The paper only states 'due to different symmetrization of f and d terms' without showing the vanishing explicitly.

how reviews work

0 comments

Cite this review

Pith. "Pith review of From noncommutative Yang-Mills to noncommutative gravity through a classical double copy map." pith.science (2026). https://pith.science/paper/FLDEODKI

@misc{pith2026250203521,
  author       = {Pith},
  title        = {Pith review of: From noncommutative Yang-Mills to noncommutative gravity through a classical double copy map},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/FLDEODKI}},
  note         = {Machine review of arXiv:2502.03521}
}

abstract

We compute the first nontrivial noncommutative correction to the Einstein-Hilbert Lagrangian, which arises from the double copy of noncommutative Yang-Mills theory (ncYM). We start by considering linear and quadratic $\theta$-corrections up to cubic order in fields in ncYM theory and in arbitrary $D$ dimensions. We compute the first nontrivial corrections to the three-points vertex operators and use them to construct a double copy theory of the form ncYM $\times$ ncYM. The resulting theory is given by a double geometrical formalism which includes noncommutative corrections to the perturbative cubic double field theory (DFT) formulation, where the star product of the theory is doubled in agreement with the doubling of the physical coordinates of the theory. Upon solving the level matching condition the noncommutative products are identified and they produced $\theta^2$-corrections to the cubic DFT action. We analyze the pure gravitational limit of this formulation considering $D=4$ and imposing the transverse-traceless gauge.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

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

Double Copy Map for Double Field Theory on an Arbitrary Constant Background
hep-th 2025-07 conditional novelty 4.0 of 10

A double copy map from two Yang-Mills theories around background gauge fields yields the double field theory action on an arbitrary constant background, up to third order.

Reference graph

Works this paper leans on

44 extracted references · 10 canonical work pages · cited by 1 Pith paper

[20]

Gravity versus Noncommutative Gauge Theory: A Double Copy Perspective

R. J. Szabo, “Gravity versus Noncommutative Gauge Theory: A Double Copy Perspective,” [arXiv:2401.16283 [hep-th]]

work page Pith review arXiv
[24]

Double ﬁeld theory as the double copy of Yang-Mills theory,

F. Diaz-Jaramillo, O. Hohm and J. Plefka, “Double ﬁeld theory as the double copy of Yang-Mills theory,” Phys. Rev. D 105, no.4, 045012 (2022), [arXiv:2109.01153 [hep- th]]

arXiv 2022
[1]

New Re- lations for Gauge-Theory Amplitudes

Z. Bern, J. J. M. Carrasco and H. Johansson, “New Re- lations for Gauge-Theory Amplitudes”, Phys. Rev. D78 (2008) 085011 [arXiv:0805.3993 [hep-ph]]

arXiv 2008
[3]

Per- turbative Quantum Gravity as a Double Copy of Gauge Theory,

Z. Bern, J. J. M. Carrasco and H. Johansson, “Per- turbative Quantum Gravity as a Double Copy of Gauge Theory,” Phys. Rev. Lett. 105 (2010), 061602 [arXiv:1004.0476 [hep-th]]

arXiv 2010
[4]

A Relation Between Tree Amplitudes of Closed and Open Strings,

H. Kawai, D. C. Lewellen and S. H. H. Tye, “A Relation Between Tree Amplitudes of Closed and Open Strings,” Nucl. Phys. B 269 (1986), 1-23

work page 1986
[5]

Black holes and the double copy,

R. Monteiro, D. O’Connell, and C. D. White, “Black holes and the double copy,” JHEP 12 (2014) 056, [arXiv:1410.0239 [hep-th]]

arXiv 2014
[6]

The double copy: Bremsstrahlung and accelerating black holes,

A. Luna, R. Monteiro, I. Nicholson, D. O’Connell, and C. D. White, “The double copy: Bremsstrahlung and accelerating black holes,” JHEP 06 (2016) 023, [arXiv:1603.05737 [hep-th]]

arXiv 2016
[7]

Radiation and the classical double copy for color charges,

W. D. Goldberger and A. K. Ridgway, “Radiation and the classical double copy for color charges,” Phys. Rev. D 95 no. 12, (2017) 125010, [arXiv:1611.03493 [hep-th]]

arXiv 2017

Show all 44 references

[8]

Perturba- tive spacetimes from Yang-Mills theory,

A. Luna, R. Monteiro, I. Nicholson, A. Ochirov, D. O’Connell, N. Westerberg, and C. D. White, “Perturba- tive spacetimes from Yang-Mills theory,” JHEP 04 (2017) 069, [arXiv:1611.07508 [hep-th]]

2017 arXiv
[9]

Bound states and the classical double copy,

W. D. Goldberger and A. K. Ridgway, “Bound states and the classical double copy,” Phys. Rev. D 97 no. 8, (2018) 085019, [arXiv:1711.09493 [hep-th]]

2018 arXiv
[10]

Eﬀective action of dilaton gravity as the classical double copy of Yang-Mills theory,

J. Plefka, J. Steinhoﬀ, and W. Wormsbecher, “Eﬀective action of dilaton gravity as the classical double copy of Yang-Mills theory,” Phys. Rev. D 99 no. 2, (2019) 024021, [arXiv:1807.09859 [hep-th]]

2019 arXiv
[11]

On-shell Techniques and Universal Results in Quantum Gravity,

N. E. J. Bjerrum-Bohr, J. F. Donoghue, and P. Vanhove, “On-shell Techniques and Universal Results in Quantum Gravity,” JHEP 02 (2014) 111, [arXiv:1309.0804 [hep- th]]

2014 arXiv
[12]

Graviton-Photon Scattering,

N. E. J. Bjerrum-Bohr, B. R. Holstein, L. Plant´ e, and P. Vanhove, “Graviton-Photon Scattering,” Phys. Rev. D 91 no. 6, (2015) 064008, [arXiv:1410.4148 [gr-qc]]

2015 arXiv
[13]

Bending of Light in Quan- tum Gravity,

N. E. J. Bjerrum-Bohr, J. F. Donoghue, B. R. Holstein, L. Plant´ e, and P. Vanhove, “Bending of Light in Quan- tum Gravity,” Phys. Rev. Lett. 114 no. 6, (2015) 061301, [arXiv:1410.7590 [hep-th]]

2015 arXiv
[14]

Light-like Scattering in Quan- tum Gravity,

N. E. J. Bjerrum-Bohr, J. F. Donoghue, B. R. Holstein, L. Plante, and P. Vanhove, “Light-like Scattering in Quan- tum Gravity,” JHEP 11 (2016) 117, [arXiv:1609.07477 [hep-th]]

2016 arXiv
[15]

General Relativity from Scat- tering Amplitudes,

N. E. J. Bjerrum-Bohr, P. H. Damgaard, G. Festuccia, L. Plant´ e, and P. Vanhove, “General Relativity from Scat- tering Amplitudes,” Phys. Rev. Lett. 121 no. 17, (2018) 171601, [arXiv:1806.04920 [hep-th]]

2018 arXiv
[16]

The pure BRST Einstein-Hilbert Lagrangian from the double-copy to cubic order

L. Borsten, S. Nagy, “The pure BRST Einstein-Hilbert Lagrangian from the double-copy to cubic order”, JHEP 07 (2020) 093, [arXiv:2004.14945 [hep-th]]

2020 arXiv
[17]

Classical gravity from loop amplitudes,

N. E. J. Bjerrum-Bohr, P. H. Damgaard, L. Plant´ e, and P. Vanhove, “Classical gravity from loop amplitudes,” Phys. Rev. D 104 no. 2, (2021) 026009, [arXiv:2104.04510 [hep-th]]

2021 arXiv
[18]

Black Hole Binary Dynamics from the Double Copy and Eﬀective Theory,

Z. Bern, C. Cheung, R. Roiban, C.-H. Shen, M. P. Solon, and M. Zeng, “Black Hole Binary Dynamics from the Double Copy and Eﬀective Theory,” JHEP 10 (2019) 206, [arXiv:1908.01493 [hep-th]]

2019 arXiv
[19]

Homotopy Double Copy of Noncommutative Gauge Theories,

R. J. Szabo and G. Trojani, “Homotopy Double Copy of Noncommutative Gauge Theories,” Symmetry 15 (2023) no.8, 1543 [arXiv:2306.12175 [hep-th]]

2023 arXiv
[21]

Double Field Theory,

C. Hull and B. Zwiebach, “Double Field Theory,” JHEP 09 (2009) 099, [arXiv:0904.4664 [hep-th]]

2009 arXiv
[22]

Two vierbein formalism for string inspired axionic gravity,

W. Siegel, “Two vierbein formalism for string inspired axionic gravity,” Phys. Rev. D 47 (1993), 5453-5459 [arXiv:hep-th/9302036]

1993 arXiv
[23]

Superspace duality in low-energy su- perstrings,

W. Siegel, “Superspace duality in low-energy su- perstrings,” Phys. Rev. D 48 (1993), 2826-2837 [arXiv:hep-th/9305073]

1993 arXiv
[25]

Aspects of Conformal Gravity and Double Field Theory from a Dou- ble Copy Map

E. Lescano, G. Menezes, and J. A. Rodriguez, “Aspects of Conformal Gravity and Double Field Theory from a Dou- ble Copy Map”, Phys.Rev.D 108, no.12, (2023) 126017, [arXiv:2307.14538 [hep-th]]

2023 arXiv
[26]

Constructing Confor- mal Double Field Theory through a Double Copy Map

E. Lescano and J. A. Rodriguez, “Constructing Confor- mal Double Field Theory through a Double Copy Map”, arXiv:2408.11892 [hep-th]

arXiv
[27]

Yılmaz, ”On the extension of double copy procedure to higher derivative double ﬁeld theory”, [arXiv:2408.16524 [hep-th]]

R. Yılmaz, ”On the extension of double copy procedure to higher derivative double ﬁeld theory”, [arXiv:2408.16524 [hep-th]]

arXiv
[28]

Quadratic Curvature Corrections in Double Field Theory via Double Copy

E. Lescano and J. A. Rodriguez, “Quadratic Curvature Corrections in Double Field Theory via Double Copy”, [arXiv:2409.05628 [hep-th]]
[29]

Construction of nonAbelian gauge theories on noncom- mutative spaces,

B. Jurco, L. M¨ oller, S. Schraml, P. Schupp and J. Wess, “Construction of nonAbelian gauge theories on noncom- mutative spaces,” Eur. Phys. J. C 21 (2001), 383-388 [arXiv:hep-th/0104153]

2001 arXiv
[30]

The Standard model on noncommu- tative space-time,

X. Calmet, B. Jurco, P. Schupp, J. Wess and M. Wohlgenannt, “The Standard model on noncommu- tative space-time,” Eur. Phys. J. C 23 (2002), 363-376 [arXiv:hep-ph/0111115]

2002 arXiv
[31]

Second order of the expansions of action func- tionals of the noncommutative standard model,

L. M¨ oller, “Second order of the expansions of action func- tionals of the noncommutative standard model,” JHEP 10 (2004), 063 [arXiv:hep-th/0409085]

2004 arXiv
[32]

Non- commutative gravity and the Seiberg-Witten map

M. Dimitrijevi´ c, V. Radovanovi´ c, I. Simonovi´ c, “Non- commutative gravity and the Seiberg-Witten map”, Part of Modern Mathematical Physics. Proceedings, 7th Sum- mer School : Belgrade, Serbia, September 9-19, 2012, 141-150 Contribution to: MPHYS7, 141-150

2012
[33]

String theory and noncommutative geometry,

N. Seiberg and E. Witten, “String theory and noncommutative geometry,” JHEP 09 (1999), 032 [arXiv:hep-th/9908142]

1999 arXiv
[34]

Noncommutative spacetimes: Symmetries in noncom- mutative geometry and ﬁeld theory

P. Aschieri, M. Dimitrijevi´ c, P. Kulish, F. Lizzi, J. W ess, “Noncommutative spacetimes: Symmetries in noncom- mutative geometry and ﬁeld theory”, Lect. Notes Phys. 774 (2009) 1-199

2009
[35]

Non- commutative geometry and gravity

P. Aschieri, M. Dimitrijevi´ c, F. Meyer, J. Wess, “Non- commutative geometry and gravity ”, Class. Quant. Grav. 23 (2006) 1883-1912, [arXiv:hep-th/0510059]. 10

2006 arXiv
[36]

A new class of vacuum solu- tions of the Einstein ﬁeld equations

R. P. Kerr and A. Schild, “A new class of vacuum solu- tions of the Einstein ﬁeld equations”, Proc. Symp. Appl. Math.17 199 (1965)

1965
[37]

Kerr-Schild Double Field Theory and Classi- cal Double Copy

K. Lee, “Kerr-Schild Double Field Theory and Classi- cal Double Copy”, JHEP 1810 027 (2018), [arXiv:hep- th/1807.08443]

2018 arXiv
[38]

Heterotic Kerr-Schild Double Field Theory and Classical Double Copy

W. Cho, K. Lee, “Heterotic Kerr-Schild Double Field Theory and Classical Double Copy”, JHEP 07 030 (2019), [arXiv:hep-th/1904.11650]

2019 arXiv
[39]

N = 1 Supersym- metric Double Field Theory and the generalized Kerr- Schild Ansatz

E. Lescano and A. Rodr ´ ıguez, “ N = 1 Supersym- metric Double Field Theory and the generalized Kerr- Schild Ansatz”, JHEP 10 (2020) 148, [arxiv:hep- th/2002.07751]

2020 arXiv
[40]

Higher-derivative Het- erotic Double Field Theory and Classical Double Copy

E. Lescano and A. Rodr ´ ıguez, “Higher-derivative Het- erotic Double Field Theory and Classical Double Copy”, JHEP 07 (2021) 072, [arXiv:hep-th/2101.03376]

2021 arXiv
[41]

Kodˇ zoman, E

T. Kodˇ zoman, E. Lescano, “Noncommutative dou- ble geometry’, Phys.Rev.D 109 (2024) 4, 046014, [arXiv:2305.13131[hep-th]]

2024 arXiv
[42]

Gauge invariant double copy of Yang-Mills theory: The quartic theory,

R. Bonezzi, C. Chiaﬀrino, F. Diaz-Jaramillo and O. Hohm, “Gauge invariant double copy of Yang-Mills theory: The quartic theory,” Phys. Rev. D 107 (2023) no.12, 126015 [arXiv:2212.04513 [hep-th]]

2023 arXiv
[43]

The BV double of a Courant algebroid,

A. M. Zeitlin, “The BV double of a Courant algebroid,” [arXiv:2410.20510 [math.QA]]

arXiv
[44]

X. O. Camanho, J. D. Edelstein, J. Maldacena, A. Zhi- boedov, ”Causality Constraints on Corrections to the Graviton Three-Point Coupling”, JHEP 02 (2016) 020 [arXiv:1407.5597 [hep-th]]

2016 arXiv
[45]

Introducing Cadabra: A Symbolic com- puter algebra system for ﬁeld theory problems,

K.Peeters, “Introducing Cadabra: A Symbolic com- puter algebra system for ﬁeld theory problems,” arXiv:hep-th/0701238

arXiv

Pith tools

Reviewed August 9, 2026 · model on record in the stance chip above.

[1] [20]

Gravity versus Noncommutative Gauge Theory: A Double Copy Perspective

R. J. Szabo, “Gravity versus Noncommutative Gauge Theory: A Double Copy Perspective,” [arXiv:2401.16283 [hep-th]]

work page Pith review arXiv

[2] [24]

Double ﬁeld theory as the double copy of Yang-Mills theory,

F. Diaz-Jaramillo, O. Hohm and J. Plefka, “Double ﬁeld theory as the double copy of Yang-Mills theory,” Phys. Rev. D 105, no.4, 045012 (2022), [arXiv:2109.01153 [hep- th]]

arXiv 2022

[3] [1]

New Re- lations for Gauge-Theory Amplitudes

Z. Bern, J. J. M. Carrasco and H. Johansson, “New Re- lations for Gauge-Theory Amplitudes”, Phys. Rev. D78 (2008) 085011 [arXiv:0805.3993 [hep-ph]]

arXiv 2008

[4] [3]

Per- turbative Quantum Gravity as a Double Copy of Gauge Theory,

Z. Bern, J. J. M. Carrasco and H. Johansson, “Per- turbative Quantum Gravity as a Double Copy of Gauge Theory,” Phys. Rev. Lett. 105 (2010), 061602 [arXiv:1004.0476 [hep-th]]

arXiv 2010

[5] [4]

A Relation Between Tree Amplitudes of Closed and Open Strings,

H. Kawai, D. C. Lewellen and S. H. H. Tye, “A Relation Between Tree Amplitudes of Closed and Open Strings,” Nucl. Phys. B 269 (1986), 1-23

work page 1986

[6] [5]

Black holes and the double copy,

R. Monteiro, D. O’Connell, and C. D. White, “Black holes and the double copy,” JHEP 12 (2014) 056, [arXiv:1410.0239 [hep-th]]

arXiv 2014

[7] [6]

The double copy: Bremsstrahlung and accelerating black holes,

A. Luna, R. Monteiro, I. Nicholson, D. O’Connell, and C. D. White, “The double copy: Bremsstrahlung and accelerating black holes,” JHEP 06 (2016) 023, [arXiv:1603.05737 [hep-th]]

arXiv 2016

[8] [7]

Radiation and the classical double copy for color charges,

W. D. Goldberger and A. K. Ridgway, “Radiation and the classical double copy for color charges,” Phys. Rev. D 95 no. 12, (2017) 125010, [arXiv:1611.03493 [hep-th]]

arXiv 2017