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REVIEW 2 major objections 5 minor 53 references

An infinite-dimensional structure group plus torsion constraints produces all NS-NS α' and α'² corrections without scattering amplitudes.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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2026-07-11 06:57 UTC pith:BUNM2VIO

load-bearing objection Clean recursive geometric algorithm that actually delivers the full a/b NS-NS towers at α' and α'² from T-duality alone, with explicit matching after documented redefinitions. the 2 major comments →

arxiv 2607.05487 v1 pith:BUNM2VIO submitted 2026-07-06 hep-th

α'-Bootstrap

Achilleas Gitsis , Falk Hassler , Luca Scala This is my paper
classification hep-th
keywords alpha-prime correctionsDouble Field TheoryT-dualityNS-NS sectorgeneralized Bergshoeff-de Roo identificationGreen-Schwarz transformationsmegaspacestructure group
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

Computing higher-derivative corrections to string theory’s low-energy action is normally blocked by an explosion of terms and the need for many scattering amplitudes. This paper shows that T-duality, made manifest by Double Field Theory on a further-extended megaspace, is enough to fix the full NS-NS towers at order α' and α'². The authors construct an infinite-dimensional structure group, impose torsion constraints and a partial gauge fixing, and obtain recursive formulae that generate every allowed coupling (the bi-parametric a/b towers) up to overall coefficients and field redefinitions. The resulting Lagrangians match the known bosonic and heterotic results. The same recursive machinery is conjectured to continue to all higher orders, although ζ-type terms that first appear at α'³ are still missing. If the construction is correct, higher-derivative string effective actions become algebraic objects rather than amplitude-by-amplitude calculations.

Core claim

The α'-bootstrap recovers all NS-NS higher-derivative corrections at order α' and α'²—the complete a and b towers—by imposing torsion constraints and a partial gauge fixing on an infinite-dimensional structure group of the megaspace. The output is a compact bi-parametric Lagrangian (equation 1.2 / 4.37) that matches the literature for both bosonic and heterotic strings after field redefinitions, without any direct scattering-amplitude computation.

What carries the argument

The infinite-dimensional structure group GS of the megaspace, whose generators and structure constants are defined recursively from a regularized ad-invariant bilinear καβ (the Killing form). Torsion constraints plus a new partial gauge fixing convert the gBdR identification into iterative algebraic relations that seed every higher-derivative term.

Load-bearing premise

That the regularized Killing form of this infinite algebra is the right bilinear, and that the same recursive identification continues without new free parameters or inconsistencies at every higher order.

What would settle it

Compute the α'³ NS-NS Lagrangian both by the bootstrap and by an independent amplitude or T-duality analysis; any mismatch that cannot be absorbed by field redefinitions or by a new admissible deformation of καβ would falsify the claim that the procedure captures the full tower.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • All a/b-tower NS-NS corrections become computable by recursion rather than by matching amplitudes.
  • The same algebraic structure yields the all-order Green-Schwarz transformations for the B-field and double Lorentz symmetry.
  • Bosonic and heterotic Lagrangians at α' and α'² are recovered as special values of a single bi-parametric action.
  • Any admissible deformation of the bilinear καβ that is still ad-invariant under GS can in principle generate new towers of corrections.

Where Pith is reading between the lines

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

  • If a systematic classification of all ad-invariant bilinears on GS exists, the missing ζ(3), ζ(5), … towers may appear as higher deformations of the same algebra rather than as entirely new geometric data.
  • The recursive formulae are already computer-algebra ready; an automated pipeline could push the known a/b towers well beyond α'³ once the ζ-sector is understood.
  • The megaspace construction may supply a geometric origin for the non-manifest T-duality that currently obstructs a complete O(d,d) description of the ζ corrections.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 5 minor

Summary. The paper develops an “α′-bootstrap” that reconstructs the NS-NS higher-derivative corrections of bosonic and heterotic string theory at orders α′ and α′^{2} (the full a/b towers) from consistency conditions alone. Starting from a Poláček–Siegel megaspace with duality group O(d+n,d+n), the authors construct an infinite-dimensional structure group GS whose regularized Killing form κ_αβ is split into independent left- and right-moving sectors controlled by two parameters a and b. Torsion constraints T_ABC = T_ABC = 0 together with a new partial gauge fixing A_iα = 0 determine the auxiliary fields order by order via recursive formulae (i0a)–(i4). The resulting four- and six-derivative Lagrangians (4.2) and (4.37) (after removal of the field-redefinition term L_redef (4.38)) are shown to match the known Metsaev–Tseytlin and Hronek–Wulff–Zacarias expressions once the concrete redefinitions of Appendix B are performed. All-order Green–Schwarz transformations are also obtained. The construction is conjectured to continue to all orders, though ζ-type corrections that begin at α′^{3} remain outside the present choice of κ_αβ.

Significance. If the recursive identification continues without obstruction, the method supplies a purely algebraic, T-duality-covariant algorithm that generates the entire a/b tower of NS-NS corrections without further amplitude input. The explicit match at α′ and α′^{2}, the transparent geometric interpretation of the gBdR identification as torsion constraints plus gauge fixing, and the all-order Green–Schwarz formulae already constitute a substantial technical advance over earlier formulations. The recursive formulae are well-suited to computer-algebra implementation, and the free choice of the ad-invariant bilinear κ_αβ offers a concrete route toward incorporating the missing ζ-towers. These features make the paper a valuable contribution to the systematic study of higher-derivative corrections in string theory.

major comments (2)
  1. The all-order claim rests on the conjecture (abstract and §5) that the same recursive identification generated by the regularized Killing form (3.25)–(3.32) continues without obstruction or new free parameters beyond a and b. While the explicit match at α′ and α′^{2} is solid, the manuscript provides no intermediate check (e.g., a partial computation of the eight-derivative sector or a consistency condition that would fail if new parameters appeared). A short discussion of possible obstructions, or an explicit statement that the conjecture is left for future work, would strengthen the central claim.
  2. Section 3.1.2 presents the regularized Killing form as “the most obvious (and relevant) example” of an ad-invariant bilinear, yet the uniqueness (or sufficiency) of this choice for generating precisely the physical a/b towers is not demonstrated. Because the abstract and §5 advertise the ease of generalization to ζ-type corrections via other bilinears, a clearer statement of the classification problem for admissible κ_αβ (even if deferred) is needed so that the reader can assess how much of the higher-order structure is already fixed.
minor comments (5)
  1. Abstract and throughout: “sting theories” should be “string theories”.
  2. Eq. (1.2) and the surrounding text introduce L^(6)_redef without an immediate forward reference to its explicit form (4.38); a parenthetical pointer would help the reader.
  3. Appendix B is essential for verifying the match with the literature; a short summary table listing which redefinitions map which scheme to which would improve readability.
  4. Notation for the two chiral sectors (under/over-bars versus (±) superscripts) is dense; a brief glossary or a consistent preference for one convention in intermediate steps would reduce cognitive load.
  5. References [1–3] are the authors’ own preceding works; a sentence clarifying what is genuinely new relative to those papers (the new gauge fixing, the recursive formulae free of tower collapse, the six-derivative match) would help situate the contribution.

Circularity Check

1 steps flagged

Minor residual self-citation of the authors' prior megaspace/gBdR framework papers; the explicit recursive identification, action computation, and matching to external Metsaev–Tseytlin/Hronek–Wulff–Zacarias results at α'/α'^{2} are independent and fully spelled out.

specific steps
  1. self citation load bearing [Abstract and §1 (Introduction); also §3 opening]
    "Building on a series of previous works by some of the authors, [1–3], we present a refined version of an elegant and effective procedure... In section 3 we revisit the results of [1–3], solving the regularization issue referred in [2] as towers collapse and clarifying the underlying algebraic structure."

    The geometric megaspace construction, Poláček–Siegel group, and gBdR-as-torsion+gauge-fixing interpretation that underwrite the entire bootstrap are introduced via self-citations to the authors' own prior papers. While the present work re-derives the algebra, supplies new recursive formulas, a new gauge fixing, and explicit α'/α'^{2} computations that match external literature, the foundational framework itself is not independently re-justified from first principles or external sources; the load-bearing geometric premise therefore rests partly on the authors' previous unverified (non-machine-checked) results.

full rationale

The paper's central claim is a constructive algebraic procedure (torsion constraints (3.36), gauge fixing (3.39)–(3.40), recursive identification (i0a)–(i4) generated from the regularized Killing form of GS via (3.24)–(3.32), and the resulting L^(4) (4.2) and L^(6) (4.37) after removing L_redef (4.38) via the redefinitions of Appendix B) that reproduces the known bi-parametric a/b towers and matches external literature for bosonic and heterotic cases. This chain is self-contained at the computed orders: the structure constants, fluxes, auxiliary fields A^(n)/Π^(n), and action terms are derived step-by-step from the stated algebraic constraints without reducing by definition to the target Lagrangians. Overall coefficients a,b are free parameters fixed by matching known theories (standard for effective actions), not fitted inputs re-labeled as predictions. The all-order conjecture and possible other καβ deformations are explicitly left open. The only mild circularity is ordinary self-citation of the authors' prior geometrization papers [1–3] for the megaspace setup and Green-Schwarz transformations; these are refined and re-derived here rather than load-bearing unverified uniqueness theorems. No self-definitional loop, no fitted-as-prediction, no smuggled ansatz that forces the α'/α'^{2} results, and no renaming of external data. Score 2 reflects the minor self-citation without elevating it to a reduction of the main claim.

Axiom & Free-Parameter Ledger

1 free parameters · 4 axioms · 2 invented entities

The construction rests on the standard DFT/section-condition framework, the existence of an infinite-dimensional structure group whose regularized Killing form supplies the a/b parameters, and the conjecture that torsion constraints plus gauge fixing continue to determine all higher-order identifications. No numerical free parameters are fitted to data; a and b are fixed by matching known string theories. The megaspace and the infinite-dimensional GS are invented entities whose only evidence is internal consistency and reproduction of known low-order results.

free parameters (1)
  • a, b (overall coefficients of the two chiral towers) = theory-dependent discrete choices
    Fixed by matching the known leading α' corrections of bosonic (a=b=-α'), heterotic (a=-α',b=0) and type-II (a=b=0) strings; not fitted to new data but still free parameters of the bi-parametric family.
axioms (4)
  • domain assumption The strong constraint / section condition of DFT holds and admits the canonical solution that reduces DFT to generalized geometry.
    Invoked throughout §2.1 and used to drop total-derivative terms in the action.
  • ad hoc to paper The structure group GS admits a regularized Killing form that can be split into independent left- and right-moving sectors controlled by a and b.
    Defined in §3.1.2 (eqs. 3.25–3.32); the regularization lim N→∞ (1/N)κ = 0 is an ad-hoc step needed to obtain a finite recursive definition.
  • ad hoc to paper Torsion constraints T_ABC = T_ABC = 0 together with the partial gauge fixing A_iα = 0 completely determine the auxiliary fields order by order.
    Stated in §3.2; the particular gauge choice is credited to Butter and is essential for the recursive formulae.
  • ad hoc to paper The same recursive identification continues to all orders in α' without obstruction (conjecture).
    Explicitly conjectured in the abstract and §5; not proved beyond α'^{2}.
invented entities (2)
  • megaspace M with duality group O(d+n,d+n) and infinite-dimensional structure group GS no independent evidence
    purpose: Provides a geometric arena in which the gBdR identification becomes torsion constraints plus gauge fixing, enabling recursive generation of α' corrections.
    Introduced in §3; independent evidence is limited to reproduction of known low-order results and internal algebraic consistency.
  • regularized infinite-dimensional Killing form κ_αβ of GS no independent evidence
    purpose: Supplies the unique (claimed) ad-invariant bilinear that seeds the a/b towers of higher-derivative corrections.
    Constructed in §3.1.2; no external measurement or independent derivation is given.

pith-pipeline@v1.1.0-grok45 · 44241 in / 3119 out tokens · 23332 ms · 2026-07-11T06:57:38.855907+00:00 · methodology

0 comments
read the original abstract

Due to the exponential growth in the number of terms, computing $\alpha'$-corrections to string theory's low-energy effective actions is a challenging matter. In order to fix all the couplings, one has usually to deal with a large number of string scattering amplitudes. This difficulty can be overcome by exploiting T-duality, which severely constrains the allowed structure of the effective action. It is then convenient to work in a formulation where T-duality is a manifest symmetry. Building on a series of previous works by some of the authors, we present a refined version of an elegant and effective procedure that allows to obtain all the higher-derivative corrections of the NS-NS sector of sting theories at order $\alpha'$ and $\alpha'^2$, up to an overall coefficient. We dub this approach $\alpha'$-bootstrap, since it is based only on consistency conditions and avoids the direct computation of scattering amplitudes. The procedure relies on an infinite dimensional algebraic structure that we present in full detail, and it is conjectured to work at all orders. Although, at the moment, it still misses the $\zeta$-like corrections starting at order $\alpha'^3$, the ease with which it can be generalized is promising for future developments in this direction.

Figures

Figures reproduced from arXiv: 2607.05487 by Achilleas Gitsis, Falk Hassler, Luca Scala.

Figure 1
Figure 1. Figure 1: Venn diagram depicting the relations between the groups in our construction. [PITH_FULL_IMAGE:figures/full_fig_p011_1.png] view at source ↗

discussion (0)

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Reference graph

Works this paper leans on

53 extracted references · 45 linked inside Pith

  1. [1]

    Hassler, D

    F. Hassler, D. Osten, and Y. Sakatani,Duality covariant curvatures for the heterotic string,JHEP09(2025) 031, [arXiv:2412.17893]

    Pith/arXiv arXiv 2025

  2. [2]

    Gitsis and F

    A. Gitsis and F. Hassler,Unraveling the generalized Bergshoeff-de Roo identification, JHEP06(2025) 048, [arXiv:2412.17900]

    Pith/arXiv arXiv 2025

  3. [3]

    Gitsis and F

    A. Gitsis and F. Hassler,All-order generalized Green-Schwarz transformations,Phys. Rev. D113(2026), no. 2 026026, [arXiv:2511.09615]. 39

    arXiv 2026

  4. [4]

    Gasperini and G

    M. Gasperini and G. Veneziano,The Pre - big bang scenario in string cosmology,Phys. Rept.373(2003) 1–212, [hep-th/0207130]

    Pith/arXiv arXiv 2003

  5. [5]

    Becker, M

    K. Becker, M. Becker, M. Haack, and J. Louis,Supersymmetry breaking and alpha-prime corrections to flux induced potentials,JHEP06(2002) 060, [hep-th/0204254]

    Pith/arXiv arXiv 2002

  6. [6]

    Buchel, J

    A. Buchel, J. T. Liu, and A. O. Starinets,Coupling constant dependence of the shear viscosity in N=4 supersymmetric Yang-Mills theory,Nucl. Phys. B707(2005) 56–68, [hep-th/0406264]

    Pith/arXiv arXiv 2005

  7. [7]

    S. S. Gubser, I. R. Klebanov, and A. A. Tseytlin,Coupling constant dependence in the thermodynamics of N=4 supersymmetric Yang-Mills theory,Nucl. Phys. B534(1998) 202–222, [hep-th/9805156]

    Pith/arXiv arXiv 1998

  8. [8]

    Banks and M

    T. Banks and M. B. Green,Nonperturbative effects in AdS in five-dimensions x S**5 string theory and d = 4 SUSY Yang-Mills,JHEP05(1998) 002, [hep-th/9804170]

    Pith/arXiv arXiv 1998

  9. [9]

    Callan, R

    C. Callan, R. Myers, and M. Perry,Black holes in string theory,Nuclear Physics B311 (1989), no. 3 673–698

    1989

  10. [10]

    R. C. Myers,Higher Derivative Gravity, Surface Terms and String Theory,Phys. Rev. D 36(1987) 392

    1987

  11. [11]

    Sen,Black hole entropy function and the attractor mechanism in higher derivative gravity,JHEP09(2005) 038, [hep-th/0506177]

    A. Sen,Black hole entropy function and the attractor mechanism in higher derivative gravity,JHEP09(2005) 038, [hep-th/0506177]

    Pith/arXiv arXiv 2005

  12. [12]

    Mohaupt,Strings, higher curvature corrections, and black holes, inWorkshop on Mathematical and Physical Aspects of Quantum Gravity, pp

    T. Mohaupt,Strings, higher curvature corrections, and black holes, inWorkshop on Mathematical and Physical Aspects of Quantum Gravity, pp. 237–262, 12, 2005. hep-th/0512048

    Pith/arXiv arXiv 2005

  13. [13]

    M. R. Garousi and H. Razaghian,Minimal independent couplings at orderα′2,Phys. Rev. D100(2019), no. 10 106007, [arXiv:1905.10800]

    Pith/arXiv arXiv 2019

  14. [14]

    M. R. Garousi,Effective action of bosonic string theory at orderα′2,Eur. Phys. J. C79 (2019), no. 10 827, [arXiv:1907.06500]

    Pith/arXiv arXiv 2019

  15. [15]

    M. R. Garousi,On NS-NS couplings at orderα’3,Nucl. Phys. B971(2021) 115510, [arXiv:2012.15091]

    Pith/arXiv arXiv 2021

  16. [16]

    Gholian and M

    H. Gholian and M. R. Garousi,More on closed string effective actions at orderα’2, Phys. Rev. D109(2024), no. 8 086007, [arXiv:2311.05207]

    Pith/arXiv arXiv 2024

  17. [17]

    Ameri, A

    M. Ameri, A. Pahlavan, and M. R. Garousi,Effective action of bosonic string theory at orderα ′3,JHEP12(2025) 132, [arXiv:2506.19471]

    arXiv 2025

  18. [18]

    M. R. Garousi,Effective action of heterotic string theory at orderα’2,JHEP09(2023) 020, [arXiv:2307.00544]

    Pith/arXiv arXiv 2023

  19. [19]

    M. R. Garousi,An NS-NS basis for odd-parity couplings cm at orderα′3,Eur. Phys. J. C84(2024), no. 4 423, [arXiv:2402.16496]

    Pith/arXiv arXiv 2024

  20. [20]

    M. R. Garousi,Minimal gauge invariant couplings at orderα′3: NS–NS fields,Eur. Phys. J. C80(2020), no. 11 1086, [arXiv:2006.09193]

    Pith/arXiv arXiv 2020

  21. [21]

    M. R. Garousi,Effective action of type II superstring theories at orderα′3: NS-NS couplings,JHEP02(2021) 157, [arXiv:2011.02753]. 40

    Pith/arXiv arXiv 2021

  22. [22]

    Hull and B

    C. Hull and B. Zwiebach,Double Field Theory,JHEP09(2009) 099, [arXiv:0904.4664]

    Pith/arXiv arXiv 2009

  23. [23]

    O. Hohm, C. Hull, and B. Zwiebach,Background independent action for double field theory,JHEP07(2010) 016, [arXiv:1003.5027]

    Pith/arXiv arXiv 2010

  24. [24]

    O. Hohm, C. Hull, and B. Zwiebach,Generalized metric formulation of double field theory,JHEP08(2010) 008, [arXiv:1006.4823]

    Pith/arXiv arXiv 2010

  25. [25]

    Hitchin,Generalized Calabi-Yau manifolds,arXiv Mathematics e-prints(Sept., 2002) math/0209099, [math/0209099]

    N. Hitchin,Generalized Calabi-Yau manifolds,arXiv Mathematics e-prints(Sept., 2002) math/0209099, [math/0209099]

    Pith/arXiv arXiv 2002

  26. [26]

    Gualtieri,Generalized complex geometry,arXiv Mathematics e-prints(Jan., 2004) math/0401221, [math/0401221]

    M. Gualtieri,Generalized complex geometry,arXiv Mathematics e-prints(Jan., 2004) math/0401221, [math/0401221]

    Pith/arXiv arXiv 2004

  27. [27]

    E. A. Bergshoeff and M. de Roo,The Quartic Effective Action of the Heterotic String and Supersymmetry,Nucl. Phys. B328(1989) 439–468

    1989

  28. [28]

    W. H. Baron, E. Lescano, and D. Marqués,The generalized Bergshoeff-de Roo identification,JHEP11(2018) 160, [arXiv:1810.01427]

    Pith/arXiv arXiv 2018

  29. [29]

    Baron and D

    W. Baron and D. Marques,The generalized Bergshoeff-de Roo identification. Part II, JHEP01(2021) 171, [arXiv:2009.07291]

    Pith/arXiv arXiv 2021

  30. [30]

    Wulff,Tree-level R4 correction from O(d, d): NS-NS five-point terms,JHEP09 (2024) 078, [arXiv:2406.15240]

    L. Wulff,Tree-level R4 correction from O(d, d): NS-NS five-point terms,JHEP09 (2024) 078, [arXiv:2406.15240]

    Pith/arXiv arXiv 2024

  31. [31]

    S. W. Hsia, A. R. Kamal, and L. Wulff,No manifest T duality at orderα’3,Phys. Rev. D111(2025), no. 6 L061904, [arXiv:2411.15302]

    Pith/arXiv arXiv 2025

  32. [32]

    Poláček and W

    M. Poláček and W. Siegel,Natural curvature for manifest T-duality,JHEP01(2014) 026, [arXiv:1308.6350]

    Pith/arXiv arXiv 2014

  33. [33]

    Hassler, O

    F. Hassler, O. Hulik, and D. Osten,Current algebra and generalized Cartan geometry, Phys. Rev. D110(2024), no. 12 126022, [arXiv:2409.00176]

    Pith/arXiv arXiv 2024

  34. [34]

    Hassler, D

    F. Hassler, D. Osten, and A. Swash,Gauged Extended Field Theory and Generalised Cartan Geometry,Phys. Rev. D113(2026) 066017, [arXiv:2509.04595]

    Pith/arXiv arXiv 2026

  35. [35]

    Aldazabal, D

    G. Aldazabal, D. Marques, and C. Nunez,Double Field Theory: A Pedagogical Review, Class. Quant. Grav.30(2013) 163001, [arXiv:1305.1907]

    Pith/arXiv arXiv 2013

  36. [36]

    Geissbuhler, D

    D. Geissbuhler, D. Marques, C. Nunez, and V. Penas,Exploring Double Field Theory, JHEP06(2013) 101, [arXiv:1304.1472]

    Pith/arXiv arXiv 2013

  37. [37]

    Hohm and S

    O. Hohm and S. K. Kwak,Double Field Theory Formulation of Heterotic Strings,JHEP 06(2011) 096, [arXiv:1103.2136]

    Pith/arXiv arXiv 2011

  38. [38]

    Lescano,α’-corrections and their double formulation,J

    E. Lescano,α’-corrections and their double formulation,J. Phys. A55(2022), no. 5 053002, [arXiv:2108.12246]

    Pith/arXiv arXiv 2022

  39. [39]

    Marques and C

    D. Marques and C. A. Nunez,T-duality andα’-corrections,JHEP10(2015) 084, [arXiv:1507.00652]

    Pith/arXiv arXiv 2015

  40. [40]

    Geissbuhler,Double Field Theory and N=4 Gauged Supergravity,JHEP11(2011) 116, [arXiv:1109.4280]

    D. Geissbuhler,Double Field Theory and N=4 Gauged Supergravity,JHEP11(2011) 116, [arXiv:1109.4280]. 41

    Pith/arXiv arXiv 2011

  41. [41]

    Aldazabal, W

    G. Aldazabal, W. Baron, D. Marques, and C. Nunez,The effective action of Double Field Theory,JHEP11(2011) 052, [arXiv:1109.0290]. [Erratum: JHEP 11, 109 (2011)]

    Pith/arXiv arXiv 2011

  42. [42]

    Grana and D

    M. Grana and D. Marques,Gauged Double Field Theory,JHEP04(2012) 020, [arXiv:1201.2924]

    Pith/arXiv arXiv 2012

  43. [43]

    M. B. Green and J. H. Schwarz,Anomaly Cancellation in Supersymmetric D=10 Gauge Theory and Superstring Theory,Phys. Lett. B149(1984) 117–122

    1984

  44. [44]

    Hassler and T

    F. Hassler and T. Rochais,α′-Corrected Poisson-Lie T-Duality,Fortsch. Phys.68 (2020), no. 9 2000063, [arXiv:2007.07897]

    Pith/arXiv arXiv 2020

  45. [45]

    Borsato and L

    R. Borsato and L. Wulff,Quantum Correction to GeneralizedTDualities,Phys. Rev. Lett.125(2020), no. 20 201603, [arXiv:2007.07902]

    Pith/arXiv arXiv 2020

  46. [46]

    Codina and D

    T. Codina and D. Marques,Generalized Dualities and Higher Derivatives,JHEP10 (2020) 002, [arXiv:2007.09494]

    Pith/arXiv arXiv 2020

  47. [47]

    Wulff,Second order bosonic string effective action from O(d, d),JHEP02(2025) 194, [arXiv:2406.15234]

    L. Wulff,Second order bosonic string effective action from O(d, d),JHEP02(2025) 194, [arXiv:2406.15234]

    Pith/arXiv arXiv 2025

  48. [48]

    R. R. Metsaev and A. A. Tseytlin,Two loop beta function for the generalized bosonic sigma model,Phys. Lett. B191(1987) 354–362

    1987

  49. [49]

    Hronek, L

    S. Hronek, L. Wulff, and S. Zacarias,Theα’2 correction from double field theory,JHEP 11(2022) 090, [arXiv:2206.10640]

    Pith/arXiv arXiv 2022

  50. [50]

    xAct: Efficient tensor computer algebra for the Wolfram Language

    José M. Martín-García, “xAct: Efficient tensor computer algebra for the Wolfram Language.”https://xact.es/, 2002

    2002

  51. [51]

    Nutma,xTras: A field-theory inspired xAct package for mathematica,Comput

    T. Nutma,xTras: A field-theory inspired xAct package for mathematica,Comput. Phys. Commun.185(2014) 1719–1738, [arXiv:1308.3493]

    Pith/arXiv arXiv 2014

  52. [52]

    Brizuela, J

    D. Brizuela, J. M. Martin-Garcia, and G. A. Mena Marugan,xPert: Computer algebra for metric perturbation theory,Gen. Rel. Grav.41(2009) 2415–2431, [arXiv:0807.0824]

    Pith/arXiv arXiv 2009

  53. [53]

    K. A. Meissner,Symmetries of higher order string gravity actions,Phys. Lett. B392 (1997) 298–304, [hep-th/9610131]. 42

    Pith/arXiv arXiv 1997