Pith. sign in

REVIEW 3 major objections 4 minor 65 references

Local symmetry and extended spacetime

T0 review · 3 major / 4 minor · reviewed 2026-08-16 · deepseek-v4-flash

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

Pith's one-line read E-theory gauge transformations close under a constraint on extended-spacetime parameters, and in the IIA level-zero limit they reproduce double field theory without the usual section conditions.

desk verdict The paper proposes a genuinely different closure constraint for the E-theory gauge transformations and checks it against DFT at level zero, but the central 'closing algebra' claim is not established: the bracket parameter is never shown to satisfy the constraint, and the constraint is pairwise rather than a well-defined single-parameter condition. read the letter →

arxiv 2504.18229 v1 pith:GMWRT25O submitted 2025-04-25 hep-th

Peter West This is my paper · ORCID
classification hep-th
keywords EtheoryE11extendedspacetimedoublefieldsectionconditionsIIAsupergravitygaugealgebraclosurebranecharges
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 attempts to show that the local symmetry transformations of E theory, the proposed eleven-dimensional symmetry underlying maximal supergravity, form a closed gauge algebra once the transformation parameters are required to obey a simple differential constraint, $C_\alpha=0$. Evaluated in the level-zero sector of the IIA decomposition, these transformations coincide with those of double field theory, but the closure constraint is not the standard section condition. The author argues that the extended spacetime coordinates of E theory encode brane positions, and that the constraints needed for invariance should therefore be specific field equations rather than generic restrictions on all fields. A sympathetic reader would care because a closed gauge algebra with a natural parameter constraint would put the gauge structure of E theory on the same footing as ordinary diffeomorphisms and suggest a brane-based origin for the extra coordinates.

What carries the argument

The load-bearing object is the proposed local transformation of the E-theory vierbein, together with the parameter constraint $C_\alpha=0$ that makes its commutator close. Here $C^{-1}$ is the inverse Killing form of $E_{11}$, $D_\alpha$ is the matrix representative of the generator $R_\alpha$ in the vector representation, and $C_\alpha$ is a specific combination of structure constants, representation matrices, and derivatives of the two parameters. In the IIA level-zero decomposition this machinery reduces to $SO(10,10)\otimes GL(1)$ data: the generalized vierbein $E_\Pi^A = e^{-\tau/2}\begin{pmatrix} e & A e^{-T} \\ 0 & e^{-T} \end{pmatrix}$, the $O(D,D)$ metric $\Omega_{\Pi\Sigma}$, and a closure condition $C_{\Pi\Lambda}=0$ that restricts how parameters may depend on the doubled coordinates $(x^\mu, y_{\mu})$. The same transformation is also reached by a Noether-style argument from linearised gauge invariance, which the paper takes as evidence that the nonlinear form is forced rather than chosen.

What would settle it

Take two parameter fields $\Lambda_1^\Pi$, $\Lambda_2^\Pi$ that obey the IIA level-zero closure condition $C_{\Pi\Lambda}=0$ of equation (5.3.4), form $\Lambda_c^\Pi = \Lambda_2^\Sigma\partial_\Sigma\Lambda_1^\Pi - \Lambda_1^\Sigma\partial_\Sigma\Lambda_2^\Pi$, and evaluate $C_{\Pi\Lambda}(\Lambda_c)$; an explicit pair for which this is nonzero would show the constrained transformations do not close, disproving the paper's central claim.

Watch

Extended reading notes

Core claim

The central claim is that the local transformation of the E-theory vierbein, $\delta E_\Pi^A = (C^{-1})^{\alpha\beta}(D_\alpha)_\Pi^\Sigma E_\Sigma^A (D_\beta)_\Lambda^\Gamma \partial_\Gamma \Lambda^\Lambda + \Lambda^\Pi \partial_\Pi E_\Pi^A$, has a closing commutator algebra: $[\delta_{\Lambda_1}, \delta_{\Lambda_2}]$ is again a transformation of the same form with parameter $\Lambda_c^\Pi = \Lambda_2^\Sigma\partial_\Sigma \Lambda_1^\Pi - \Lambda_1^\Sigma\partial_\Sigma\Lambda_2^\Pi$, provided the combination $C_\alpha$ of equation (3.5) vanishes. In the IIA level-zero decomposition, the same fields, spacetime, and local transformations as double field theory appear, and the closure condition reduces to $C_{\Pi\Lambda}=0$ of equation (5.3.4), which is not one of the weak or strong section conditions of equations (1.2)-(1.3). The paper further argues from the irreducible representation analysis that fields' dependence on the extra coordinates is sourced by branes, and that the proper non-linear constraints replacing the section conditions should be specific equations on the fields, not generic conditions on products of derivatives.

Load-bearing premise

The paper's central claim depends on the unverified premise that the composite parameter $\Lambda_c^\Pi$ obtained from commuting two allowed transformations again satisfies the same constraint $C_\alpha=0$; the text checks that the commutator has the right form only when $C_\alpha=0$ for the original pair, but does not prove closure of the constrained parameter set itself.

Editorial extensions

If this is right

  • A closed gauge algebra for E theory's local transformations would let one treat the E-theory vierbein transformations as an ordinary parameter-constrained gauge symmetry, with diffeomorphisms and form-field gauge transformations appearing as low-level components.
  • At level zero of the IIA decomposition, the paper's transformations reproduce the known double-field-theory gauge transformations, so E theory contains that symmetry structure without assuming the section conditions from the outset.
  • The closure constraint (5.3.4) is not implied by, nor does it imply, the weak or strong section conditions; the two routes to a consistent doubled theory are therefore genuinely different.
  • If the field-dependent conditions suggested by the irreducible-representation analysis are the correct non-linear constraints, then invariance of the level-zero action follows without imposing generic section conditions.
  • The extended coordinates of E theory are tied to brane charges: non-trivial dependence on those coordinates corresponds to the presence of branes, so a theory truncated to point particles breaks the $E_{11}$ symmetry.

Reading between the lines

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

  • A direct test the paper leaves open is whether the bracket parameter $\Lambda_c^\Pi$ itself satisfies the closure constraint $C_\alpha=0$; if it does not, the constrained parameter space is not closed under commutation, and the algebra claim needs an additional condition. This check is not carried out in the text.
  • If the parameter constraint proves consistent, it suggests a hierarchy: each level of the $E_{11}$ decomposition may carry its own analogue of (5.3.4), so extending the calculation to level one (the Ramond-Ramond sector) would produce a testable generalization of the doubled gauge algebra.
  • The linearised conditions (5.4.9), which kill the parameter components absent from lowest-order gauge transformations, resemble a gauge-fixing of the parameter redundancy rather than a restriction on fields; making this precise could clarify when the action variation (5.4.2) vanishes without section conditions.
  • Because the paper shows the level-zero IIA closure condition differs from section conditions, any derivation of double field theory from E theory would need to explain how the usual section-condition-based proofs of gauge invariance emerge from the new field equations, or whether they are replaced by them.
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 / 4 minor

Summary. The paper studies a class of local gauge transformations in E theory (the non-linear realisation of E11 ⊗ sl1), previously proposed by the author. Its main technical claim is that these transformations form a closing algebra provided the gauge parameters are restricted by the constraint Cα = 0, Eq. (3.5). The paper then evaluates the transformations at level zero of the IIA decomposition, finds that they coincide with the gauge transformations of Siegel theory / double field theory, but that the closure constraint (5.3.4) is not equivalent to the weak or strong section conditions (1.2) and (1.3). It closes with a discussion of alternative constraints that might make the level-zero action invariant, and of how dependence on the additional coordinates beyond standard spacetime should be understood as arising from the presence of branes.

Significance. If the closure claim and the proposed replacement of the section conditions were fully established, the paper would provide a derivation of double-field-theory gauge transformations from E11 and a new perspective on the role of extended spacetime in E theory. The explicit commutator computation, the identification of the obstruction term Cα, and the detailed level-zero comparison with the Siegel/Hull–Zwiebach/Hohm literature are concrete and checkable contributions. The paper also makes a sharp falsifiable statement: its closure constraint (5.3.4) is different from the generic section conditions. However, the central gauge-algebra claim is incomplete, and the action-invariance part is explicitly deferred, so the significance is conditional on future checks rather than established by the present manuscript.

major comments (3)
  1. [Sec. 3, Eqs. (3.2)–(3.5)] The paper's central closure claim is incomplete. Equation (3.2) computes the commutator of two transformations and identifies the extra term Cα; setting Cα = 0 makes the commutator take the form of a transformation with parameter Λ_c. However, for the set of allowed parameters to be a gauge algebra, the parameter Λ_c itself must be an allowed parameter: one must verify Cα(Λ_c, Λ_3) = 0 for every allowed parameter Λ_3 (or the intended analogue). This check is never performed. The issue is not cosmetic, because Cα(Λ, Λ) vanishes identically by antisymmetry, so (3.5) is not a restriction on a single parameter but a pairwise condition; without the closure check, the abstract's statement that the transformations 'have a closing algebra' is not established.
  2. [Sec. 5.4, Eqs. (5.4.1)–(5.4.6)] The invariance of the type-II level-zero action under the proposed local transformations is not demonstrated. The variation is reduced to Eq. (5.4.2), but the text then states that the precise conditions for the action to be invariant are left to a future paper. The suggested alternatives, such as (5.4.6) and (5.4.9), are not shown to make (5.4.2) vanish. Because Section 6 presents these alternatives as leading to a 'new much more interesting theory', this missing verification is load-bearing for one of the paper's advertised conclusions, even if the abstract only promises a discussion.
  3. [Sec. 3, Noether argument, Eqs. (3.6)–(3.11)] The derivation of the non-linear transformation (3.1) is carried out only to first order in the fields. The text acknowledges that the full Noether procedure at higher levels has not been performed and that confirmation is expected but not shown. Consequently (3.1) remains an ansatz from the earlier literature rather than a derived consequence, and the constraint (3.5) inherits this status. A reader can accept (3.1) as a proposal, but the paper's language of 'strong evidence' should be made precise, and the unresolved higher-order terms should be stated as an assumption rather than as a settled result.
minor comments (4)
  1. [Eq. (3.1)] Equation (3.1) contains an index clash in the final term, Λ^Π ∂_Π E_Π^A, which presumably should read Λ^Σ ∂_Σ E_Π^A; please correct the repeated index.
  2. [Sec. 5.1] The equation numbering in Section 5.1 is disordered: after (5.1.13) the text introduces (5.1.4), (5.1.5), and (5.1.6), which duplicates numbers already used earlier in the paper.
  3. [Sec. 4, Eqs. (4.7)–(4.8)] Equation (4.8) is assigned twice, once to the momentum component p_i and once to the Casimir operator L^2; please renumber to avoid ambiguity.
  4. [Sec. 5.4, Eqs. (5.4.8)–(5.4.10)] The barred derivative appearing in (5.4.8)–(5.4.10) is not defined in the text; from the context it appears to be the doubled-coordinate derivative ∂_μ̇, but this should be stated explicitly.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the central closure claim is conditional and the new IIA constraint is checked against the independent Siegel/DFT literature; the main gaps are unproven closure of the constrained parameter space and unfinished action-invariance analysis, which are correctness issues rather than circularity.

full rationale

The paper's central claim is explicitly conditional: the local transformations close only if one adopts the constraint Cα = 0 in equation (3.5). Equation (3.2) shows that the commutator equals a transformation with parameter Λ_c plus a remainder proportional to Cα, and equation (3.5) is exactly the vanishing of that remainder. Thus the statement 'the algebra closes if Cα = 0' is true by construction. This is a definitional caveat rather than a circular prediction, because the paper does not present the condition as independently derived or fitted; its substantive content is the explicit evaluation of the condition in the IIA level-zero theory, equation (5.3.4), and the demonstration that it is not the same as the independently established section conditions (1.2)-(1.3). The level-zero gauge transformations (5.2.2)-(5.2.8) are matched against Siegel theory / double field theory, an external benchmark, so the agreement is not manufactured from the author's own framework. The reviewer's objection that the bracket parameter Λ_c^Π of equation (3.3) is never shown to satisfy the closure condition (3.5) is a real mathematical gap: without that check, the constrained parameter space is not proven to close, and the gauge algebra is not fully established. Similarly, section 5.4 explicitly defers the action-invariance conditions ('We leave it to a future paper to determine what are the precise conditions for the action to be invariant under local transformations'), which is an acknowledged omission. These are correctness or completeness concerns, not circularity under the pass rules. Self-citations to earlier E-theory papers provide the framework and the starting transformation (3.1), but the load-bearing comparison with double field theory is external, and no uniqueness theorem from prior work is invoked to forbid alternatives. Overall, no claimed prediction reduces to a fitted input or to a self-citation chain; the paper is not significantly circular.

Assumptions & free parameters 1 free parameters · 4 assumptions · 0 invented entities

The central claim rests on the proposed transformation (3.1) and the ad hoc closure condition (3.5), neither of which is derived from an independent principle. The E11 algebra and the IIA level-zero data are drawn from the author's prior papers. No new entities are postulated; the paper instead gives an interpretation of the existing extended spacetime coordinates in terms of branes.

free parameters (1)
  • Action coefficients e1, e2, e4, e5 (and c3) = e1=1/4, e2=-1, e4=2, e5=2, c3=0
    Chosen by hand in §5.1 to give the action of equation (5.1.13) the usual diffeomorphism and two-form gauge symmetries. The text states the level-zero symmetries do not determine these constants.
assumptions (4)
  • ad hoc to paper The local non-linear gauge transformation of the vierbein is δE_Π^A = (C^{-1})^{αβ}(D_α)_Π^Σ E_Σ^A (D_β)_Λ^Γ ∂_Γ Λ^Λ + Λ^Π ∂_Π E_Π^A, equation (3.1).
    Taken as a postulate from the author's earlier paper [50]; the paper supplies only a linearized Noether check and states the all-orders verification is future work.
  • ad hoc to paper The gauge parameters are restricted to those satisfying Cα=0, equation (3.5).
    Imposed by hand to make the commutator of two local transformations reduce to the standard form; not derived from the non-linear realisation or from an action, and the paper does not prove the bracket parameter preserves the condition.
  • domain assumption The IIA level-zero sector of E11 is described by the algebra SO(10,10)⊗GL(1) with the commutators of appendix A, equations (A.3)-(A.4), and the identifications (A.5).
    Taken from the author's earlier work [46]; the paper refers to appendix A of that paper for the derivation and lists only the final commutators.
  • domain assumption The E11 commutation relations (2.4), Killing form (2.6)-(2.7), and vector representation matrices (2.5) are background input from the E11 literature.
    Used throughout the calculation without proof; they are standard within the E11 program.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Local symmetry and extended spacetime." pith.science (2026). https://pith.science/paper/GMWRT25O

@misc{pith2026250418229,
  author       = {Pith},
  title        = {Pith review of: Local symmetry and extended spacetime},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/GMWRT25O}},
  note         = {Machine review of arXiv:2504.18229}
}
read the original abstract

We show that the previously proposed local transformations in E theory have a closing algebra if one adopts a simple constraint on the parameters of the transformations that constrains their dependence on the extended spacetime of E theory. We evaluate these local transformations for the decomposition of E11 that leads to the IIA theory at level zero. This has the same fields and spacetime as Siegel theory (Double field theory) and although the local transformations agree, the constraint is different to the generic section conditions used in that theory. We discuss what additional alternative constraints might be required for the invariance of this theory and also argue that the dependence on the coordinates beyond those of the usual spacetime is due to the presence of branes.

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

65 extracted references · 27 canonical work pages

  1. [1]

    Algebraic Properti es of Extended Supersym- metry

    S. Ferrara, J. Scherk and B. Zumino, “Algebraic Properti es of Extended Supersym- metry”, Nucl. Phys. B121 (1977) 393; E. Cremmer, J. Scherk and S. Ferrara, “SU(4) Invariant Supergravity Theory” , Phys. Lett. 74B (1978) 61

    work page 1977

  2. [2]

    TheN = 8 supergravity theory. I. The Lagrangian

    E. Cremmer and B. Julia, “TheN = 8 supergravity theory. I. The Lagrangian ”, Phys. Lett. 80B (1978) 48

    work page 1978

  3. [3]

    Group Disintegrations

    B. Julia, “Group Disintegrations” , in Superspace & Supergravity , p. 331, eds. S.W. Hawking and M. Roˇ cek, Cambridge University Press (1981)

    work page 1981

  4. [4]

    Julia, in Vertex Operators in Mathematics and Physics , Publications of the Math- ematical Sciences Research Institute no 3, Springer Verlag 1984

    B. Julia, in Vertex Operators in Mathematics and Physics , Publications of the Math- ematical Sciences Research Institute no 3, Springer Verlag 1984

    work page 1984

  5. [5]

    Cremmer, B

    E. Cremmer, B. Julia and J. Scherk, Phys. Lett. 76B (1978) 409

    work page 1978

  6. [6]

    N = 2 D = 10 nonchiral supergravity and its spontaneous compactification

    C. Campbell and P. West, “N = 2 D = 10 nonchiral supergravity and its spontaneous compactification.” Nucl. Phys. B243 (1984) 112

    work page 1984

  7. [7]

    Kaluza–Klein supergravity in ten dimensions

    M. Huq and M. Namazie, “Kaluza–Klein supergravity in ten dimensions” , Class. Q. Grav. 2 (1985). 30

    work page 1985

  8. [8]

    N = 2 supergravity in ten dimensions

    F. Giani and M. Pernici, “N = 2 supergravity in ten dimensions” , Phys. Rev. D30 (1984) 325

    work page 1984

Show all 65 references
  1. [9]

    Symmetries and Transformation of Chiral N = 2 D = 10 Supergravity

    J, Schwarz and P. West, “Symmetries and Transformation of Chiral N = 2 D = 10 Supergravity”, Phys. Lett. 126B (1983) 301

    1983

  2. [10]

    The Complete N = 2 D = 10 Supergravity

    P. Howe and P. West, “The Complete N = 2 D = 10 Supergravity”, Nucl. Phys. B238 (1984) 181

    1984

  3. [11]

    Covariant Field Equations of Chiral N = 2 D = 10 Supergravity

    J. Schwarz, “Covariant Field Equations of Chiral N = 2 D = 10 Supergravity”, Nucl. Phys. B226 (1983) 269

    1983

  4. [12]

    Callan, S

    C. Callan, S. Coleman, J. Wess and B. Zumino, Structure of Phenomenological La- grangians. 1 , Phys.Rev. 177 (1969) 2239; Structure of phenomenological Lagrangians. 2, Phys. Rev. 177 (1969) 2247

    1969

  5. [13]

    West, E11 and M Theory , Class

    P. West, E11 and M Theory , Class. Quant. Grav. 18, (2001) 4443, hep-th/ 0104081

    2001

  6. [14]

    Infinite-dimensional algebra of general covariance group as the closure of the finite dimensional algebras of conformal and linear gr oups

    V. Ogievetsky, “Infinite-dimensional algebra of general covariance group as the closure of the finite dimensional algebras of conformal and linear gr oups”, Nuovo. Cimento, 8 (1973) 988

    1973

  7. [15]

    Theory of dynamical affine and conformal symmetries as the theory of the gravitational field

    A. Borisov and V. Ogievetsky, “Theory of dynamical affine and conformal symmetries as the theory of the gravitational field” , Teor. Mat. Fiz. 21 (1974) 329

    1974

  8. [16]

    West, E11, SL(32) and Central Charges , Phys

    P. West, E11, SL(32) and Central Charges , Phys. Lett. B 575 (2003) 333-342, hep- th/0307098

    2003

  9. [18]

    West, The IIA, IIB and eleven dimensional theories and their commo n E11 origin, Nucl

    P. West, The IIA, IIB and eleven dimensional theories and their commo n E11 origin, Nucl. Phys. B693 (2004) 76-102, hep-th/0402140

    2004 arXiv

  10. [19]

    West, Introduction to Strings and Branes , Cambridge University Press, 2012

    P. West, Introduction to Strings and Branes , Cambridge University Press, 2012

    2012

  11. [20]

    Riccioni and P

    F. Riccioni and P. West, E(11)-extended spacetime and gauged supergravities , JHEP 0802 (2008) 039, arXiv:0712.1795

    2008 arXiv

  12. [21]

    Riccioni and P

    F. Riccioni and P. West, The E(11) origin of all maximal supergravities , JHEP 07 (2007) 063, arXiv:0705.0752

    2007 arXiv

  13. [22]

    Bergshoeff, I

    E. Bergshoeff, I. De Baetselier, and T. Nutma, E(11) and the embedding tensor , JHEP 09 (2007) 047, arXiv:0705.1304

    2007 arXiv

  14. [23]

    Kleinschmidt and P

    A. Kleinschmidt and P. West, Representations of G+++ and the role of space-time , JHEP 0402 (2004) 033, hep-th/0312247

    2004 arXiv

  15. [24]

    Tumanov and P

    A. Tumanov and P. West, E11 must be a symmetry of strings and branes , Phys. Lett. B759 (2016), 663, arXiv:1512.01644

    2016 arXiv

  16. [25]

    Tumanov and P

    A. Tumanov and P. West, E11 in 11D , Phys.Lett. B758 (2016) 278, arXiv:1601.03974

    2016 arXiv

  17. [26]

    Glennon and P

    K. Glennon and P. West, The non-linear dual gravity equation of motion in eleven dimensions, Phys.Lett.B 809 (2020) 135714, arXiv:2006.02383

    2020 arXiv

  18. [27]

    Tumanov and P

    A. Tumanov and P. West, E11, Romans theory and higher level duality relations , Int. J. Mod. Phys. A 32 (2017) no. 05, 1750023, arXiv:1611.03369

    2017 arXiv

  19. [28]

    L. J. Romans, Massive N=2a Supergravity in Ten-Dimensions , Phys. Lett. B 169 (1986) 374

    1986

  20. [29]

    Pettit and P

    M. Pettit and P. West, E theory in seven dimensions , Int. J. Mod. Phys. A 34 (2019) no. 25, 1950135, arXiv:1905.07330. 31

    2019 arXiv

  21. [30]

    West, A brief review of E theory , Proceedings of Abdus Salam’s 90th Birthday meet- ing, 25-28 January 2016, NTU, Singapore, Editors L

    P. West, A brief review of E theory , Proceedings of Abdus Salam’s 90th Birthday meet- ing, 25-28 January 2016, NTU, Singapore, Editors L. Brink, M . Duff and K. Phua, World Scientific Publishing and IJMPA, V ol 31, No 26 (2016) 1630043, arXiv:1609.06863

    2016 arXiv

  22. [31]

    Riccioni and P

    F. Riccioni and P. West, Dual fields and E(11) , Phys. Lett. B 645 (2007) 286, arXiv:hep-th/0612001

    2007 arXiv

  23. [32]

    West, Irreducible representations of E theory , Int.J.Mod.Phys

    P. West, Irreducible representations of E theory , Int.J.Mod.Phys. A34 (2019) no.24, 1950133, arXiv:1905.07324

    2019 arXiv

  24. [33]

    Glennon and P

    K. Glennon and P. West, The massless irreducible representation in E theory and how bosons can appear as spinors , Int. J. Mod. Phys. A 36 (2021) no. 16, 2150096, arXiv:2102.02152 [hep-th]

    2021 arXiv

  25. [34]

    West, E11 origin of Brane charges and U-duality multiplets , JHEP 0408 (2004) 052, hep-th/0406150

    P. West, E11 origin of Brane charges and U-duality multiplets , JHEP 0408 (2004) 052, hep-th/0406150

    2004 arXiv

  26. [35]

    Cook and P

    P. Cook and P. West, Charge multiplets and masses for E(11) , JHEP 11 (2008) 091, arXiv:0805.4451

    2008 arXiv

  27. [36]

    West, Brane dynamics, central charges and E11, JHEP 0503 (2005) 077, hep- th/0412336

    P. West, Brane dynamics, central charges and E11, JHEP 0503 (2005) 077, hep- th/0412336

    2005

  28. [37]

    West, Spacetime and large local transformations , Int.J.Mod.Phys.A 38 (2023) 08, 2350045, arXiv:2302.02199

    P. West, Spacetime and large local transformations , Int.J.Mod.Phys.A 38 (2023) 08, 2350045, arXiv:2302.02199

    2023 arXiv

  29. [38]

    W. Siegel. Superspace duality in low-energy superstrings . Phys. Rev. D,48:28262837, 1993

    1993

  30. [39]

    W. Siegel. Two vierbein formalism for string inspired axionic gravity . Phys.Rev. D, 47:54535459, 1993

    1993

  31. [40]

    Hull and B

    C. Hull and B. Zwiebach, Double Field Theory, JHEP 0909 (2009) 099, hep-th/0904.4664

    2009 arXiv

  32. [41]

    Hull and B

    C. Hull and B. Zwiebach, The gauge algebra of double field theory and Courant brack- ets, JHEP 0909 (2009) 090, hep-th0908.1792

    2009 arXiv

  33. [42]

    O. Hohm, C. Hull and B. Zwiebach, Background independent action for double field theory, hep-th/1003.5027

    arXiv

  34. [43]

    O. Hohm, C. Hull and B. Zwiebach, Generalised metric formulation of double field theory, hep-th/1006.4823

    arXiv

  35. [44]

    Kugo and B

    T. Kugo and B. Zwiebach, Target space duality as a symmetry of string field theory , Prog. Theor. Phys. 87, 801 (1992) hep-th/9201040

    1992 arXiv

  36. [45]

    Hohm and S

    O. Hohm and S. Kwak, Frame-like Geometry of Double Field Theory , J.Phys.A44 (2011) 085404, arXiv:1011.4101

    2011 arXiv

  37. [46]

    West, E11, generalised space-time and IIA string theory , Phys.Lett.B 696 (2011) 403-409, arXiv:1009.2624

    P. West, E11, generalised space-time and IIA string theory , Phys.Lett.B 696 (2011) 403-409, arXiv:1009.2624

    2011 arXiv

  38. [47]

    Rocen and P

    A. Rocen and P. West, E11, generalised space-time and IIA string theory the R-R sector, in Strings, Gauge fields and the Geometry behind:The Legacy of Maximilian Kreuzer, edited by Anton Rebhan, Ludmil Katzarkov, Johanna Knapp, Radoslav Rashkov, Emanuel Scheid, World Scientific,...

    2013

  39. [48]

    O. Hohm, S. Ki Kwak and B. Zwiebach, Unification of Type II Strings and T-duality , PhysRevLett.107.171603, arXiv:1106.5452

    arXiv

  40. [49]

    I. Jeon, K. Lee and J. Park, Ramond-Ramond Cohomology and O(D, D) T-duality , JHEP 09 (2012) 079, arXiv:1206.3478 32

    2012 arXiv

  41. [50]

    West, Generalised Space-time and Gauge Transformations , JHEP 08 (2014) 050, arXiv:1403.6395

    P. West, Generalised Space-time and Gauge Transformations , JHEP 08 (2014) 050, arXiv:1403.6395

    2014 arXiv

  42. [51]

    West, Generalised Geometry, eleven dimensions, JHEP 1202 (2012) 018, arXiv:1111.1642

    P. West, Generalised Geometry, eleven dimensions, JHEP 1202 (2012) 018, arXiv:1111.1642

    2012 arXiv

  43. [52]

    Tumanov and P

    A. Tumanov and P. West, Generalised vielbeins and non-linear realisations , JHEP 1410 (2014) 009, arXiv:1405.7894

    2014 arXiv

  44. [53]

    Schnakenburg and P

    I. Schnakenburg and P. West, Kac-Moody Symmetries of IIB Supergravity , Phys.Lett. B517 (2001) 421-428, hep-th/0107181

    2001 arXiv

  45. [54]

    Hillmann, Generalized E(7(7)) coset dynamics and D=11 supergravity , JHEP 03 (2009) 135, hep-th/0901.1581

    C. Hillmann, Generalized E(7(7)) coset dynamics and D=11 supergravity , JHEP 03 (2009) 135, hep-th/0901.1581

    2009 arXiv

  46. [55]

    Hillmann, E(7(7)) and d=11 supergravity hep-th/0902.1509

    C. Hillmann, E(7(7)) and d=11 supergravity hep-th/0902.1509

    arXiv

  47. [56]

    West, E11, generalised space-time and equations of motion in four dimensions, JHEP 12 (2012) 068, arXiv:1206.7045 [hep-th]

    P. West, E11, generalised space-time and equations of motion in four dimensions, JHEP 12 (2012) 068, arXiv:1206.7045 [hep-th]

    2012 arXiv

  48. [57]

    West, Generalised BPS conditions, Mod.Phys.Lett

    P. West, Generalised BPS conditions, Mod.Phys.Lett. A27 (2012) 1250202, arXiv:1208.3397

    2012 arXiv

  49. [58]

    Berman, H

    D. Berman, H. Godazgar, M. Perry and P. West, Duality Invariant Actions and Gen- eralised Geometry., JHEP 1202 (2012) 108, arXiv:1111.0459

    2012 arXiv

  50. [59]

    Pettit and P

    M. Pettit and P. West, An E11 invariant gauge fixing , Int.J.Mod.Phys. A33 (2018) no.01, 1850009, Int.J.Mod.Phys. A33 (2018) no.01, 1850009 , arXiv:1710.11024

    2018 arXiv

  51. [60]

    Bossard, A

    G. Bossard, A. Kleinschmidt, J. Palmkvist, C. N. Pope, a nd E. Sezgin, Beyond E11, JHEP 05 (2017) 020, arXiv:1703.01305 [hep-th]. )

    2017 arXiv

  52. [61]

    Bossard, A

    G. Bossard, A. Kleinschmidt, and E. Sezgin, On supersym metric E11 exceptional field theory, JHEP 10 (2019) 165, arXiv:1907.02080 [hep-th]

    2019 arXiv

  53. [62]

    Bossard, A

    G. Bossard, A. Kleinschmidt, and E. Sezgin, A master exc eptional field theory, JHEP 06 (2021) 185, arXiv:2103.13411 [hep-th]

    2021 arXiv

  54. [63]

    Hohm and H

    O. Hohm and H. Samtleben, Exceptional Form of D=11 Super gravity, Phys. Rev. Lett. 111 (2013) 231601, arXiv:1308.1673

    2013 arXiv

  55. [65]

    Hohm and H

    O. Hohm and H. Samtleben, Exceptional Field Theory II: E 7(7) , arXiv:1312.0614

    arXiv

  56. [66]

    Godazgar, M

    H. Godazgar, M. Godazgar, O. Hohm, H. Nicolai, Henning S amtleben, Supersymmet- ric E7(7) Exceptional Field Theory, arXiv:1406.3235

    arXiv

  57. [67]

    Hohm and H

    O. Hohm and H. Samtleben, Exceptional Field Theory III: E8(8), Phys. Rev. D 90, (2014) 066002, arXiv:1406.3348 33

    2014 arXiv

Pith tools

Reviewed August 16, 2026 · model on record in the stance chip above.