Bosonic sectorized strings and the $(DF)^{2}$ theory

Matheus Lize; Renann Lipinski Jusinskas; Thales Azevedo

REVIEW 2 major objections 4 minor 32 references

Bosonic sectorized strings and the $(DF)^{2}$ theory

T0 review · 2 major / 4 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read Sectorized bosonic string with current algebras yields the mass-deformed (DF)^2 + YM + φ^3 theory from worldsheet data.

desk verdict A serious chiral-string construction matching (DF)^2+YM+phi^3, but the Clebsch-Gordan identity (3.22c) contradicts the appendix (A.18), so the cubic amplitudes that anchor the result are not reliable as written. read the letter →

arxiv 1908.11371 v3 pith:CK4UZWYV submitted 2019-08-29 hep-th

Thales Azevedo , Renann Lipinski Jusinskas , Matheus Lize This is my paper · ORCID

classification hep-th PACS 11.25.-w

keywords sectorizedstringchiralambitwistorcurrentalgebra(DF)^2theoryeffectiveactionBRSTcohomologyworldsheetderivation

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 argues that the bosonic chiral string, in its sectorized interpretation, provides a worldsheet derivation of a known field theory: the mass-deformed $(DF)^2+YM+\varphi^3$ theory of [17]. Starting from the first-order Polyakov action, the authors define a chiral worldsheet whose fields split into plus and minus sectors, and they compute the BRST spectrum, kinetic action, and three-point amplitudes. For the pure bosonic model they recover the massless graviton/dilaton/Kalb-Ramond sector together with two spin-2 fields with $m^2=\pm 4T$, and in the tensionless limit the bosonic ambitwistor string. Adding current algebras produces a massless vector, a vector with $m^2=-4T$, and a scalar in the traceless-symmetric bi-adjoint representation; the inferred effective action matches the $(DF)^2+YM+\varphi^3$ action, including the scalar that had appeared artificial in the field-theory construction.

What carries the argument

The central object is the sectorized form of the bosonic chiral string: after a singular gauge choice in the first-order Polyakov action, the worldsheet is chiral but carries two sectors (plus and minus) with separate BRST charges $Q=Q_++Q_-$, and nilpotency fixes $d=26$. For the gauge extension, the load-bearing identity is the Sugawara energy-momentum tensor $T_C^\pm$ with central charge $c^{(\pm)}=k\Delta/(k+g)=26-d$, together with the dimension-two primary $J_\alpha$ built from traceless-symmetric ordered pairs of currents via Clebsch-Gordan coefficients $C_{\alpha ab}$. These objects determine the BRST cohomology (which states exist) and the three-point functions (which vertices they have); integrating out the auxiliary vector $B^m_a$ converts the opposite-sign kinetic terms into the $(DF)^2$ kinetic operator.

What would settle it

Compute the four-point tree amplitude of the worldsheet model, once a definition of integrated vertex operators is fixed, and compare it with the four-point amplitude of the proposed action (3.54). Any discrepancy in the contact terms would show that the cubic-level inference does not determine the full nonlinear theory.

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Extended reading notes

Core claim

The paper's central claim is that standard worldsheet techniques, applied to the sectorized bosonic chiral string, reproduce the entire field content and cubic couplings of the mass-deformed $(DF)^2+YM+\varphi^3$ theory. In the pure bosonic model the physical spectrum is the usual massless gravity sector (graviton, dilaton, Kalb-Ramond) plus two massive spin-2 fields with mass-squared $\pm 4T$; the kinetic action shows opposite signs for these massive states, a symptom of the ghosts. In the current-algebra extension, BRST cohomology yields a massless vector $F^m_a$, a massive vector $G^m_a$ with $m^2=-4T$, and a scalar $\varphi_\alpha$ in the traceless-symmetric bi-adjoint representation, with a second gauge sector adding a mirror spectrum and a massless bi-adjoint scalar $\varphi_{aA}$. The three-point worldsheet amplitudes are evaluated through current-algebra OPEs, and the effective action inferred from them, completed by non-linear gauge invariance, is precisely the action (3.42)/(3.54), with all couplings expressed in terms of current-algebra data. In particular, integrating out the auxiliary vector $B^m_a$ converts the opposite-sign kinetic terms into the $(DF)^2$ kinetic operator.

Load-bearing premise

The full nonlinear effective action is inferred from kinetic terms and cubic vertices together with a gauge-invariance requirement; the paper does not compute four-, five-, or six-point vertices, so if higher-point contributions fail to assemble as assumed, the identification with the complete $(DF)^2+YM+\varphi^3$ theory would not follow.

Editorial extensions

If this is right

In the tensionless limit $T\to 0$, the extra states become massless and the BRST charge reduces to that of the bosonic ambitwistor string, so the sectorized model interpolates between tensionful and ambitwistor strings.
The current-algebra extension predicts a massless vector and a vector with $m^2=-4T$ whose opposite-sign kinetic terms combine, after integrating out an auxiliary field, into a $(DF)^2$ kinetic operator with propagator $\eta_{mn}\delta_{ab}/[p^2(p^2-4T)]$.
The scalar $\varphi_\alpha$ in the traceless-symmetric bi-adjoint representation and the couplings $C_{\alpha ab}$ and $d_{\alpha\beta\gamma}$ are not inserted by hand; they come from the worldsheet current-algebra data and remain valid for generic level $k$.
Treating one of the two gauge sectors as a global symmetry yields the full $(DF)^2+YM+\varphi^3$ Lagrangian with mass-squared $m^2=-4T$, tying the tachyon of the field theory to the string tension.

Reading between the lines

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

Beyond the paper: if the cubic-level identification is genuine, the four-point function of the chiral string should match the field-theory amplitude of [17] once integrated vertex operators are defined; this is a concrete test rather than an assumption.
Beyond the paper: the same construction may generalize to other gauge groups or supersymmetric sectors, with the central-charge constraint $c=k\Delta/(k+g)=26-d$ selecting admissible groups and levels for the same kind of mass-deformed $(DF)^2$ effective action.
Beyond the paper: because $(DF)^2$ theories enter as double-copy constituents of bosonic and heterotic string amplitudes, a closed-string worldsheet realization may imply that the chiral string's own amplitudes admit a double-copy form.

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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

You should know two things. First, this is real work: the sectorized bosonic chiral string with current algebras is constructed carefully, the kinetic action is computed from vertex operators, and the matching to the (DF)^2+YM+phi^3 theory of Johansson and Nohle is extracted rather than assumed. Second, as written the central three-point calculation rests on an internal contradiction in the Clebsch-Gordan identities, and that needs to be fixed before the result can be trusted.

What is actually new: the current-algebra extension of the bosonic sectorized string, the worldsheet derivation of the kinetic terms and cubic couplings, and the claim that the mass-deformed (DF)^2+YM+phi^3 action emerges from standard chiral-string technology. The tensionless limit to the ambitwistor string is recovered as a consistency check, and the spectrum matches earlier work. The derivation is not circular: the target-space action is used as a benchmark, not as an input.

The soft spot is load-bearing. Equation (3.22c) says C_{alpha ab} C_{alpha cd} = Delta_{(ab)(cd)} + 2k delta_{(ab)(cd)}, while the appendix's series (A.17), identified with the same coefficients, satisfies (A.18): C_{(ab)(ef)} C_{(ef)(cd)} = delta + Delta/(2k). Since C is symmetric in the index pairs, the left-hand sides are the same matrix product, so the two identities disagree for every finite k. The OPEs involving J_alpha, the claimed symmetry/tracelessness of d_{alpha beta gamma}, and the three-point amplitudes (3.29) all rely on these relations. That makes the cubic vertices that seed the effective action unsupported as written. This is not a minor typo in one unnumbered equation; it sits in the chain connecting the worldsheet to the field theory.

There is a second, smaller caveat the authors themselves flag: only three-point amplitudes are computed, and the full non-linear action (3.42)/(3.54) is inferred from cubic data plus gauge invariance. Gauge invariance does not uniquely determine quartic and higher vertices, so the identification with the full (DF)^2+YM+phi^3 theory is a proposal, not a derivation. I would not call the paper circular or dishonest; it just promises more than the computed evidence delivers at this point.

Who is this for? People working on chiral strings, ambitwistor strings, and double-copy constructions of string amplitudes. The paper is clearly written and technically dense, and a competent reader can re-derive the main steps. It deserves refereeing, but the referee should demand that the Clebsch-Gordan identities be made consistent and the higher-point logic be sharpened. I would not cite it in its current form.

Referee Report

2 major / 4 minor

Summary. This paper studies the bosonic chiral string in the 'sectorized' gauge, a singular chiral limit of the first-order Polyakov action. The authors compute the BRST cohomology, the kinetic action, and the three-point amplitudes of the model, showing that the tensionless limit reproduces the bosonic ambitwistor string. When two current algebras are added, one in each sector, the spectrum consists of a massless vector, a massive vector with m^2 = -4T, and a scalar in the traceless-symmetric bi-adjoint representation. From the three-point amplitudes the paper proposes an effective action, Eq. (3.42), later extended to Eq. (3.54), and identifies it with the mass-deformed (DF)^2 + YM + phi^3 theory of Johansson and Nohle [17].

Significance. If established, the result is significant: it provides a worldsheet origin for a field theory that plays a role in double-copy constructions of bosonic and heterotic string amplitudes, and it explains the otherwise ad hoc scalar representation as a current-algebra composite. The worldsheet computations are self-contained: the spectrum and kinetic terms are derived from the BRST charge, the tensionless limit is checked, and the authors are explicit about which parts are derived and which are conjectural. The main caveats are the normalization of the Clebsch-Gordan coefficients used for the three-point amplitudes and the fact that the full non-linear action is inferred from cubic data plus gauge invariance rather than computed.

major comments (2)

[Eqs. (3.22c) and (A.18)] As written, the normalization of the Clebsch-Gordan coefficients is ambiguous, and this is load-bearing. If C_alpha_ab is identified literally with the series C_(ab)(cd) of (A.17), as the appendix states, then (3.22c) and (A.18) are incompatible: the same product gives Delta + 2k delta in one place and delta + (1/2k) Delta in the other. The two equations are compatible only if C_alpha_ab = sqrt(2k) C_(ab)(cd), but this scaling is never stated and it is not obviously consistent with the OPE (A.20) or with the normalization of the J_alpha two-point function (3.26c). Since the OPEs (3.20) and the definitions (3.24)-(3.25) of d_alpha_beta_gamma feed directly into the three-point amplitudes (3.27)-(3.29), the cubic input to the proposed action (3.42) is not reliably fixed until this normalization is resolved.
[Section 3.3.2, Eq. (3.42)] The central identification with the full (DF)^2 + YM + phi^3 theory is not established. The paper computes only kinetic terms and three-point vertices; as the authors state, higher-point vertices are not computed and 'we expect this integration to hold for higher point vertices as well.' Non-linear gauge invariance restricts but does not uniquely determine the 4-, 5-, and 6-point vertices. Thus the claim in the conclusion that the model 'effectively leads to' the full Lagrangian of [17] is stronger than the derivation supports. The paper should either compute at least the four-point amplitude or explicitly present (3.42)/(3.54) as a conjecture based on cubic data.

minor comments (4)

[Section 3.2, after Eq. (3.20c)] The sentence saying that the dimension-three operators in (3.20c) 'do not contribute to A3' would be clearer if it stated that this is because their two-point functions with the operators in (3.19) vanish.
[Appendix A, Eq. (A.17)] Writing the first two terms of the series explicitly, C = delta + (1/4k) Delta + O(Delta^2), would make the compatibility with (A.18) transparent and would remove part of the normalization ambiguity flagged above.
[Section 3.4, Eqs. (3.48)-(3.54)] The rescaling leading from (3.52) to (3.54) is described only verbally; please specify the field rescaling and verify that the coefficient of the phi^3 term is g lambda/3! with lambda = sqrt(k_hat), or state the convention that makes this true.
[Conclusion, k to 0 limit] The statement that the results agree with [17] in the k to 0 limit should be qualified, because the appendix's power series (A.17) is an expansion in 1/k and k to 0 is not a regular limit of that expansion.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the worldsheet computation is self-contained and the (DF)^2 action is used as a benchmark, not as an input.

full rationale

The paper's derivation chain starts from the first-order Polyakov action, performs a singular gauge fixing to obtain the chiral/sectorized model, computes the BRST cohomology, kinetic action, and 3-point amplitudes from the CFT, and only then compares the inferred effective action with the (DF)^2+YM+phi^3 action of [17]. The target action is not substituted into the worldsheet computation; it appears at the end as an external benchmark. The current-algebra extension introduces J_alpha, C_{alpha ab}, and d_{alpha beta gamma} through CFT definitions/OPEs rather than by fitting to [17]; the agreement at k->0 is presented as a check. Self-citations to [12,14,15,19,20] concern the sectorized framework and methods, but the paper rederives the spectrum, kinetic terms, and amplitudes within its own BRST analysis, so these citations are not load-bearing circularity. Concerns that the full nonlinear action is inferred from kinetic and cubic data plus gauge invariance (Section 3.3.2), and the apparent inconsistency between (3.22c) and (A.18), are substantive correctness/completeness risks, not cases of the output being equivalent to the input by construction. No fitted parameter is renamed as a prediction, and no uniqueness theorem is imported from the authors' prior work.

Assumptions & free parameters 4 free parameters · 4 assumptions · 0 invented entities

The central claim rests on the sectorized chiral string background (tension T, gauge choice), the current algebra CFT with levels k and k_hat, and the existence of the composite primary J_alpha. The free parameters are the string tension T, the effective gauge coupling g, and the affine levels, none of which is fitted to data. The most fragile assumption is the use of non-linear gauge invariance to fix vertices beyond the computed three-point amplitudes.

free parameters (4)

String tension T
Dimensionful parameter of the string model introduced in Eq (2.1). It sets the masses of the massive spin-2 fields and the vector, m^2 = plus or minus 4T, and controls the mass deformation of the (DF)^2 action. It is an input parameter of the model, not fitted to data, but the central mass-deformed claim depends on it.
Gauge coupling g
Introduced in Eq (3.41) when promoting the Abelian field strength to the non-Abelian field strength. It is a free coupling constant of the effective action (3.42)/(3.54), not determined by the worldsheet computation.
Affine level k (minus sector)
Level of the current algebra in the minus sector, constrained by BRST nilpotency through c^(minus) = k dim(G)/(k + dual Coxeter number) = 26 - d (Eq 3.8). For a chosen gauge group it is fixed, but the group and level are model inputs.
Affine level k_hat (plus sector)
Level of the current algebra in the plus sector, subject to an analogous central charge constraint. It appears in the final Lagrangian through lambda = sqrt(k_hat) after rescaling the bi-adjoint scalar (Section 3.4).

assumptions (4)

domain assumption BRST cohomology at ghost number two with b0-invariance defines the physical spectrum.
Standard string theory method used throughout Sections 2.3 and 3.1 to extract the physical fields and their equations of motion.
domain assumption The singular gauge beta going to infinity is legitimate and the sectorized chiral action (2.7) is equivalent to the conformal gauge string with a different vacuum.
Section 2.2 argues this, citing Siegel [9] and Lee-Rey-Rosabal [25]. The whole sectorized description and its BRST charge depend on this gauge choice.
domain assumption The dimension-2 primary operator J_alpha exists and satisfies the OPE (3.20c), with the last-line operators J_(abc), J_[ab] and (J_a, T_C) not contributing to the 3-point amplitude A3.
Section 3 and Appendix A construct J_alpha via Clebsch-Gordan coefficients. The non-contribution of the dimension-3 operators to A3 is asserted, not demonstrated.
ad hoc to paper Non-linear gauge invariance fixes the form of the 4-, 5- and 6-point vertices in the effective action.
Section 3.3.2: 'The form of the higher point vertices (4, 5 and 6) is severely restricted by the non-linear gauge invariance of the effective action.' This is used to propose the full action (3.42) without computing higher-point amplitudes.

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Cite this review

Pith. "Pith review of Bosonic sectorized strings and the $(DF)^{2}$ theory." pith.science (2026). https://pith.science/paper/CK4UZWYV

@misc{pith2026190811371,
  author       = {Pith},
  title        = {Pith review of: Bosonic sectorized strings and the $(DF)^2$ theory},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/CK4UZWYV}},
  note         = {Machine review of arXiv:1908.11371}
}

abstract

In this work, we investigate the bosonic chiral string in the sectorized interpretation, computing its spectrum, kinetic action and $3$-point amplitudes. As expected, the bosonic ambitwistor string is recovered in the tensionless limit. We also consider an extension of the bosonic model with current algebras. In that case, we compute the effective action and show that it is essentially the same as the action of the mass-deformed $(DF)^{2}$ theory found by Johansson and Nohle. Aspects which might seem somewhat contrived in the original construction --- such as the inclusion of a scalar transforming in some real representation of the gauge group --- are shown to follow very naturally from the worldsheet formulation of the theory.

Discussion (0). Continue with ORCID to comment.

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Works this paper leans on

32 extracted references · 4 canonical work pages

[17]

Conformal Gravity from Gauge Theory,

H. Johansson and J. Nohle, “Conformal Gravity from Gauge Theory,” arXiv:1707.02965 [hep-th]

arXiv
[1]

Scattering of Massless Particles in Arbitrary Di- mensions,

F. Cachazo, S. He and E. Y. Yuan, “Scattering of Massless Particles in Arbitrary Di- mensions,” Phys.Rev.Lett.113, no. 17, 171601 (2014) doi:10.1103/PhysRevLett.113.171601 [arXiv:1307.2199 [hep-th]]

arXiv 2014
[2]

Scattering of Massless Particles: Scalars, Gluons and Gravitons,

F. Cachazo, S. He and E. Y. Yuan, “Scattering of Massless Particles: Scalars, Gluons and Gravitons,” JHEP 1407, 033 (2014) doi:10.1007/JHEP07(2014)033 [arXiv:1309.0885 [hep- th]]

arXiv 2014
[3]

Ambitwistor strings and the scattering equations,

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

arXiv 2014
[4]

Inﬁnite Tension Limit of the Pure Spinor Superstring,

N. Berkovits, “Inﬁnite Tension Limit of the Pure Spinor Superstring,” JHEP1403, 017 (2014) doi:10.1007/JHEP03(2014)017 [arXiv:1311.4156 [hep-th]]

arXiv 2014
[5]

Einstein-Yang-Mills Scattering Amplitudes From Scat- tering Equations,

F. Cachazo, S. He and E. Y. Yuan, “Einstein-Yang-Mills Scattering Amplitudes From Scat- tering Equations,” JHEP1501, 121 (2015) doi:10.1007/JHEP01(2015)121 [arXiv:1409.8256 [hep-th]]

arXiv 2015
[6]

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

F. Cachazo, S. He and E. Y. Yuan, “Scattering Equations and Matrices: From Einstein To Yang-Mills, DBI and NLSM,” JHEP1507, 149 (2015) doi:10.1007/JHEP07(2015)149 [arXiv:1412.3479 [hep-th]]. 29

arXiv 2015
[7]

New Ambitwistor String Theories

E. Casali, Y. Geyer, L. Mason, R. Monteiro and K. A. Roehrig, “New Ambitwistor String Theories,” JHEP 1511, 038 (2015) doi:10.1007/JHEP11(2015)038 [arXiv:1506.08771 [hep- th]]

work page Pith review arXiv 2015

Show all 32 references

[8]

Twistor/ambitwistor strings and null-superstrings in spacetime of D=4, 10 and 11 dimensions,

I. Bandos, “Twistor/ambitwistor strings and null-superstrings in spacetime of D=4, 10 and 11 dimensions,” JHEP1409, 086 (2014) doi:10.1007/JHEP09(2014)086 [arXiv:1404.1299 [hep-th]]

2014 arXiv
[9]

Amplitudes for left-handed strings,

W. Siegel, “Amplitudes for left-handed strings,” arXiv:1512.02569 [hep-th]

arXiv
[10]

On the null origin of the ambitwistor string,

E. Casali and P. Tourkine, “On the null origin of the ambitwistor string,” JHEP1611, 036 (2016) doi:10.1007/JHEP11(2016)036 [arXiv:1606.05636 [hep-th]]

2016 arXiv
[11]

Factorization of Chiral String Amplitudes,

Y. t. Huang, W. Siegel and E. Y. Yuan, “Factorization of Chiral String Amplitudes,” JHEP 1609, 101 (2016) doi:10.1007/JHEP09(2016)101 [arXiv:1603.02588 [hep-th]]

2016 arXiv
[12]

Notes on the ambitwistor pure spinor string,

R. L. Jusinskas, “Notes on the ambitwistor pure spinor string,” JHEP1605, 116 (2016) doi:10.1007/JHEP05(2016)116 [arXiv:1604.02915 [hep-th]]

2016 arXiv
[13]

Ambitwistor pure spinor string in a type II supergrav- ity background,

O. Chandia and B. C. Vallilo, “Ambitwistor pure spinor string in a type II supergrav- ity background,” JHEP1506, 206 (2015) doi:10.1007/JHEP06(2015)206 [arXiv:1505.05122 [hep-th]]

2015 arXiv
[14]

Connecting the ambitwistor and the sectorized heterotic strings,

T. Azevedo and R. L. Jusinskas, “Connecting the ambitwistor and the sectorized heterotic strings,” JHEP1710, 216(2017)doi:10.1007/JHEP10(2017)216[arXiv:1707.08840[hep-th]]

2017 arXiv
[15]

Field theory actions for ambitwistor string and superstring,

N. Berkovits and M. Lize, “Field theory actions for ambitwistor string and superstring,” JHEP 1809, 097 (2018) doi:10.1007/JHEP09(2018)097 [arXiv:1807.07661 [hep-th]]

2018 arXiv
[16]

Closed string ﬁeld theory: Quantum action and the B-V master equation,

B. Zwiebach, “Closed string ﬁeld theory: Quantum action and the B-V master equation,” Nucl. Phys. B390, 33 (1993) doi:10.1016/0550-3213(93)90388-6 [hep-th/9206084]

1993 arXiv
[18]

NewRelationsforGauge-TheoryAmplitudes,

Z.Bern, J.J.M.CarrascoandH.Johansson, “NewRelationsforGauge-TheoryAmplitudes,” Phys. Rev. D78, 085011 (2008) doi:10.1103/PhysRevD.78.085011 [arXiv:0805.3993 [hep- ph]]

2008 arXiv
[19]

Ambitwistor formulations of R2 gravity and (DF)2 gauge theories,

T. Azevedo and O. T. Engelund, “Ambitwistor formulations of R2 gravity and (DF)2 gauge theories,” JHEP1711, 052 (2017) doi:10.1007/JHEP11(2017)052 [arXiv:1707.02192 [hep- th]]. 30

2017 arXiv
[20]

Heterotic and bosonic string amplitudes via ﬁeld theory,

T. Azevedo, M. Chiodaroli, H. Johansson and O. Schlotterer, “Heterotic and bosonic string amplitudes via ﬁeld theory,” JHEP1810, 012 (2018) doi:10.1007/JHEP10(2018)012 [arXiv:1803.05452 [hep-th]]

2018 arXiv
[21]

String amplitudes from ﬁeld-theory amplitudes and vice versa,

S. He, F. Teng and Y. Zhang, “String amplitudes from ﬁeld-theory amplitudes and vice versa,” Phys. Rev. Lett.122, no. 21, 211603 (2019) doi:10.1103/PhysRevLett.122.211603 [arXiv:1812.03369 [hep-th]]

2019 arXiv
[22]

String Correlators: Recursive Expansion, Integration-by- Parts and Scattering Equations,

S. He, F. Teng and Y. Zhang, “String Correlators: Recursive Expansion, Integration-by- Parts and Scattering Equations,” arXiv:1907.06041 [hep-th]

1907 arXiv
[23]

C. R. Mafra, O. Schlotterer and S. Stieberger,Complete N-Point Superstring Disk Amplitude I. Pure Spinor Computation , Nucl. Phys. B873 (2013) 419–460, [arXiv:1106.2645 [hep-th]]

2013 arXiv
[24]

Doubledα′-geometry,

O. Hohm, W. Siegel and B. Zwiebach, “Doubledα′-geometry,” JHEP1402, 065 (2014) doi:10.1007/JHEP02(2014)065 [arXiv:1306.2970 [hep-th]]

2014 arXiv
[25]

K. Lee, S. J. Rey and J. A. Rosabal, JHEP1711, 172 (2017) doi:10.1007/JHEP11(2017)172 [arXiv:1708.05707 [hep-th]]

2017 arXiv
[26]

The complex null string, Galilean conformal al- gebra and scattering equations,

E. Casali, Y. Herfray and P. Tourkine, “The complex null string, Galilean conformal al- gebra and scattering equations,” JHEP1710, 164 (2017) doi:10.1007/JHEP10(2017)164 [arXiv:1707.09900 [hep-th]]

2017 arXiv
[27]

Chiral Closed strings: Four massless states scattering ampli- tude,

M. M. Leite and W. Siegel, “Chiral Closed strings: Four massless states scattering ampli- tude,” JHEP1701, 057 (2017) doi:10.1007/JHEP01(2017)057 [arXiv:1610.02052 [hep-th]]

2017 arXiv
[28]

Perturbative gauge theory as a string theory in twistor space,

E. Witten, “Perturbative gauge theory as a string theory in twistor space,” Commun. Math. Phys. 252, 189 (2004) doi:10.1007/s00220-004-1187-3 [hep-th/0312171]

2004 arXiv
[29]

Conformal supergravity in twistor-string theory,

N. Berkovits and E. Witten, “Conformal supergravity in twistor-string theory,” JHEP0408 (2004) 009 doi:10.1088/1126-6708/2004/08/009 [hep-th/0406051]

2004 arXiv
[30]

Abelian Z-theory: NLSM amplitudes and α’-corrections from the open string,

J. J. M. Carrasco, C. R. Mafra and O. Schlotterer, “Abelian Z-theory: NLSM amplitudes and α’-corrections from the open string,” JHEP1706, 093 (2017) doi:10.1007/JHEP06(2017)093 [arXiv:1608.02569 [hep-th]]

2017 arXiv
[31]

Non-abelianZ-theory: Berends-Giele recursion for the α′-expansion of disk integrals,

C. R. Mafra and O. Schlotterer, “Non-abelianZ-theory: Berends-Giele recursion for the α′-expansion of disk integrals,” JHEP1701, 031 (2017) doi:10.1007/JHEP01(2017)031 [arXiv:1609.07078 [hep-th]]. 31

2017 arXiv
[32]

Semi-abelian Z-theory: NLSM+φ3 from the open string,

J. J. M. Carrasco, C. R. Mafra and O. Schlotterer, “Semi-abelian Z-theory: NLSM+φ3 from the open string,” JHEP1708, 135 (2017) doi:10.1007/JHEP08(2017)135 [arXiv:1612.06446 [hep-th]]. 32

2017 arXiv

Pith tools

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

[1] [17]

Conformal Gravity from Gauge Theory,

H. Johansson and J. Nohle, “Conformal Gravity from Gauge Theory,” arXiv:1707.02965 [hep-th]

arXiv

[2] [1]

Scattering of Massless Particles in Arbitrary Di- mensions,

F. Cachazo, S. He and E. Y. Yuan, “Scattering of Massless Particles in Arbitrary Di- mensions,” Phys.Rev.Lett.113, no. 17, 171601 (2014) doi:10.1103/PhysRevLett.113.171601 [arXiv:1307.2199 [hep-th]]

arXiv 2014

[3] [2]

Scattering of Massless Particles: Scalars, Gluons and Gravitons,

F. Cachazo, S. He and E. Y. Yuan, “Scattering of Massless Particles: Scalars, Gluons and Gravitons,” JHEP 1407, 033 (2014) doi:10.1007/JHEP07(2014)033 [arXiv:1309.0885 [hep- th]]

arXiv 2014

[4] [3]

Ambitwistor strings and the scattering equations,

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

arXiv 2014

[5] [4]

Inﬁnite Tension Limit of the Pure Spinor Superstring,

N. Berkovits, “Inﬁnite Tension Limit of the Pure Spinor Superstring,” JHEP1403, 017 (2014) doi:10.1007/JHEP03(2014)017 [arXiv:1311.4156 [hep-th]]

arXiv 2014

[6] [5]

Einstein-Yang-Mills Scattering Amplitudes From Scat- tering Equations,

F. Cachazo, S. He and E. Y. Yuan, “Einstein-Yang-Mills Scattering Amplitudes From Scat- tering Equations,” JHEP1501, 121 (2015) doi:10.1007/JHEP01(2015)121 [arXiv:1409.8256 [hep-th]]

arXiv 2015

[7] [6]

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

F. Cachazo, S. He and E. Y. Yuan, “Scattering Equations and Matrices: From Einstein To Yang-Mills, DBI and NLSM,” JHEP1507, 149 (2015) doi:10.1007/JHEP07(2015)149 [arXiv:1412.3479 [hep-th]]. 29

arXiv 2015

[8] [7]

New Ambitwistor String Theories

E. Casali, Y. Geyer, L. Mason, R. Monteiro and K. A. Roehrig, “New Ambitwistor String Theories,” JHEP 1511, 038 (2015) doi:10.1007/JHEP11(2015)038 [arXiv:1506.08771 [hep- th]]

work page Pith review arXiv 2015