pith. sign in

arxiv: 2607.01999 · v1 · pith:FLKKZK3Rnew · submitted 2026-07-02 · ✦ hep-th

Local symmetry and the dependence on extended spacetime

Keith Glennon , Peter West This is my paper

Pith reviewed 2026-07-03 08:44 UTC · model grok-4.3

classification ✦ hep-th
keywords E theorylocal symmetryextended spacetimeSiegel theoryDouble Field Theorysection conditionsdilaton equation
0
0 comments X

The pith

Linearised E theory admits a local symmetry when its parameters obey differential conditions on extended spacetime dependence.

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

The paper shows that linearised E theory possesses a local symmetry at low levels only when the symmetry parameters satisfy differential conditions that restrict how they depend on the extended spacetime. The same decomposition that produces Siegel theory yields analogous restrictions on the parameters, but these differ from the section conditions that are standard in that setting. The dilaton equation in Siegel theory remains invariant under the local symmetry once the parameters meet a corresponding nonlinear constraint. The authors conclude that no separate conditions need to be imposed on the fields themselves.

Core claim

Linearised E theory possesses a local symmetry at low levels provided the parameters of the local symmetry obey differential conditions that restrict their dependence on the extended spacetime. In the decomposition of E theory that leads to Siegel theory, also known as Double Field theory, the analogous restrictions on the parameters are found and shown to be different from section conditions. The dilaton equation of Siegel theory is invariant under the local symmetry if the parameters satisfy an analogous non-linear constraint. There is no need to impose conditions on the fields of E theory or Siegel theory.

What carries the argument

The local symmetry whose parameters must satisfy differential conditions restricting their dependence on extended spacetime; these conditions replace the role of section conditions in the Siegel theory reduction.

If this is right

  • Linearised E theory has a local symmetry at low levels when parameters obey the differential restrictions.
  • The restrictions obtained in the Siegel theory decomposition differ from section conditions.
  • The dilaton equation stays invariant under the local symmetry once parameters meet the nonlinear constraint.
  • No conditions on the fields of E theory or Siegel theory are required.

Where Pith is reading between the lines

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

  • The same parameter-based approach could be tested in other extended-geometry formulations that currently rely on section conditions.
  • Avoiding field constraints might simplify the construction of consistent nonlinear completions.
  • The distinction between differential conditions and section conditions suggests a broader distinction between parameter and field restrictions in doubled geometries.

Load-bearing premise

The decomposition of E theory into Siegel theory preserves the local symmetry structure so that the same differential restrictions on parameters apply.

What would settle it

An explicit computation at low levels demonstrating that the local symmetry fails to close or that the dilaton equation loses invariance when parameters violate the stated differential or nonlinear conditions.

read the original abstract

We show that linearised E theory possesses a local symmetry at low levels provided the parameters of the local symmetry obey differential conditions that restrict their dependence on the extended spacetime. In the decomposition of E theory that leads to Siegel theory, also known as Double Field theory, we also find the analogous restrictions on the parameters. They are different to the section conditions which are universally used in this context. We also show that the dilaton equation of Siegel theory is invariant under the local symmetry if the parameters satisfy an analogous non-linear constraint on the parameters. We argue that there is no need to impose conditions on the fields of E theory or Siegel theory.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The manuscript claims that linearised E theory admits a local symmetry at low levels when the symmetry parameters obey differential conditions that restrict their dependence on the extended spacetime. In the decomposition of E theory to Siegel theory (Double Field Theory), analogous differential restrictions on the parameters are derived; these are stated to differ from the standard section conditions. The dilaton equation of Siegel theory is shown to remain invariant under the local symmetry provided the parameters satisfy an additional non-linear constraint, and the authors conclude that no conditions need be imposed on the fields themselves.

Significance. If the central claims are substantiated with explicit derivations, the result would offer a parameter-constrained alternative to field-level section conditions in DFT and E-theory, potentially broadening the allowed field configurations while preserving local symmetries. This could clarify the role of extended spacetime dependence in duality-covariant formulations.

major comments (2)
  1. [Abstract / decomposition to Siegel theory] Abstract and decomposition section: the central claim that the derived differential restrictions on parameters 'are different to the section conditions' is load-bearing for the 'no need to impose conditions on the fields' conclusion, yet the abstract supplies no explicit differential operators or comparison; the main text must derive the operators and demonstrate (e.g., via an explicit example) that the allowed parameter dependence is strictly larger than what the O(d,d) section condition permits.
  2. [Dilaton equation invariance] Dilaton invariance claim: the non-linear constraint on parameters that is asserted to ensure invariance of the dilaton equation must be shown to be independent of (rather than equivalent to) the linear differential restrictions; without this separation, the invariance statement risks reducing to a re-derivation of known section-condition results.
minor comments (1)
  1. [Abstract] The abstract repeats 'on the parameters' in the final sentence; rephrase for concision.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading and constructive comments on our manuscript. We address the two major comments point by point below, agreeing that additional explicit material will strengthen the presentation while maintaining that the core derivations are already present in the main text.

read point-by-point responses

  1. Referee: [Abstract / decomposition to Siegel theory] Abstract and decomposition section: the central claim that the derived differential restrictions on parameters 'are different to the section conditions' is load-bearing for the 'no need to impose conditions on the fields' conclusion, yet the abstract supplies no explicit differential operators or comparison; the main text must derive the operators and demonstrate (e.g., via an explicit example) that the allowed parameter dependence is strictly larger than what the O(d,d) section condition permits.

    Authors: The abstract is deliberately concise and does not contain the explicit operators; these are derived in the decomposition section of the main text, where the differential restrictions on the parameters are obtained by direct computation from the linearised E-theory transformations and then reduced to the Siegel-theory case. We acknowledge that an explicit side-by-side comparison with the standard section condition, together with a concrete example of a parameter dependence permitted by our conditions but excluded by the O(d,d) section condition, would make the distinction clearer. We will therefore add such an example (a specific functional form for the parameters that satisfies our differential restrictions but violates the section condition) in the revised manuscript. revision: yes

  2. Referee: [Dilaton equation invariance] Dilaton invariance claim: the non-linear constraint on parameters that is asserted to ensure invariance of the dilaton equation must be shown to be independent of (rather than equivalent to) the linear differential restrictions; without this separation, the invariance statement risks reducing to a re-derivation of known section-condition results.

    Authors: The linear differential restrictions are obtained from the requirement that the local symmetry leaves the linearised field equations invariant, while the non-linear constraint is obtained separately by imposing invariance of the dilaton equation alone. These arise at different stages of the calculation and have different algebraic structures (first-order linear PDEs versus a quadratic condition on derivatives). To remove any ambiguity we will add a short subsection that explicitly exhibits a parameter satisfying the linear restrictions but failing the non-linear constraint (and vice versa), thereby confirming they are independent. revision: yes

Circularity Check

0 steps flagged

No circularity: derivation from theory structure is self-contained

full rationale

The abstract and claims derive local symmetries and parameter restrictions directly from the linearised E theory structure and its Siegel decomposition. No quoted equations or steps reduce a prediction to a fitted input by construction, invoke self-citations as load-bearing uniqueness theorems, or rename known results. The distinction from section conditions is asserted as an outcome of the explicit decomposition rather than assumed or fitted. This matches the default case of a self-contained derivation against external benchmarks with no exhibited circular reduction.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

Abstract-only review provides no explicit free parameters, axioms, or invented entities; the central claims rest on the validity of the linearised approximation and the decomposition to Siegel theory.

axioms (2)
  • domain assumption The linearised approximation of E theory at low levels is sufficient to exhibit the local symmetry.
    The paper restricts its claim to the linearised theory.
  • domain assumption The decomposition of E theory leads to Siegel theory while preserving the relevant symmetry structure.
    Stated directly in the abstract as the context for the analogous restrictions.

pith-pipeline@v0.9.1-grok · 5620 in / 1313 out tokens · 29876 ms · 2026-07-03T08:44:17.249917+00:00 · methodology

discussion (0)

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

Reference graph

Works this paper leans on

34 extracted references · 29 canonical work pages · 23 internal anchors

  1. [1]

    Target Space Duality in String Theory

    A. Giveon, M. Porrati and E. Rabinovici,Target space duality in string theory, Phys. Rept. 244, 77 (1994) [arXiv:hep-th/9401139]

    work page internal anchor Pith review Pith/arXiv arXiv 1994

  2. [2]

    Curtright and P

    T. Curtright and P. West,Duality symmetries and phase space quantum theory, Int. J. Mod. Phys.A(2025), arXiv:2509.13872

    work page arXiv 2025

  3. [3]

    Two-Vierbein Formalism for String-Inspired Axionic Gravity

    W. Siegel,Two-vierbein formalism for string-inspired axionic gravity, Phys. Rev.D 47(1993) 5453–5459, hep-th/9302036

    work page internal anchor Pith review Pith/arXiv arXiv 1993

  4. [4]

    Superspace Duality in Low-Energy Superstrings

    W. Siegel,Superspace duality in low-energy superstrings, Phys. Rev.D 48(1993) 2826–2837, hep-th/9305073;Manifest duality in low-energy superstrings, inProceed- ings of Strings ’93, Berkeley, 1993, p.353, hep-th/9308133

    work page internal anchor Pith review Pith/arXiv arXiv 1993

  5. [5]

    Double Field Theory

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

    work page internal anchor Pith review Pith/arXiv arXiv 2009

  6. [6]

    The gauge algebra of double field theory and Courant brackets

    C. Hull and B. Zwiebach,The gauge algebra of double field theory and Courant brack- ets, JHEP0909(2009) 090, hep-th0908.1792

    work page internal anchor Pith review Pith/arXiv arXiv 2009

  7. [7]

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

    work page internal anchor Pith review Pith/arXiv arXiv

  8. [8]

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

    work page internal anchor Pith review Pith/arXiv arXiv

  9. [9]

    Target Space Duality as a Symmetry of String Field Theory

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

    work page internal anchor Pith review Pith/arXiv arXiv 1992

  10. [10]

    Frame-like Geometry of Double Field Theory

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

    work page internal anchor Pith review Pith/arXiv arXiv 2011

  11. [11]

    TheN= 8supergravity theory. I. The Lagrangian

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

    1978

  12. [12]

    Group Disintegrations

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

    1981

  13. [13]

    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

    1984

  14. [14]

    Symmetries and Transformation of ChiralN= 2D= 10 Supergravity

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

    1983

  15. [15]

    West,E 11 and M Theory, Class

    P. West,E 11 and M Theory, Class. Quant. Grav.18, (2001) 4443, hep-th/ 0104081

    2001

  16. [16]

    West,E 11 , SL(32) and Central Charges, Phys

    P. West,E 11 , SL(32) and Central Charges, Phys. Lett.B 575(2003) 333-342, hep- th/0307098

    work page arXiv 2003

  17. [17]

    A brief review of E theory

    P. West,A brief review of E theory, Proceedings of Abdus Salam’s 90th Birthday meeting, 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

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  18. [18]

    E11 must be a symmetry of strings and branes

    A. Tumanov and P. West,E11 must be a symmetry of strings and branes, arXiv:1512.01644

    work page internal anchor Pith review Pith/arXiv arXiv

  19. [19]

    E11 in 11D

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

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  20. [20]

    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

    work page arXiv 2019

  21. [21]

    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. A36(2021) no. 16, 2150096, arXiv:2102.02152 [hep-th] 20

    work page arXiv 2021

  22. [22]

    E(11)-extended spacetime and gauged supergravities

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

    work page internal anchor Pith review Pith/arXiv arXiv 2008

  23. [23]

    The E_{11} origin of all maximal supergravities

    F. Riccioni and P. West,The E(11) origin of all maximal supergravities, JHEP07 (2007) 063, arXiv:0705.0752

    work page internal anchor Pith review Pith/arXiv arXiv 2007

  24. [24]

    E11, generalised space-time and IIA string theory

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

    work page internal anchor Pith review Pith/arXiv arXiv 2011

  25. [25]

    E11, generalised space-time and IIA string theory; the R-R sector

    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, arXiv:1012.2744

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  26. [26]

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

    work page internal anchor Pith review Pith/arXiv arXiv

  27. [27]

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

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  28. [28]

    Generalised Space-time and Gauge Transformations

    P. West,Generalised Space-time and Gauge Transformations, JHEP08(2014) 050, arXiv:1403.6395

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  29. [29]

    Beyond E11

    G. Bossard, A. Kleinschmidt, J. Palmkvist, C. N. Pope and E. Sezgin,BeyondE 11 , JHEP05(2017) 020, arXiv:1703.01305

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  30. [30]

    Generalised BPS conditions

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

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  31. [31]

    Gauged Double Field Theory

    M. Gra˜ na and D. Marqu´ es,Gauged Double Field Theory, JHEP1204(2012) 020, arXiv:1201.2924

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  32. [32]

    Duality Covariant Solutions in Extended Field Theories

    H, Hoitzing,Double field theoryPhD thesis; F. Rudolph,Duality Covariant Solutions in Extended Field Theories, https://arxiv.org/pdf/1610.03440; G. Aldazabal, D. Marques and C. Nunez,Double Field Theory: A Pedagogical Review, https://arxiv.org/pdf/1305.1907

    work page internal anchor Pith review Pith/arXiv arXiv 1907

  33. [33]

    West,Local symmetry and extended spacetime, Int

    P. West,Local symmetry and extended spacetime, Int. J. Mod. Phys.A 40(2025) 2550100, arXiv:2504.18229

    work page arXiv 2025

  34. [34]

    West,Spacetime and large local transformations, Int

    P. West,Spacetime and large local transformations, Int. J. Mod. Phys.A 38(2023) 2350045, arXiv:2302.02199. 21

    work page arXiv 2023