Pith. sign in

REVIEW 3 major objections 5 minor 79 references

On polarized scattering equations for superamplitudes of 11D supergravity and ambitwistor superstring

T0 review · 3 major / 5 minor · reviewed 2026-08-14 · deepseek-v4-flash

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

Pith's one-line read The paper derives the 11D polarized scattering equation from the equations of motion of the 11D ambitwistor superstring and finds its fermionic superpartner as a differential equation on superamplitudes.

desk verdict Cleanest SO(16)-covariant derivation to date of the 11D polarized scattering equation from the ambitwistor string, plus a genuinely new fermionic superpartner equation; the covariant core rests on a labeled-but-unproven factorization, and the 10D right-chiral equation is honestly flagged as conjectural. read the letter →

arxiv 1908.07482 v2 pith:XRTCF3DK submitted 2019-08-20 hep-th gr-qchep-ph

Igor Bandos This is my paper · ORCID
classification hep-thgr-qchep-ph MSC 81T3081T6083E50
keywords supersymmetrysupergravityscatteringamplitudestwistorapproachspinormovingframepolarizedequationsambitwistorsuperstringSO(16)symmetry
topics Quantum Gravity
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper aims to show that the 11D polarized scattering equation, previously proposed as an ansatz for superamplitudes, is actually a consequence of the 11D ambitwistor superstring. Working in the supertwistor form of the action, the paper obtains the meromorphic spinor function on the Riemann sphere from the worldsheet equations of motion with vertex-operator sources, and then derives the polarized scattering equation from it. The same calculation yields a fermionic meromorphic function, and the paper proves that its supersymmetric counterpart is a differential equation imposed on the superamplitude, called here the spolarized scattering equation. If this is right, the 11D and 10D CHY-type superamplitude formulae are placed on a worldsheet footing, and the polarized scattering equation acquires a fermionic partner.

What carries the argument

The central object is the supertwistor form of the 11D ambitwistor superstring action, in which a supertwistor is a constrained collection $(\lambda^\alpha_q,\mu^\alpha_q,\eta_q)$ on the Riemann sphere built from a spinor, a position-like spin-tensor, and a fermionic coordinate. The key step is to treat $\mu^\alpha_q$ as unconstrained by enforcing the constraint with an SO(16) gauge field $\bar A_{pq}$ as a Lagrange multiplier; the hidden SO(16) gauge symmetry is what turns the polarization matrices $W^A_{qi}$ into $\sigma$-dependent functions $W^A_{qi}(\sigma)=W^A_{pi}\tilde O_{pq}(\sigma)$. The mechanism that carries the argument is the saddle-point approximation of the action deformed by vertex-operator source terms: varying with respect to $\mu^\alpha_q$ gives the equations whose solution is the meromorphic spinor function, and the same mechanism produces the fermionic partner function.

What would settle it

Compute a low-point 11D superamplitude from (4.10) with the derived spinor function (5.33) and check whether it obeys the spolarized equation (6.4); a failure there, or the existence of any nonzero solution of $\bar\partial\lambda^\alpha_q=0$ that can be added to (5.33), would show the derivation is incomplete.

Watch

Extended reading notes

Core claim

The central claim is that the 11D polarized scattering equation, written as $\lambda_q^\alpha(\sigma_i)W^A_{qi}(\sigma_i)=\bar\lambda^{A\alpha}_i$, follows from the dynamics of the 11D ambitwistor superstring rather than being put in by hand. Starting from the supertwistor action in which the component $\mu^\alpha_q$ is made unconstrained by adding an SO(16) Lagrange multiplier, the paper adds the vertex-operator source term and varies the resulting effective action. The equations of motion for $\mu^\alpha_q$ reduce, after gauging away the SO(16) connection, to first-order equations whose meromorphic solution is the SO(16)-covariant spinor function (5.33); requiring this function to square to the CHY momentum function produces the polarized scattering equation. The same saddle-point equations give a fermionic function $\eta_q(\sigma)$, and the paper shows that supersymmetry invariance of the amplitude turns this into the linear differential equation (6.4) on the superamplitude.

Load-bearing premise

The derivation of the spinor function and of the polarized scattering equation assumes that the amplitude is governed by the saddle point of the supertwistor action with vertex-operator sources, that the SO(16) connection can be gauged away, and that the solution of the resulting equations has no additional holomorphic piece.

Editorial extensions

If this is right

  • The polarized scattering equation becomes a derived statement, so every 11D superamplitude written in CHY form is tied to a worldsheet model whose equations of motion enforce the scattering data.
  • Every meromorphic spinor function in the formalism is accompanied by a fermionic function, and supersymmetry maps the pair of functions to each other.
  • Tree-level 11D superamplitudes satisfy the new differential equation (6.4), which is a genuine constraint on the amplitude and not merely a support condition on scattering data.
  • In $D=10$ the same derivation produces a doubled polarized scattering equation for the two chiral spinor functions, with the hidden symmetry reduced from SO(16) to SO(8).
  • The SO(16) symmetry is realized as a Stückelberg symmetry after vertex insertion, explaining why the matrix $W^A_{qi}$ in the solution carries a universal $\sigma$-dependent SO(16) rotation.

Reading between the lines

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

  • A direct check of the paper's gauge argument would be to verify numerically that the CHY integral (4.10), built with the derived spinor function (5.33), is invariant under the SO(16) rotation $\tilde O_{pq}(\sigma)$; the paper's derivation implies this invariance exactly.
  • The spolarized equation being a differential constraint on the amplitude suggests that supersymmetric CHY integrals in higher dimensions may need constraints on the integrand beyond the support conditions, a feature that would also affect 10D type II formulae.
  • If the rational-map program mentioned in the conclusion is to work in 11D, the rational spinor map would have to reproduce the same square-root structure, so the residue computation in (8.5) provides a concrete target for that extension.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. The paper revisits the 11D polarized scattering equations of Geyer and Mason from the perspective of the spinor-frame/spinor-moving-frame formulation of the 11D ambitwistor superstring. It derives the meromorphic spinor function λ_αq(σ), its SO(16)-covariant form, and the polarized scattering equation (3.18)/(3.19) from the supertwistor form of the 11D ambitwistor superstring action, making use of the enlarged superspace with 528 bosonic coordinates and the hidden SO(16) gauge symmetry. The paper also proposes a fermionic superpartner, the 'spolarized scattering equation' (6.4), which is a differential equation on superamplitudes rather than a condition on scattering data, and discusses the analogous 10D formalism. The central derivation is presented with many explicit intermediate steps, but it rests on an explicitly labeled factorization assumption that is essential for converting the action solution into the polarized scattering equation.

Significance. If the derivation is accepted, the paper provides a useful clarification of the origin of the 11D polarized scattering equations within the ambitwistor superstring framework, and it identifies a new fermionic equation obeyed by 11D superamplitudes. The strengths of the paper are its explicit derivations: the constraints (3.6), the solution (3.10), the consistency condition (3.18), the action (5.13), the equations of motion (5.23)-(5.24), and the solutions (5.33)-(5.34) are all written out, and the claim is not circular in the sense that the polarized scattering equation emerges as a consistency condition and from the action rather than being fitted to the desired output. However, the central claim is conditional on the factorization assumption (3.16)/(5.29) and on the saddle-point/vertex-operator prescription, and these points are not fully justified. The paper's honesty in labeling the main assumption is commendable, but the announced 'rigorous' derivation is not complete without a justification of that assumption.

major comments (3)
  1. [Sec. 5.2, Eqs. (5.22), (5.29); Sec. 3.4, Eq. (3.20)] The step from the solution (5.31) to the SO(16)-covariant solution (5.33), and hence the derivation of the polarized scattering equation (3.19) through Eq. (3.20), requires the factorization W^A_qi(σ)=W^A_pi \tilde O_pq(σ) with a single i-independent \tilde O(σ). The manuscript labels this as an assumption at (5.29) and notes at (5.22) that W is a Stückelberg field with no equation of motion. No argument is given that the vertex operator's worldsheet dependence or its conformal-weight properties force the σ-dependence of W to be a common SO(16) rotation. If the factorization fails, the product W^B_qj(σ)W^A_qi(σ) is σ-dependent, Eq. (3.20) does not hold, and the derivation of the polarized scattering equation from the action does not go through. This is the load-bearing step of the central claim, so the assumption must either be proved or explicitly stated as a condition on the class of vertex operators considered.
  2. [Sec. 5.2, Eqs. (5.27)-(5.31)] The solution (5.31) is presented as the unique solution of the saddle-point equation (5.27), but the homogeneous equation \bar∂λ=0 has nontrivial holomorphic solutions on the Riemann sphere. The manuscript does not specify the boundary condition or the path-integral measure that eliminates these zero modes. Without such a condition, the identification of (5.33) as the physical spinor function is incomplete, and the subsequent equations derived from it may not be forced. Please justify that the constraints (3.6) or the worldsheet field content remove the holomorphic ambiguity, or state the additional boundary condition explicitly.
  3. [Sec. 5.2, Eq. (5.18) and (5.22)] The effective action (5.22) is obtained by adding linearized source terms from the vertex operator (5.18), but the operator W in (5.18) is left unspecified. If W depends on the worldsheet fields λ, μ, or η, its variation contributes to the saddle-point equations (5.23)-(5.24) and the solutions (5.33)-(5.34) are not the correct saddle points. If W is assumed to depend only on the fixed scattering data, that should be stated explicitly; otherwise the derivation of the equations of motion from (5.22) is incomplete.
minor comments (5)
  1. [Abstract and Sec. 6] The phrase 'rather then' appears in the abstract and later in the text; it should be 'rather than'.
  2. [Sec. 5.2, Eq. (5.22)] The coefficient of the fermionic kinetic term changes from -i\bar∂ηη in Eqs. (5.5) and (5.13) to -2i\bar∂ηη in Eq. (5.22), without comment. Please check the normalization and make it consistent, or explain the rescaling.
  3. [Sec. 7.4, Eqs. (7.54)-(7.57)] The right-chiral spinor function (7.57) is not derived from the 10D action (7.51) but is instead justified by the coset-space argument and a reference to [27]. Since the 10D discussion is secondary, this is acceptable, but it should be clearly marked as an argument by analogy rather than a derivation from the action.
  4. [Introduction, reference list] Reference [44] appears to be uncited in the text: the list of ambitwistor string references in the introduction jumps from [43] to [45]. Please check the citation numbering.
  5. [Sec. 7.3, Eqs. (7.27)-(7.28)] The factor of 2 appearing in the 10D polarized scattering equations (7.27)-(7.28) relative to the 11D equation (3.18) is not explained. A brief comment on the source of this normalization difference would improve readability.

Circularity Check

0 steps flagged · score 0.0 of 10

No circular reduction; the SO(16)-covariant derivation is conditional on an explicit factorization assumption, not on a self-referential fit.

full rationale

The paper's central derivation is conditional but not circular. In Sec. 3.4, the polarized scattering equation (3.18) is obtained as the residue-consistency condition of the square-root constraint (3.6) evaluated on the meromorphic ansatz (3.10); this is a direct equivalence (the residue of 2lambda_q lambda_q equals k_i/ iff (3.18) holds), not a fit. In Sec. 5.2, the spinor function (5.33) is not fitted to the polarized equation; it is the solution of the sourced saddle-point equation (5.27) obtained from the supertwistor action (5.13) plus the vertex operator (5.18), and the polarized equation is then re-derived as the residue condition. The only load-bearing input that is not derived is the factorization W^A_qi(sigma)=W^A_pi tildeO_pq(sigma), which the paper states as an assumption at (5.29): 'we have assumed that W^A_qi = tildeO_qp(sigma_i) W^A_pi(sigma_i) is independent on sigma_i. This assumption is equivalent to (3.16)'. This is an explicit unproven assumption, not a circular reduction: the target equation is not used to justify it, and if the factorization fails the claimed SO(16)-covariant form is invalid, but the derivation would simply be conditional. The fermionic 'spolarized' equation (6.4) is an immediate identity following from the definition of F in (4.8) and the fermionic solution (5.34), and the paper presents it as such ('we can easily find that F from (4.8) satisfies ...'), so it is a consequence of the amplitude ansatz rather than an independent prediction. Self-citations [25,26,27,45,61] supply the spinor-frame formalism, the enlarged-superspace action, and the supertwistor constraints; none of these contains the polarized scattering equation, and they are independent published results with stated assumptions. No step reduces by construction to its own input.

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

No fitted constants appear; all quantities are scattering data, gauge fields, or derived functions. The 517 tensor central-charge coordinates and the SO(16) gauge symmetry are inherited from [45,61], not introduced here. The main axioms are the validity of the ambitwistor superstring description and the vertex-operator/saddle-point prescription, both standard in the field.

assumptions (5)
  • standard math The 11D spinor frame and helicity variables satisfy the constraints (2.2), (2.8), (2.13)-(2.16), (A.1)-(A.12).
    Used throughout, especially in deriving (2.27)-(2.28) and (3.6)-(3.8).
  • domain assumption The 11D ambitwistor superstring action (5.2)/(5.5) and its enlarged-superspace form correctly describe 11D supergravity amplitudes.
    Taken from [45]; the paper builds on this rather than proving it. Invoked in Sec. 5.
  • domain assumption The vertex operator (5.18) is the correct SO(16)-covariant source for the superamplitude in the path integral.
    Generalizes the Geyer-Mason [28] vertex operator; the form of W^A_qi(σ) and the effective action (5.22) are assumed.
  • domain assumption The saddle-point equations (5.23)-(5.24) with gauge (5.26) have unique meromorphic solutions (5.31)-(5.34) with poles only at σ_i.
    Standard ambitwistor-string assumption; not proved in the paper.
  • ad hoc to paper Complexification of spinor variables, replacing reality by analyticity, is valid for the meromorphic functions.
    Stated in Sec. 3.2: 'the usual strategy... is to substitute reality by analyticity'. Needed to treat λ_α^q(σ) as complex meromorphic functions.

how reviews work

0 comments
Cite this review

Pith. "Pith review of On polarized scattering equations for superamplitudes of 11D supergravity and ambitwistor superstring." pith.science (2026). https://pith.science/paper/XRTCF3DK

@misc{pith2026190807482,
  author       = {Pith},
  title        = {Pith review of: On polarized scattering equations for superamplitudes of 11D supergravity and ambitwistor superstring},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/XRTCF3DK}},
  note         = {Machine review of arXiv:1908.07482}
}
abstract

We revisited the formalism of 11D polarized scattering equation by Geyer and Mason from the perspective of spinor frame approach and spinor moving frame formulation of the 11D ambitwistor superstring action. In particular, we rigorously obtain the equation for the spinor function on Riemann sphere from the supertwistor form of the ambitwistor superstring action, write its general solution and use it to derive the polarized scattering equation. We show that the expression used by Geyer and Mason to motivate their ansatz for the solution of polarized scattering equation can be obtained from our solution after a suitable gauge fixing. To this end we use the hidden gauge symmetries of the 11D ambitwistor superstring, including $SO(16)$, and the description of ambitwistor superstring as a dynamical system in an 11D superspace enlarged by bosonic directions parametrized by 517 tensorial central charge coordinates $Z^{\underline{\mu} \underline{\nu}}$ and $Z^{\underline{\mu}\underline{\nu}\underline{\rho}\underline{\sigma}\underline{\kappa}}$. We have also found the fermionic superpartner of the polarized scattering equation. This happens to be a differential equation in fermionic variables imposed on the superamplitude, rather then just a condition on the scattering data as the bosonic polarized scattering equation is. D=10 case is also discussed stressing the similarities and differences with 11D systems. The useful formulation of 10D ambitwistor superstring considers it as a dynamical system in superspace enlarged with 126 tensorial central charge coordinates $Z^{\mu\nu\rho\sigma\kappa}$.

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

79 extracted references · 33 canonical work pages

  1. [28]

    The M-theory S-matrix,

    Y. Geyer and L. Mason, “The M-theory S-matrix,” arXiv:1901.00 134 [hep-th]

    work page 1901

  2. [1]

    Amplitudes and Ultravio- let Behavior of N = 8 Supergravity,

    Z. Bern, J. J. Carrasco, L. J. Dixon, H. Johansson and R. Roiba n, “Amplitudes and Ultravio- let Behavior of N = 8 Supergravity,” Fortsch. Phys. 59 (2011) 561 doi:10.1002/prop.201100037 [arXiv:1103.1848 [hep-th]]

    arXiv 2011

  3. [2]

    Dual superconformal sym- metry of scattering amplitudes in N=4 super-Yang-Mills theory,

    J. M. Drummond, J. Henn, G. P. Korchemsky and E. Sokatchev, “Dual superconformal sym- metry of scattering amplitudes in N=4 super-Yang-Mills theory,” Nuc l. Phys. B 828 (2010) 317 doi:10.1016/j.nuclphysb.2009.11.022 [arXiv:0807.1095 [hep-th]]

    arXiv 2010

  4. [3]

    Yangian symmetry of scattering amplitudes in N=4 su- per Yang-Mills theory,

    J. M. Drummond, J. M. Henn and J. Plefka, “Yangian symmetry of scattering amplitudes in N=4 su- per Yang-Mills theory,” JHEP 0905 (2009) 046 doi:10.1088/1126-6708/2009/05/046 [arXiv:0902.2987 [hep-th]]

    arXiv 2009

  5. [4]

    B. Eden, P. Heslop, G. P. Korchemsky and E. Sokatchev, Nucl. P hys. B 869 (2013) 378 doi:10.1016/j.nuclphysb.2012.12.014 [arXiv:1103.4353 [hep-th]]

    arXiv 2013

  6. [5]

    New E77 invariants and amplitudes,

    R. Kallosh and T. Ortin, “New E77 invariants and amplitudes,” JHEP 1209 (2012) 137 doi:10.1007/JHEP09(2012)137 [arXiv:1205.4437 [hep-th]]

    arXiv 2012

  7. [6]

    Elvang and Y.t

    H. Elvang and Y.t. Huang, Scattering Amplitudes in Gauge Theory a nd Gravity. Cambridge: CUP, 2015

    work page 2015

  8. [7]

    Arkani-Hamed, J.L

    N. Arkani-Hamed, J.L. Bourjaily, F. Cachazo, A.B. Goncharov, A . Postnikov and J. Trnka, Grass- mannian Geometry of Scattering Amplitudes. Cambridge: CUP, 2015 , 194pp

    work page 2015

Show all 79 references
  1. [8]

    Six- Gluon amplitudes in planar N = 4 super-Yang-Mills theory at six and seven loops,

    S. Caron-Huot, L. J. Dixon, F. Dulat, M. von Hippel, A. J. McLeod and G. Papathanasiou, “Six- Gluon amplitudes in planar N = 4 super-Yang-Mills theory at six and seven loops,” JHEP 1908 (2019) 016 doi:10.1007/JHEP08(2019)016 [arXiv:1903.10890 [hep-t h]]

    2019 arXiv

  2. [9]

    Twistor algebra,

    R. Penrose, “Twistor algebra,” J. Math. Phys. 8 (1967) 345. doi:10.1063/1.1705200

    1967 doi

  3. [10]

    Twistor theory: An Approa ch to the quantization of fields and space-time,

    R. Penrose and M. A. H. MacCallum, “Twistor theory: An Approa ch to the quantization of fields and space-time,” Phys. Rept. 6 (1972) 241. doi:10.1016/0370-1573(73)90008-2

    1972 doi

  4. [11]

    Twistor theory at fifty : from contour integrals to twistor strings,

    M. Atiyah, M. Dunajski and L. Mason, “Twistor theory at fifty : from contour integrals to twistor strings,” Proc. Roy. Soc. Lond. A 473 (2017) no.2206, 20170530 doi:10.1098/rspa.2017.0530 [arXiv:1704.07464 [hep-th]] and refs. therein

    2017

  5. [12]

    Direct proof of tree-level recursion relation in Yang-Mills theory,

    R. Britto, F. Cachazo, B. Feng and E. Witten, “Direct proof of tree-level recursion relation in Yang-Mills theory,” Phys. Rev. Lett. 94 (2005) 181602 doi:10.1103/PhysRevLett.94.181602 [hep- th/0501052]

    2005

  6. [13]

    Generating Tree Amp litudes in N=4 SYM and N = 8 SG,

    M. Bianchi, H. Elvang and D. Z. Freedman, “Generating Tree Amp litudes in N=4 SYM and N = 8 SG,” JHEP 0809 (2008) 063 doi:10.1088/1126-6708/2008/09/063 [arXiv:0805.0757 [hep-th]]

    2008 arXiv

  7. [14]

    What is the Simples t Quantum Field Theory?,

    N. Arkani-Hamed, F. Cachazo and J. Kaplan, “What is the Simples t Quantum Field Theory?,” JHEP 1009 (2010) 016 doi:10.1007/JHEP09(2010)016 [arXiv:0808.1446 [hep-th ]]

    2010 arXiv

  8. [15]

    A Note on dual sup erconformal symmetry of the N=4 super Yang-Mills S-matrix,

    A. Brandhuber, P. Heslop and G. Travaglini, “A Note on dual sup erconformal symmetry of the N=4 super Yang-Mills S-matrix,” Phys. Rev. D 78 (2008) 125005 doi:10.1103/PhysRevD.78.125005 [arXiv:0807.4097 [hep-th]]

    2008 arXiv

  9. [16]

    Dual Superconformal Invarianc e, Momentum Twistors and Grassman- nians,

    L. J. Mason and D. Skinner, “Dual Superconformal Invarianc e, Momentum Twistors and Grassman- nians,” JHEP 0911 (2009) 045 doi:10.1088/1126-6708/2009/11/045 [arXiv:0909.0250 [hep-th]]. 37

    2009 arXiv

  10. [17]

    On-shell diagrams for N = 8 supergravity amplitudes,

    P. Heslop and A. E. Lipstein, “On-shell diagrams for N = 8 supergravity amplitudes,” JHEP 1606 (2016) 069 doi:10.1007/JHEP06(2016)069 [arXiv:1604.03046 [hep-t h]]

    2016 arXiv

  11. [18]

    Gravity On-shell Diagrams,

    E. Herrmann and J. Trnka, “Gravity On-shell Diagrams,” JHEP 1611 (2016) 136 doi:10.1007/JHEP11(2016)136 [arXiv:1604.03479 [hep-th]]

    2016 arXiv

  12. [19]

    Amplitudes and Spinor-Helicity in Six Dim ensions,

    C. Cheung and D. O’Connell, “Amplitudes and Spinor-Helicity in Six Dim ensions,” JHEP 0907 (2009) 075 doi:10.1088/1126-6708/2009/07/075 [arXiv:0902.0981 [hep-th]]

    2009 arXiv

  13. [20]

    Spinor Helicity and Dual Confor mal Symmetry in Ten Dimen- sions,

    S. Caron-Huot and D. O’Connell, “Spinor Helicity and Dual Confor mal Symmetry in Ten Dimen- sions,” JHEP 1108 (2011) 014 [arXiv:1010.5487 [hep-th]]

    2011 arXiv

  14. [21]

    Simple superamplitudes in higher dimen sions,

    R. H. Boels and D. O’Connell, “Simple superamplitudes in higher dimen sions,” JHEP 1206 (2012) 163 [arXiv:1201.2653 [hep-th]]

    2012 arXiv

  15. [22]

    Maximal R-symmetry violating amplitudes in type IIB superstring theory,

    R. H. Boels, “Maximal R-symmetry violating amplitudes in type IIB superstring theory,” Phys. Rev. Lett. 109 (2012) 081602 [arXiv:1204.4208 [hep-th]]

    2012 arXiv

  16. [23]

    Constraining Higher Derivative Supergravit y with Scattering Amplitudes,

    Y. Wang and X. Yin, “Constraining Higher Derivative Supergravit y with Scattering Amplitudes,” Phys. Rev. D 92 (2015) no.4, 041701 doi:10.1103/PhysRevD.92.041701 [arXiv:1502.03 810 [hep-th]]

    2015 doi

  17. [24]

    Supervertices and Non-renormalization Co nditions in Maximal Supergravity Theories,

    Y. Wang and X. Yin, “Supervertices and Non-renormalization Co nditions in Maximal Supergravity Theories,” arXiv:1505.05861 [hep-th]

    arXiv

  18. [25]

    Britto-Cachazo-Feng-WittenType recurrent r elations for tree amplitudes of D = 11 supergravity,

    I. Bandos, “Britto-Cachazo-Feng-WittenType recurrent r elations for tree amplitudes of D = 11 supergravity,” Phys. Rev. Lett. 118 (2017) no.3, 031601 doi:10.1103/PhysRevLett.118.031601 [arXiv:1605.00036 [hep-th]]

    2017 arXiv

  19. [26]

    An analytic superfield formalism for tree superamp litudes in D=10 and D=11,

    I. Bandos, “An analytic superfield formalism for tree superamp litudes in D=10 and D=11,” JHEP 1805 (2018) 103 doi:10.1007/JHEP05(2018)103 [arXiv:1705.09550 [hep-t h]]

    2018 arXiv

  20. [27]

    Spinor frame formalism for amplitudes and constra ined superamplitudes of 10D SYM and 11D supergravity,

    I. Bandos, “Spinor frame formalism for amplitudes and constra ined superamplitudes of 10D SYM and 11D supergravity,” JHEP 1811 (2018) 017 doi:10.1007/JHEP11(2018)017 [arXiv:1711.00914 [hep-th]]

    2018 arXiv

  21. [29]

    Spinor description of D = 5 massless low-spin gaug e fields,

    D. V. Uvarov, “Spinor description of D = 5 massless low-spin gaug e fields,” Class. Quant. Grav. 33 (2016) no.13, 135010 doi:10.1088/0264-9381/33/13/135010 [arX iv:1506.01881 [hep-th]]

    2016 arXiv

  22. [30]

    Twistor methods for AdS 5,

    T. Adamo, D. Skinner and J. Williams, “Twistor methods for AdS 5,” JHEP 1608 (2016) 167 doi:10.1007/JHEP08(2016)167 [arXiv:1607.03763 [hep-th]]

    2016 arXiv

  23. [31]

    Multitwistor mechanics of massless superpartic le on AdS5 ×S5 superbackground,

    D. V. Uvarov, “Multitwistor mechanics of massless superpartic le on AdS5 ×S5 superbackground,” arXiv:1907.13613 [hep-th]

    1907 arXiv

  24. [32]

    Holog raphy from Conformal Field Theory,

    I. Heemskerk, J. Penedones, J. Polchinski and J. Sully, “Holog raphy from Conformal Field Theory,” JHEP 0910 (2009) 079 doi:10.1088/1126-6708/2009/10/079 [arXiv:0907.0151 [hep-th]]

    2009 arXiv

  25. [33]

    New relation for AdS amplitudes,

    S. Albayrak, C. Chowdhury and S. Kharel, “New relation for AdS amplitudes,” JHEP 1910 (2019) 274 doi:10.1007/JHEP10(2019)274 [arXiv:1904.10043 [hep-th]]

    2019 arXiv

  26. [34]

    Spinor-Helicity Formalism for Ma ssless Fields in AdS 4,

    B. Nagaraj and D. Ponomarev, “Spinor-Helicity Formalism for Ma ssless Fields in AdS 4,” Phys. Rev. Lett. 122 (2019) no.10, 101602 doi:10.1103/PhysRevLett.122.101602 [arXiv:1 811.08438 [hep-th]]

    2019 doi

  27. [35]

    Scattering of Massless Par ticles in Arbitrary Dimensions,

    F. Cachazo, S. He and E. Y. Yuan, “Scattering of Massless Par ticles in Arbitrary Dimensions,” Phys. Rev. Lett. 113 (2014) no.17, 171601 doi:10.1103/PhysRevLett.113.171601 [arXiv:1 307.2199 [hep-th]]. 38

    2014 doi

  28. [36]

    Scattering Equations and M atrices: From Einstein To Yang-Mills, DBI and NLSM,

    F. Cachazo, S. He and E. Y. Yuan, “Scattering Equations and M atrices: From Einstein To Yang-Mills, DBI and NLSM,” JHEP 1507 (2015) 149 doi:10.1007/JHEP07(2015)149 [arXiv:1412.3479 [hep-th ]]

    2015 arXiv

  29. [37]

    The High-Energy Behavior of Str ing Scattering Amplitudes,

    D. J. Gross and P. F. Mende, “The High-Energy Behavior of Str ing Scattering Amplitudes,” Phys. Lett. B 197 (1987) 129. doi:10.1016/0370-2693(87)90355-8

    1987 doi

  30. [38]

    String Theory Beyond the Planck Scale,

    D. J. Gross and P. F. Mende, “String Theory Beyond the Planck Scale,” Nucl. Phys. B 303 (1988)

    1988

  31. [39]

    The High-energy Behavior of Ope n String Scattering,

    D. J. Gross and J. L. Manes, “The High-energy Behavior of Ope n String Scattering,” Nucl. Phys. B 326 (1989) 73. doi:10.1016/0550-3213(89)90435-5

    1989 doi

  32. [40]

    Scattering E quations: From Projective Spaces to Tropical Grassmannians,

    F. Cachazo, N. Early, A. Guevara and S. Mizera, “Scattering E quations: From Projective Spaces to Tropical Grassmannians,” JHEP 1906 (2019) 039 doi:10.1007/JHEP06(2019)039 [arXiv:1903.08904 [hep-th]]

    2019 arXiv

  33. [41]

    Polarized Scattering Equations for 6D Superamplitudes,

    Y. Geyer and L. Mason, “Polarized Scattering Equations for 6D Superamplitudes,” Phys. Rev. Lett. 122 (2019) no.10, 101601 doi:10.1103/PhysRevLett.122.101601 [arXiv:1 812.05548 [hep-th]]

    2019 doi

  34. [42]

    Ambitwistor strings and the scatter ing equations,

    L. Mason and D. Skinner, “Ambitwistor strings and the scatter ing equations,” JHEP 1407 (2014) 048 doi:10.1007/JHEP07(2014)048 [arXiv:1311.2564 [hep-th]]

    2014 arXiv

  35. [43]

    Ambitwistor strings and th e scattering equations at one loop,

    T. Adamo, E. Casali and D. Skinner, “Ambitwistor strings and th e scattering equations at one loop,” JHEP 1404 (2014) 104 [arXiv:1312.3828 [hep-th]]

    2014 arXiv

  36. [44]

    A Worldsheet Theory for S upergravity,

    T. Adamo, E. Casali and D. Skinner, “A Worldsheet Theory for S upergravity,” JHEP 1502 (2015) 116 [arXiv:1409.5656 [hep-th]]

    2015 arXiv

  37. [45]

    Twistor/ambitwistor strings and null-superstring s in spacetime of D=4, 10 and 11 di- mensions,

    I. Bandos, “Twistor/ambitwistor strings and null-superstring s in spacetime of D=4, 10 and 11 di- mensions,” JHEP 1409 (2014) 086 doi:10.1007/JHEP09(2014)086 [arXiv:1404.1299 [hep-th ]]

    2014 arXiv

  38. [46]

    Ambitwistor Strings in Four Dimensions,

    Y. Geyer, A. E. Lipstein and L. J. Mason, “Ambitwistor Strings in Four Dimensions,” Phys. Rev. Lett. 113 (2014) 8, 081602 [arXiv:1404.6219 [hep-th]]

    2014 arXiv

  39. [47]

    Towards a Worldsheet Descript ion of N=8 Supergravity,

    A. Lipstein and V. Schomerus, “Towards a Worldsheet Descript ion of N=8 Supergravity,” arXiv:1507.02936 [hep-th]

    arXiv

  40. [48]

    On the null origin of the ambitwistor s tring,

    E. Casali and P. Tourkine, “On the null origin of the ambitwistor s tring,” JHEP 1611 (2016) 036 doi:10.1007/JHEP11(2016)036 [arXiv:1606.05636 [hep-th]]

    2016 arXiv

  41. [49]

    The complex null string, Galilean conformal algebra and scattering equations,

    E. Casali, Y. Herfray and P. Tourkine, “The complex null string, Galilean conformal algebra and scattering equations,” JHEP 1710 (2017) 164 doi:10.1007/JHEP10(2017)164 [arXiv:1707.09900 [hep- th]]

    2017 arXiv

  42. [50]

    Ambitwistor string verte x operators on curved backgrounds,

    T. Adamo, E. Casali and S. Nekovar, “Ambitwistor string verte x operators on curved backgrounds,” JHEP 1901 (2019) 213 doi:10.1007/JHEP01(2019)213 [arXiv:1809.04489 [hep-t h]]

    2019 arXiv

  43. [51]

    An Alternative Perspect ive on Ambitwistor String Theory,

    N. Carabine and R. A. Reid-Edwards, “An Alternative Perspect ive on Ambitwistor String Theory,” arXiv:1809.05177 [hep-th]

    arXiv

  44. [52]

    D=11 massless superparticle covariant quantiz ation, pure spinor BRST charge and hidden symmetries,

    I. A. Bandos, “D=11 massless superparticle covariant quantiz ation, pure spinor BRST charge and hidden symmetries,” Nucl. Phys. B 796 (2008) 360 [arXiv:0710.4342 [hep-th]]

    2008 arXiv

  45. [53]

    Unconstrained N=2 Matter, Yang-Mills and Supergravity Theories in Harmonic Superspace,

    A. Galperin, E. Ivanov, S. Kalitsyn, V. Ogievetsky and E. Sokat chev, “Unconstrained N=2 Matter, Yang-Mills and Supergravity Theories in Harmonic Superspace,” Class . Quant. Grav. 1 (1984) 469 Erratum: [Class. Quant. Grav. 2 (1985) 127]. doi:10.1088/0264-9381/1/5/004 39

    1984 doi

  46. [54]

    Twistor transf orm for superfields,

    A. S. Galperin, P. S. Howe and P. K. Townsend, “Twistor transf orm for superfields,” Nucl. Phys. B 402 (1993) 531. doi:10.1016/0550-3213(93)90651-5

    1993 doi

  47. [55]

    Generalization of Newman-P enrose dyads in connection with the action integral for supermembranes in an eleven-dimensional s pace,

    I. A. Bandos and A. A. Zheltukhin, “Generalization of Newman-P enrose dyads in connection with the action integral for supermembranes in an eleven-dimensional s pace,” JETP Lett. 55 (1992) 81 [Pisma Zh. Eksp. Teor. Fiz. 55 (1992) 81]

    1992

  48. [56]

    Eleven-dimensional superm embrane in a spinor moving repere formalism,

    I. A. Bandos and A. A. Zheltukhin, “Eleven-dimensional superm embrane in a spinor moving repere formalism,” Int. J. Mod. Phys. A 8 (1993) 1081. doi:10.1142/S0217751X93000424

    1993 doi

  49. [57]

    Light Cone Harmonic Superspace and Its Applic ations,

    E. Sokatchev, “Light Cone Harmonic Superspace and Its Applic ations,” Phys. Lett. 169B (1986)

    1986

  50. [58]

    Harmonic Superparticle,

    E. Sokatchev, “Harmonic Superparticle,” Class. Quant. Grav. 4 (1987) 237. doi:10.1088/0264- 9381/4/2/007

    1987 doi

  51. [59]

    Sup erspace formulations of the (su- per)twistor string,

    I. A. Bandos, J. A. de Azcarraga and C. Miquel-Espanya, “Sup erspace formulations of the (su- per)twistor string,” JHEP 0607 (2006) 005 doi:10.1088/1126-6708/2006/07/005 [hep-th/06040 37]

    2006 doi

  52. [60]

    Twis tor string as tensionless superstring,

    I. A. Bandos, J. A. de Azcarraga and C. Miquel-Espanya, “Twis tor string as tensionless superstring,” Fortsch. Phys. 55 (2007) 573 doi:10.1002/prop.200610340 [hep-th/0702133 [HEP-TH ]]

    2007 arXiv

  53. [61]

    On D=11 s upertwistors, superparticle quantiza- tion and a hidden SO(16) symmetry of supergravity,

    I. A. Bandos, J. A. de Azcarraga and D. P. Sorokin, “On D=11 s upertwistors, superparticle quantiza- tion and a hidden SO(16) symmetry of supergravity,” in: ”Proceedin gs, 22nd Max Born Symposium on Quantum, Super and Twistors: A Conference in Honor of Jerzy L ukierski on His ...

    2006 arXiv

  54. [62]

    The Superparticle an d the Lorentz group,

    A. S. Galperin, P. S. Howe and K. S. Stelle, “The Superparticle an d the Lorentz group,” Nucl. Phys. B 368 (1992) 248 [hep-th/9201020]

    1992 arXiv

  55. [63]

    Lorentz harmonic (s uper)fields and (super)particles,

    F. Delduc, A. Galperin and E. Sokatchev, “Lorentz harmonic (s uper)fields and (super)particles,” Nucl. Phys. B 368 (1992) 143

    1992

  56. [64]

    Twistor-like ap proach in the Green-Schwarz D=10 superstring theory,

    I. A. Bandos and A. A. Zheltukhin, Spinor Cartan moving n hedron, Lorentz harmonic formulatio ns of superstrings, and kappa symmetry , JETP Lett. 54 (1991) 421–424; I. A. Bandos and A. A. Zheltukhin, Green-Schwarz superstrings in spinor moving frame formali sm, Phys. Lett. B28...

    1991

  57. [65]

    Superstrings and supermembranes in the doubly supersymmetric geometrical approach,

    I. A. Bandos, D. P. Sorokin, M. Tonin, P. Pasti and D. V. Volkov , “Superstrings and supermembranes in the doubly supersymmetric geometrical approach,” Nucl. Phys. B 446 (1995) 79 [hep-th/9501113]

    1995 arXiv

  58. [66]

    Superbranes and superembeddings,

    D. P. Sorokin, “Superbranes and superembeddings,” Phys. Re pt. 329 (2000) 1 doi:10.1016/S0370- 1573(99)00104-0 [hep-th/9906142]

    2000 arXiv

  59. [67]

    Super Poincare covariant quantization of the s uperstring,

    N. Berkovits, “Super Poincare covariant quantization of the s uperstring,” JHEP 0004 (2000) 018 doi:10.1088/1126-6708/2000/04/018 [hep-th/0001035]

    2000 arXiv

  60. [68]

    Multiloop amplitudes and vanishing theorems using the pure spinor formalism for the superstring,

    N. Berkovits, “Multiloop amplitudes and vanishing theorems using the pure spinor formalism for the superstring,” JHEP 0409 (2004) 047 doi:10.1088/1126-6708/2004/09/047 [hep-th/04060 55]

    2004 doi

  61. [69]

    Multiloop superstring amplitude s from non-minimal pure spinor formalism,

    N. Berkovits and N. Nekrasov, “Multiloop superstring amplitude s from non-minimal pure spinor formalism,” JHEP 0612 (2006) 029 doi:10.1088/1126-6708/2006/12/029 [hep-th/06090 12]. 40

    2006 doi

  62. [70]

    An Introduction to Pure Spinor Su perstring Theory,

    N. Berkovits and H. Gomez, “An Introduction to Pure Spinor Su perstring Theory,” Math. Phys. Stud. (2017) 221 doi:10.1007/978-3-319-65427-0 6 [arXiv:1711.09966 [hep-th]]

    2017 arXiv

  63. [71]

    M5-Brane and D-Bra ne Scattering Amplitudes,

    M. Heydeman, J. H. Schwarz and C. Wen, “M5-Brane and D-Bra ne Scattering Amplitudes,” JHEP 1712 (2017) 003 doi:10.1007/JHEP12(2017)003 [arXiv:1710.02170 [hep-t h]]

    2017 arXiv

  64. [72]

    The S Matrix of 6D Super Yang-Mills and Maximal Supergravity from Rational Maps ,

    F. Cachazo, A. Guevara, M. Heydeman, S. Mizera, J. H. Schwa rz and C. Wen, “The S Matrix of 6D Super Yang-Mills and Maximal Supergravity from Rational Maps ,” JHEP 1809 (2018) 125 doi:10.1007/JHEP09(2018)125 [arXiv:1805.11111 [hep-th]]

    2018 arXiv

  65. [73]

    All Tree Amplitudes of 6D (2, 0) Supergrav- ity: Interacting Tensor Multiplets and the K3 Moduli Space,

    M. Heydeman, J. H. Schwarz, C. Wen and S. Q. Zhang, “All Tree Amplitudes of 6D (2, 0) Supergrav- ity: Interacting Tensor Multiplets and the K3 Moduli Space,” Phys. Rev. Lett. 122 (2019) no.11, 111604 doi:10.1103/PhysRevLett.122.111604 [arXiv:1812.06111 [hep -th]]

    2019 arXiv

  66. [74]

    Unified Formalism for 6D Superamplitu des Based on a Symplectic Grassmannian,

    J. H. Schwarz and C. Wen, “Unified Formalism for 6D Superamplitu des Based on a Symplectic Grassmannian,” JHEP 1908 (2019) 125 doi:10.1007/JHEP08(2019)125 [arXiv:1907.03485 [hep-t h]]

    2019 arXiv

  67. [75]

    Supertwistor descriptio n of ambitwistor strings,

    N. Berkovits, M. Guillen and L. Mason, “Supertwistor descriptio n of ambitwistor strings,” arXiv:1908.06899 [hep-th]

    1908 arXiv

  68. [76]

    A Supertwistor Description of the Massless Sup erparticle in Ten-dimensional Super- space,

    N. Berkovits, “A Supertwistor Description of the Massless Sup erparticle in Ten-dimensional Super- space,” Phys. Lett. B 247 (1990) 45 [Nucl. Phys. B 350 (1991) 193]. doi:10.1016/0370-2693(90)91047- F, 10.1016/0550-3213(91)90258-Y

    1990 doi

  69. [77]

    Twistor - Like Transform in Ten-Dimensions,

    E. Witten, “Twistor - Like Transform in Ten-Dimensions,” Nucl. Ph ys. B 266 (1986) 245. doi:10.1016/0550-3213(86)90090-8 41

    1986 doi

  70. [209]

    doi:10.1016/0370-2693(86)90652-0

    doi

  71. [407]

    doi:10.1016/0550-3213(88)90390-2

    doi

Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.