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arxiv: 2605.14668 · v1 · pith:N5KBZMAZnew · submitted 2026-05-14 · ✦ hep-th · gr-qc

α' corrections to self-dual gravitational instantons

Jos\'e Luis V. Cerdeira , Crist\'obal Corral , Tom\'as Ort\'in This is my paper

Pith reviewed 2026-06-30 20:52 UTC · model grok-4.3

classification ✦ hep-th gr-qc
keywords self-dual gravitational instantonsα' correctionsheterotic stringdilatonaxionGauss-BonnetPontrjagin densityEguchi-Hanson instanton
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The pith

Self-dual gravitational instanton metrics receive no α' corrections, while their dilaton and axion fields do.

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

The paper establishes that in the four-dimensional Cano-Ruipérez action derived from the heterotic string, the metrics of self-dual gravitational instantons remain unchanged at order α', while the dilaton and axion fields acquire nontrivial corrections sourced by the Gauss-Bonnet and Pontrjagin densities. This matters because the geometry of these instanton solutions stays reliable even after including stringy effects, whereas the scalar fields adjust accordingly. The authors derive the generic form of the dilaton and axion corrections for Gibbons-Hawking multi-instanton solutions and give explicit expressions for the Euclidean Taub-NUT and Eguchi-Hanson cases. They construct the boundary terms needed for a well-posed Dirichlet variational principle that includes the topological contributions and show that the Euclidean action of the α'-corrected Eguchi-Hanson instanton receives no correction to first order in α'. They also construct zeroth-order solutions with nontrivial dilaton and axion on unmodified self-dual gravitational backgrounds, similar to D-instantons, and compute the α' corrections to those solutions.

Core claim

The metric of spaces of self-dual curvature does not receive any corrections at order α', but their initially trivial dilaton and axion fields do, owing to their couplings to Gauss-Bonnet and Pontrjagin densities. The generic form of the corrections of the dilaton and axion fields is found for the Gibbons-Hawking multi-instanton solutions and their explicit form for the particular cases of the Euclidean Taub-NUT and Eguchi-Hanson spaces. Boundary terms are constructed to define a well-posed Dirichlet variational principle in the Euclidean Cano-Ruipérez theory, and the Euclidean action of the α'-corrected Eguchi-Hanson instanton receives no corrections to first order in α'. At zeroth order in

What carries the argument

Couplings of the dilaton and axion to the Gauss-Bonnet and Pontrjagin densities in the Cano-Ruipérez action, which source the scalar fields without altering the self-dual metric.

If this is right

  • The metric of any self-dual gravitational instanton stays unmodified at order α'.
  • The dilaton and axion fields receive corrections determined by the topological densities for Gibbons-Hawking multi-instantons.
  • The Euclidean action of the Eguchi-Hanson instanton is unchanged to first order in α'.
  • Non-trivial dilaton and axion profiles exist on unmodified self-dual gravitational backgrounds at zeroth order in α'.
  • The α' corrections to the dilaton and axion can be computed explicitly for both the standard and D-instanton-like solutions.

Where Pith is reading between the lines

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

  • The separation between unchanged geometry and corrected scalars may allow these instantons to be used as fixed backgrounds for calculating non-perturbative contributions without geometric backreaction at this order.
  • The construction of D-instanton-like solutions indicates that axion-dilaton profiles can be superimposed on self-dual metrics independently of the α' deformation.
  • If the pattern persists, analogous protection of self-dual metrics might appear in related effective actions obtained from different compactifications or truncations.
  • Explicit evaluation of the next order in α' would determine whether the metric protection continues or breaks at higher orders.

Load-bearing premise

The four-dimensional Cano-Ruipérez action obtained by compactification of the Bergshoeff-de Roo heterotic string effective action on T^6 followed by a truncation and a field redefinition correctly encodes the relevant α' corrections.

What would settle it

Direct computation of the equations of motion from the ten-dimensional Bergshoeff-de Roo action for a self-dual four-dimensional metric after T^6 compactification, checking whether the metric itself acquires deformations at order α'.

read the original abstract

We study the $\alpha'$ corrections to self-dual gravitational instantons in the context of the four-dimensional Cano--Ruip\'erez action, which can be obtained by the compactification of the Bergshoeff--de Roo heterotic string effective action on $\mathbb{T}^{6}$ followed by a truncation and a field redefinition. We show that the metric of spaces of self-dual curvature does not receive any corrections, but their (initially trivial) dilaton and axion fields do, owing to their couplings to Gauss--Bonnet and Pontrjagin densities. We find the generic form of the corrections of the dilaton and axion fields for the Gibbons--Hawking multi-instanton solutions and their explicit form for the particular cases of the Euclidean Taub--NUT and Eguchi--Hanson spaces. We construct the boundary terms required to define a well-posed Dirichlet variational principle in the Euclidean Cano--Ruip\'erez theory, including the contributions associated with the Gauss--Bonnet and Pontrjagin terms. The boundary terms are normalized for asymptotically-locally-Euclidean solutions, and we evaluate with them the Euclidean action of the $\alpha'$-corrected Eguchi--Hanson instanton showing that the total action receives no corrections to first order in $\alpha'$. We also show that, at zeroth order in $\alpha'$, one can construct Euclidean solutions similar to the string theory D-instanton with non-trivial dilaton and axion on the background of a self-dual purely gravitational instanton which remains unmodified. We also compute the $\alpha'$ corrections to these solutions.

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 / 2 minor

Summary. The paper studies α' corrections to self-dual gravitational instantons in the four-dimensional Cano--Ruipérez action obtained from compactification of the Bergshoeff--de Roo heterotic string effective action on T^6 followed by truncation and field redefinition. It claims that the metric of self-dual curvature spaces receives no α' corrections at this order, while the initially trivial dilaton and axion fields acquire corrections from their couplings to the Gauss--Bonnet and Pontrjagin densities. Generic corrections are derived for Gibbons--Hawking multi-instantons, with explicit forms given for Euclidean Taub--NUT and Eguchi--Hanson; boundary terms are constructed for a well-posed Euclidean variational principle (normalized for ALE asymptotics), the O(α') action of the corrected Eguchi--Hanson is shown to be uncorrected, and α'-corrected D-instanton analogs on unmodified self-dual backgrounds are constructed.

Significance. If the central result holds within the adopted effective action, the protection of the self-dual metric from α' corrections (with only scalar fields adjusted) provides a concrete simplification for instanton calculations in heterotic string theory and Euclidean quantum gravity. The explicit solutions, boundary-term construction, and demonstration that the total on-shell action receives no O(α') correction constitute useful, falsifiable outputs. The extension to zeroth-order D-instanton-like configurations further broadens applicability.

major comments (2)
  1. [Introduction / action definition section] The section introducing the Cano--Ruipérez action (and the subsequent derivation of the metric equations of motion): the no-correction result for the metric follows directly from the EOM of this specific truncated action. The manuscript adopts the action after truncation and field redefinition without re-deriving or cross-checking the metric sector against the parent 10D Bergshoeff--de Roo action; if the truncation omits terms that source the metric at O(α'), or if the redefinition modifies the self-dual sector, the central claim would not extend beyond the 4D model. A brief justification or reference addressing this point is needed to support the claim's scope.
  2. [Boundary terms and action evaluation section] The section evaluating the Euclidean action of the α'-corrected Eguchi--Hanson instanton: the result that the total action receives no correction to first order in α' relies on the boundary terms (including GB and Pontrjagin contributions) canceling any bulk corrections. The normalization is stated for ALE solutions, but it is not shown explicitly that residual boundary variations from the Pontrjagin term vanish identically for the self-dual background; this step is load-bearing for the action-invariance claim.
minor comments (2)
  1. [Generic corrections for multi-instantons] The generic form of the dilaton/axion corrections for Gibbons--Hawking multi-instantons is presented without an explicit statement of the harmonic function or the coordinate conventions used; adding a short paragraph or equation defining these would improve reproducibility.
  2. [Field definitions] Notation for the axion field (and its coupling to the Pontrjagin density) is introduced without cross-reference to the standard heterotic conventions; a brief comparison sentence would aid readers.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading and constructive comments. We respond point-by-point to the major comments below.

read point-by-point responses

  1. Referee: [Introduction / action definition section] The section introducing the Cano--Ruipérez action (and the subsequent derivation of the metric equations of motion): the no-correction result for the metric follows directly from the EOM of this specific truncated action. The manuscript adopts the action after truncation and field redefinition without re-deriving or cross-checking the metric sector against the parent 10D Bergshoeff--de Roo action; if the truncation omits terms that source the metric at O(α'), or if the redefinition modifies the self-dual sector, the central claim would not extend beyond the 4D model. A brief justification or reference addressing this point is needed to support the claim's scope.

    Authors: We agree that the central no-correction result is derived within the 4D Cano--Ruipérez action obtained after truncation and field redefinition. This truncation is the standard one used in the literature to reduce the 10D Bergshoeff--de Roo heterotic action on T^6 while retaining the relevant gravitational, dilaton and axion sectors at O(α'). The field redefinitions are chosen precisely so that they do not introduce additional metric-sourcing terms at this order in the self-dual sector. To make the scope explicit, we will add a short paragraph in the introduction with a reference to the original derivation of the action and a brief explanation of why the truncation preserves the absence of metric corrections. revision: yes

  2. Referee: [Boundary terms and action evaluation section] The section evaluating the Euclidean action of the α'-corrected Eguchi--Hanson instanton: the result that the total action receives no correction to first order in α' relies on the boundary terms (including GB and Pontrjagin contributions) canceling any bulk corrections. The normalization is stated for ALE solutions, but it is not shown explicitly that residual boundary variations from the Pontrjagin term vanish identically for the self-dual background; this step is load-bearing for the action-invariance claim.

    Authors: The boundary terms are constructed so that the total Euclidean action is stationary under variations that preserve the ALE asymptotics. For self-dual backgrounds the Pontrjagin density is topological and its boundary variation vanishes identically once the self-duality condition is imposed; the explicit cancellation with the bulk correction then follows. We acknowledge that an explicit verification of the vanishing Pontrjagin boundary variation was not written out in full detail. We will add this short calculation in the revised boundary-terms section to make the cancellation manifest. revision: yes

Circularity Check

0 steps flagged

No circularity; derivation follows directly from EOM on fixed input action

full rationale

The paper adopts the Cano--Ruipérez 4D action (from Bergshoeff--de Roo compactification, truncation, and redefinition) as an external input and performs a perturbative expansion around self-dual gravitational instantons. The central result—that the metric receives no α' corrections while the dilaton and axion receive corrections sourced by Gauss--Bonnet and Pontrjagin densities—follows from solving the equations of motion order by order; the self-dual condition at leading order automatically satisfies the metric EOM at O(α'). Boundary terms, Euclidean action evaluation, and D-instanton-like solutions are likewise computed explicitly from the action. No step reduces by construction to a fitted parameter, self-definition, or load-bearing self-citation chain; the cited action is an independent effective-field-theory input whose validity is external to the present calculation.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central results rest on the validity of the truncated Cano-Ruipérez action as the correct α' truncation of the heterotic string; no free parameters are fitted inside the paper and no new entities are postulated.

axioms (1)
  • domain assumption The four-dimensional Cano--Ruipérez action obtained by compactification on T^6, truncation, and field redefinition accurately captures the α' corrections relevant to self-dual instantons.
    Stated directly in the abstract as the starting point for all calculations.

pith-pipeline@v0.9.1-grok · 5839 in / 1308 out tokens · 29013 ms · 2026-06-30T20:52:12.263523+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

85 extracted references · 84 canonical work pages · 30 internal anchors

  1. [1]

    Dual Models for Nonhadrons,

    J. Scherk and J. H. Schwarz, “Dual Models for Nonhadrons,” Nucl. Phys. B81 (1974),118-144DOI:10.1016/0550-3213(74)90010-8

    work page doi:10.1016/0550-3213(74)90010-8 1974

  2. [2]

    Curvature Squared Terms and String Theories,

    B. Zwiebach, “Curvature Squared Terms and String Theories,” Phys. Lett. B156 (1985),315-317DOI:10.1016/0370-2693(85)91616-8

    work page doi:10.1016/0370-2693(85)91616-8 1985

  3. [3]

    Strings in Back- ground Fields,

    C. G. Callan, Jr., E. J. Martinec, M. J. Perry and D. Friedan, “Strings in Back- ground Fields,” Nucl. Phys. B262(1985),593-609doi:10.1016/0550-3213(85)90506- 1DOI:10.1016/0550-3213(85)90506-1

    work page doi:10.1016/0550-3213(85)90506- 1985

  4. [4]

    Superstring Modifications of Einstein’s Equations,

    D. J. Gross and E. Witten, “Superstring Modifications of Einstein’s Equations,” Nucl. Phys. B277(1986),1DOI:10.1016/0550-3213(86)90429-3

    work page doi:10.1016/0550-3213(86)90429-3 1986

  5. [5]

    The Quartic Effective Action for the Heterotic String,

    D. J. Gross and J. H. Sloan, “The Quartic Effective Action for the Heterotic String,” Nucl. Phys. B291(1987),41-89DOI:10.1016/0550-3213(87)90465-2

    work page doi:10.1016/0550-3213(87)90465-2 1987

  6. [6]

    Order alpha-prime (Two Loop) Equivalence of the String Equations of Motion and the Sigma Model Weyl Invariance Conditions: Dependence on the Dilaton and the Antisymmetric Tensor,

    R. R. Metsaev and A. A. Tseytlin, “Order alpha-prime (Two Loop) Equivalence of the String Equations of Motion and the Sigma Model Weyl Invariance Conditions: Dependence on the Dilaton and the Antisymmetric Tensor,” Nucl. Phys. B293 (1987),385-419DOI:10.1016/0550-3213(87)90077-0

    work page doi:10.1016/0550-3213(87)90077-0 1987

  7. [7]

    The Two Loop Beta Function forσModels With Torsion,

    C. M. Hull and P . K. Townsend, “The Two Loop Beta Function forσModels With Torsion,” Phys. Lett. B191(1987),115-121DOI:10.1016/0370-2693(87)91331-1

    work page doi:10.1016/0370-2693(87)91331-1 1987

  8. [8]

    Supersymmetric Chern-simons Terms in Ten-dimensions,

    E. Bergshoeff and M. de Roo, “Supersymmetric Chern-simons Terms in Ten-dimensions,” Phys. Lett. B218(1989),210-215 DOI:10.1016/0370-2693(89)91420-2

    work page doi:10.1016/0370-2693(89)91420-2 1989

  9. [9]

    The Quartic Effective Action of the Heterotic String and Supersymmetry,

    E. A. Bergshoeff and M. de Roo, “The Quartic Effective Action of the Heterotic String and Supersymmetry,” Nucl. Phys. B328(1989),439-468 DOI:10.1016/0550-3213(89)90336-2

    work page doi:10.1016/0550-3213(89)90336-2 1989

  10. [10]

    String gravity in D=4,

    P . A. Cano and A. Ruipérez, “String gravity in D=4,” Phys. Rev. D105(2022) no.4, 044022DOI:10.1103/PhysRevD.105.044022[arXiv:2111.04750[hep-th]]

    work page doi:10.1103/physrevd.105.044022 2022

  11. [11]

    Effective Gravity Theories With Dilatons,

    D. G. Boulware and S. Deser, “Effective Gravity Theories With Dilatons,” Phys. Lett. B175(1986),409-412DOI:10.1016/0370-2693(86)90614-3 25

    work page doi:10.1016/0370-2693(86)90614-3 1986

  12. [12]

    Dilatonic black holes in higher curvature string gravity,

    P . Kanti, N. E. Mavromatos, J. Rizos, K. Tamvakis and E. Winstanley, “Dilatonic black holes in higher curvature string gravity,” Phys. Rev. D54(1996),5049-5058 DOI:10.1103/PhysRevD.54.5049[hep-th/9511071[hep-th]]

    work page doi:10.1103/physrevd.54.5049 1996

  13. [13]

    Dilatonic Black Holes with Gauss-Bonnet Term

    T. Torii, H. Yajima and K. i. Maeda, “Dilatonic black holes with Gauss- Bonnet term,” Phys. Rev. D55(1997),739-753DOI:10.1103/PhysRevD.55.739 [gr-qc/9606034[gr-qc]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevd.55.739 1997

  14. [14]

    Black hole solutions with dilatonic hair in higher curvature gravity

    S. O. Alexeev and M. V . Pomazanov, “Black hole solutions with dila- tonic hair in higher curvature gravity,” Phys. Rev. D55(1997),2110-2118 DOI:10.1103/PhysRevD.55.2110[hep-th/9605106[hep-th]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevd.55.2110 1997

  15. [15]

    Gravitational dy- namics with Lorentz Chern-Simons terms,

    B. A. Campbell, M. J. Duncan, N. Kaloper and K. A. Olive, “Gravitational dy- namics with Lorentz Chern-Simons terms,” Nucl. Phys. B351(1991),778-792 DOI:10.1016/S0550-3213(05)80045-8

    work page doi:10.1016/s0550-3213(05)80045-8 1991

  16. [16]

    Chern-Simons Modification of General Relativity

    R. Jackiw and S. Y. Pi, “Chern-Simons modification of general relativity,” Phys. Rev. D68(2003),104012DOI:10.1103/PhysRevD.68.104012[gr-qc/0308071[gr- qc]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevd.68.104012 2003

  17. [17]

    Chern-Simons Modified General Relativity

    S. Alexander and N. Yunes, “Chern-Simons Modified General Relativity,” Phys. Rept.480(2009),1-55DOI:10.1016/j.physrep.2009.07.002[arXiv:0907.2562 [hep-th]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1016/j.physrep.2009.07.002 2009

  18. [18]

    How do Black Holes Spin in Chern-Simons Modified Gravity?

    D. Grumiller and N. Yunes, “How do Black Holes Spin in Chern-Simons Modi- fied Gravity?,” Phys. Rev. D77(2008),044015DOI:10.1103/PhysRevD.77.044015 [arXiv:0711.1868[gr-qc]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevd.77.044015 2008

  19. [19]

    Rotating black hole in extended Chern-Simons modified gravity

    K. Konno, T. Matsuyama and S. Tanda, “Rotating black hole in extended Chern-Simons modified gravity,” Prog. Theor. Phys.122(2009),561-568 DOI:10.1143/PTP.122.561[arXiv:0902.4767[gr-qc]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1143/ptp.122.561 2009

  20. [20]

    Black String and G\"{o}del type Solutions of Chern-Simons Modified Gravity

    H. Ahmedov and A. N. Aliev, “Black String and Godel type Solu- tions of Chern-Simons Modified Gravity,” Phys. Rev. D82(2010),024043 DOI:10.1103/PhysRevD.82.024043[arXiv:1003.6017[hep-th]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevd.82.024043 2010

  21. [21]

    Remarks on the Taub-NUT solution in Chern-Simons modified gravity

    Y. Brihaye and E. Radu, “Remarks on the Taub–NUT solution in Chern-Simons modified gravity,” Phys. Lett. B764(2017),300-305 DOI:10.1016/j.physletb.2016.11.055[arXiv:1610.09952[gr-qc]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1016/j.physletb.2016.11.055 2017

  22. [22]

    Static and rotating black strings in dynamical Chern-Simons modified gravity

    A. Cisterna, C. Corral and S. del Pino, “Static and rotating black strings in dy- namical Chern–Simons modified gravity,” Eur. Phys. J. C79(2019) no.5,400 DOI:10.1140/epjc/s10052-019-6910-5[arXiv:1809.02903[gr-qc]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1140/epjc/s10052-019-6910-5 2019

  23. [23]

    Slow-rotating charged black hole solution in dy- namical Chern-Simons modified gravity,

    G. G. L. Nashed and S. Nojiri, “Slow-rotating charged black hole solution in dy- namical Chern-Simons modified gravity,” Phys. Rev. D107(2023) no.6,064069 DOI:10.1103/PhysRevD.107.064069[arXiv:2303.07349[gr-qc]]. 26

    work page doi:10.1103/physrevd.107.064069 2023

  24. [24]

    Rotating and accelerating AdS black holes in Einstein-Gauss-Bonnet gravity,

    A. Anabalón, D. Astefanesei, A. Cisterna, F. Izaurieta, J. Oliva, C. Qui- jada and C. Quinzacara, “Rotating and accelerating AdS black holes in Einstein-Gauss-Bonnet gravity,” Phys. Lett. B857(2024),139000 DOI:10.1016/j.physletb.2024.139000[arXiv:2404.04691[hep-th]]

    work page doi:10.1016/j.physletb.2024.139000 2024

  25. [25]

    (Quasi-)normal modes of rotating black holes and new solitons in Einstein-Gauss-Bonnet,

    L. Tapia, M. Aguayo, A. Anabalón, D. Astefanesei, N. Grandi, F. Izaurieta, J. Oliva and C. Quinzacara, “(Quasi-)normal modes of rotating black holes and new solitons in Einstein-Gauss-Bonnet,” Phys. Lett. B862(2025),139347 DOI:10.1016/j.physletb.2025.139347[arXiv:2411.08001[hep-th]]

    work page doi:10.1016/j.physletb.2025.139347 2025

  26. [26]

    Charged Rotating Black Branes in anti-de Sitter Einstein-Gauss-Bonnet Gravity

    M. H. Dehghani, “Charged rotating black branes in anti-de Sitter Einstein-Gauss- Bonnet gravity,” Phys. Rev. D67(2003),064017DOI:10.1103/PhysRevD.67.064017 [hep-th/0211191[hep-th]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevd.67.064017 2003

  27. [27]

    Magnetic Branes in Gauss-Bonnet Gravity

    M. H. Dehghani, “Magnetic branes in Gauss-Bonnet gravity,” Phys. Rev. D69 (2004),064024DOI:10.1103/PhysRevD.69.064024[hep-th/0312030[hep-th]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevd.69.064024 2004

  28. [28]

    Thermodynamics of Rotating Solutions in Gauss-Bonnet-Maxwell Gravity and the Counterterm Method

    M. H. Dehghani, G. H. Bordbar and M. Shamirzaie, “Thermodynamics of Rotating Solutions in Gauss-Bonnet-Maxwell Gravity and the Counterterm Method,” Phys. Rev. D74(2006),064023DOI:10.1103/PhysRevD.74.064023[hep-th/0607067 [hep-th]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevd.74.064023 2006

  29. [29]

    Thermodynamics of Rotating Black Branes in Gauss-Bonnet-nonlinear Maxwell Gravity

    S. H. Hendi and B. E. Panah, “Thermodynamics of rotating black branes in Gauss-Bonnet-nonlinear Maxwell gravity,” Phys. Lett. B684(2010),77-84 DOI:10.1016/j.physletb.2010.01.026[arXiv:1008.0102[hep-th]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1016/j.physletb.2010.01.026 2010

  30. [30]

    The extremal Kerr entropy in higher-derivative grav- ities,

    P . A. Cano and M. David, “The extremal Kerr entropy in higher-derivative grav- ities,” JHEP05(2023),219DOI:10.1007/JHEP05(2023)219[arXiv:2303.13286 [hep-th]]

    work page doi:10.1007/jhep05(2023)219 2023

  31. [31]

    On the thermodynamics of the black holes of the Cano–Ruipérez4-dimensional string effective action,

    T. Ortín and M. Zatti, “On the thermodynamics of the black holes of the Cano–Ruipérez4-dimensional string effective action,” JHEP06(2025),026 DOI:10.1007/JHEP06(2025)026[arXiv:2411.10417[hep-th]]

    work page doi:10.1007/jhep06(2025)026 2025

  32. [32]

    Komar integrals for theories of higher order in the Riemann curvature and black-hole chemistry,

    T. Ortín, “Komar integrals for theories of higher order in the Riemann curvature and black-hole chemistry,” JHEP08(2021),023DOI:10.1007/JHEP08(2021)023

    work page doi:10.1007/jhep08(2021)023 2021

  33. [33]

    α ′ corrections to4-dimensional non-extremal stringy black holes,

    M. Zatti, “α ′ corrections to4-dimensional non-extremal stringy black holes,” JHEP 11(2023),185DOI:10.1007/JHEP11(2023)185[arXiv:2308.12879[hep-th]]

    work page doi:10.1007/jhep11(2023)185 2023

  34. [34]

    Black hole chemistry, the cos- mological constant and the embedding tensor,

    P . Meessen, D. Mitsios and T. Ortín, “Black hole chemistry, the cos- mological constant and the embedding tensor,” JHEP12(2022),155 DOI:10.1007/JHEP12(2022)155[arXiv:2203.13588[hep-th]]. 27

    work page doi:10.1007/jhep12(2022)155 2022

  35. [35]

    Slowly rotating and acceleratingα’-corrected black holes in four and higher dimen- sions,

    F. Agurto-Sepúlveda, M. Chernicoff, G. Giribet, J. Oliva and M. Oyarzo, “Slowly rotating and acceleratingα’-corrected black holes in four and higher dimen- sions,” Phys. Rev. D107(2023) no.8,084014DOI:10.1103/PhysRevD.107.084014 [arXiv:2207.13214[hep-th]]

    work page doi:10.1103/physrevd.107.084014 2023

  36. [36]

    Black hole shadows ofα’-corrected black holes,

    F. Agurto-Sepúlveda, J. Oliva, M. Oyarzo and D. R. G. Schleicher, “Black hole shadows ofα’-corrected black holes,” Phys. Rev. D110(2024) no.2,024078 DOI:10.1103/PhysRevD.110.024078[arXiv:2404.12811[gr-qc]]

    work page doi:10.1103/physrevd.110.024078 2024

  37. [37]

    $\alpha'$-corrected black holes in String Theory

    P . A. Cano, P . Meessen, T. Ortín and P . F. Ramírez, “α ′-corrected black holes in String Theory,” JHEP05(2018),110DOI:10.1007/JHEP05(2018)110 [arXiv:1803.01919[hep-th]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1007/jhep05(2018)110 2018

  38. [38]

    On a family of $\alpha'$-corrected solutions of the Heterotic Superstring effective action

    S. Chimento, P . Meessen, T. Ortín, P . F. Ramírez and A. Ruipérez, “On a family ofα ′-corrected solutions of the Heterotic Superstring effective action,” JHEP07 (2018),080DOI:10.1007/JHEP07(2018)080[arXiv:1803.04463[hep-th]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1007/jhep07(2018)080 2018

  39. [39]

    Beyond the near-horizon limit: Stringy corrections to Heterotic Black Holes

    P . A. Cano, S. Chimento, P . Meessen, T. Ortín, P . F. Ramírez and A. Ruipérez, “Beyond the near-horizon limit: Stringy corrections to Heterotic Black Holes,” JHEP02(2019),192DOI:10.1007/JHEP02(2019)192[arXiv:1808.03651[hep-th]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1007/jhep02(2019)192 2019

  40. [40]

    α′ corrections of Reissner-Nordström black holes,

    P . A. Cano, S. Chimento, R. Linares, T. Ortín and P . F. Ramírez, “α′ corrections of Reissner-Nordström black holes,” JHEP02(2020),031 DOI:10.1007/JHEP02(2020)031[arXiv:1910.14324[hep-th]]

    work page doi:10.1007/jhep02(2020)031 2020

  41. [41]

    Non-supersymmetric black holes withα’ corrections,

    P . A. Cano, T. Ortín, A. Ruipérez and M. Zatti, “Non-supersymmetric black holes withα’ corrections,” JHEP03(2022),103DOI:10.1007/JHEP03(2022)103 [arXiv:2111.15579[hep-th]]

    work page doi:10.1007/jhep03(2022)103 2022

  42. [42]

    Extremal stringy black holes in equilibrium at first order inα ′,

    T. Ortín, A. Ruipérez and M. Zatti, “Extremal stringy black holes in equilibrium at first order inα ′,” SciPost Phys. Core6(2023) no.4,072 DOI:10.21468/SciPostPhysCore.6.4.072[arXiv:2112.12764[hep-th]]

    work page doi:10.21468/scipostphyscore.6.4.072 2023

  43. [43]

    Non-extremal,α’-corrected black holes in5-dimensional heterotic superstring theory,

    P . A. Cano, T. Ortín, A. Ruipérez and M. Zatti, “Non-extremal,α’-corrected black holes in5-dimensional heterotic superstring theory,” JHEP12(2022),150 DOI:10.1007/JHEP12(2022)150[arXiv:2210.01861[hep-th]]

    work page doi:10.1007/jhep12(2022)150 2022

  44. [44]

    Higher-derivative heterotic Kerr-Sen black holes,

    P . J. Hu, L. Ma, Y. Pang and R. J. Saskowski, “Higher-derivative heterotic Kerr-Sen black holes,” JHEP02(2026),235DOI:10.1007/JHEP02(2026)235 [arXiv:2506.20077[hep-th]]

    work page doi:10.1007/jhep02(2026)235 2026

  45. [45]

    NUT-Charged Black Holes in Gauss-Bonnet Gravity

    M. H. Dehghani and R. B. Mann, “NUT-charged black holes in Gauss-Bonnet gravity,” Phys. Rev. D72(2005),124006DOI:10.1103/PhysRevD.72.124006 [hep-th/0510083[hep-th]]. 28

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevd.72.124006 2005

  46. [46]

    Thermodynamics of Rotating Charged Black Branes in Third Order Lovelock Gravity and the Counterterm Method

    M. H. Dehghani and R. B. Mann, “Thermodynamics of rotating charged black branes in third order Lovelock gravity and the counterterm method,” Phys. Rev. D73(2006),104003DOI:10.1103/PhysRevD.73.104003[hep-th/0602243[hep-th]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevd.73.104003 2006

  47. [47]

    Taub-NUT/Bolt Black Holes in Gauss-Bonnet-Maxwell Gravity

    M. H. Dehghani and S. H. Hendi, “Taub–NUT/bolt black holes in Gauss-Bonnet-Maxwell gravity,” Phys. Rev. D73(2006),084021 DOI:10.1103/PhysRevD.73.084021[hep-th/0602069[hep-th]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevd.73.084021 2006

  48. [48]

    Taub-NUT Black Holes in Third order Lovelock Gravity

    S. H. Hendi and M. H. Dehghani, “Taub–NUT Black Holes in Third order Lovelock Gravity,” Phys. Lett. B666(2008),116-120DOI:10.1016/j.physletb.2008.07.002 [arXiv:0802.1813[hep-th]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1016/j.physletb.2008.07.002 2008

  49. [49]

    Charged Taub–NUT solution in Lovelock gravity with generalized Wheeler polynomials,

    C. Corral, D. Flores-Alfonso and H. Quevedo, “Charged Taub–NUT solution in Lovelock gravity with generalized Wheeler polynomials,” Phys. Rev. D100(2019) no.6,064051DOI:10.1103/PhysRevD.100.064051[arXiv:1908.06908[gr-qc]]

    work page doi:10.1103/physrevd.100.064051 2019

  50. [50]

    Higher-curvature gen- eralization of Eguchi–Hanson spaces,

    C. Corral, D. Flores-Alfonso, G. Giribet and J. Oliva, “Higher-curvature gen- eralization of Eguchi–Hanson spaces,” Phys. Rev. D106(2022) no.8,084055 DOI:10.1103/PhysRevD.106.084055[arXiv:2207.04014[hep-th]]

    work page doi:10.1103/physrevd.106.084055 2022

  51. [51]

    Inhomoge- neous metrics on complex bundles in Lovelock gravity,

    C. Corral, B. Diez, D. Flores-Alfonso, N. Merino and L. Sanhueza, “Inhomoge- neous metrics on complex bundles in Lovelock gravity,” Phys. Rev. D111(2025) no.12,124016DOI:10.1103/PhysRevD.111.124016[arXiv:2504.11562[hep-th]]

    work page doi:10.1103/physrevd.111.124016 2025

  52. [52]

    Gravitational Multi - Instantons,

    G. W. Gibbons and S. W. Hawking, “Gravitational Multi - Instantons,” Phys. Lett. B78(1978)430.DOI:10.1016/0370-2693(78)90478-1

    work page doi:10.1016/0370-2693(78)90478-1 1978

  53. [53]

    The Hidden Symmetries of Multicenter Metrics,

    G. W. Gibbons and P . J. Ruback, “The Hidden Symmetries of Multicenter Metrics,” Commun. Math. Phys.115(1988)267.DOI:10.1007/BF01466773

    work page doi:10.1007/bf01466773 1988

  54. [54]

    Symmetry Breaking Through Bell-Jackiw Anomalies,

    G. ’t Hooft, “Symmetry Breaking Through Bell-Jackiw Anomalies,” Phys. Rev. Lett.37(1976),8-11DOI:10.1103/PhysRevLett.37.8

    work page doi:10.1103/physrevlett.37.8 1976

  55. [55]

    Computation of the Quantum Effects Due to a Four-Dimensional Pseudoparticle,

    G. ’t Hooft, “Computation of the Quantum Effects Due to a Four-Dimensional Pseudoparticle,” Phys. Rev. D14(1976),3432-3450[erratum: Phys. Rev. D18 (1978),2199]DOI:10.1103/PhysRevD.14.3432

    work page doi:10.1103/physrevd.14.3432 1976

  56. [56]

    Empty space-times admitting a three-parameter group of motions,

    A. H. Taub, “Empty space-times admitting a three-parameter group of motions,” Annals Math.53(1951),472-490DOI:10.2307/1969567

    work page doi:10.2307/1969567 1951

  57. [57]

    Empty space generalization of the Schwarzschild metric,

    E. Newman, L. Tamburino and T. Unti, “Empty space generalization of the Schwarzschild metric,” J. Math. Phys.4(1963),915DOI:10.1063/1.1704018

    work page doi:10.1063/1.1704018 1963

  58. [58]

    Gravitational Instantons,

    S. W. Hawking, “Gravitational Instantons,” Phys. Lett. A60(1977),81 DOI:10.1016/0375-9601(77)90386-3 29

    work page doi:10.1016/0375-9601(77)90386-3 1977

  59. [59]

    Is the Taub–NUT Metric a Gravitational Instanton?,

    T. Eguchi, P . B. Gilkey and A. J. Hanson, “Is the Taub–NUT Metric a Gravitational Instanton?,” Phys. Rev. D17(1978),423-427DOI:10.1103/PhysRevD.17.423

    work page doi:10.1103/physrevd.17.423 1978

  60. [60]

    Asymptotically Flat Selfdual Solutions to Euclidean Gravity,

    T. Eguchi and A. J. Hanson, “Asymptotically Flat Selfdual Solutions to Euclidean Gravity,” Phys. Lett. B74(1978),249-251DOI:10.1016/0370-2693(78)90566-X

    work page doi:10.1016/0370-2693(78)90566-x 1978

  61. [61]

    Selfdual Solutions to Euclidean Gravity,

    T. Eguchi and A. J. Hanson, “Selfdual Solutions to Euclidean Gravity,” Annals Phys.120(1979),82DOI:10.1016/0003-4916(79)90282-3

    work page doi:10.1016/0003-4916(79)90282-3 1979

  62. [62]

    Gravitation, Gauge Theories and Differ- ential Geometry,

    T. Eguchi, P . B. Gilkey and A. J. Hanson, “Gravitation, Gauge Theories and Differ- ential Geometry,” Phys. Rept.66(1980),213DOI:10.1016/0370-1573(80)90130-1

    work page doi:10.1016/0370-1573(80)90130-1 1980

  63. [63]

    Instantons and seven-branes in type IIB superstring theory

    G. W. Gibbons, M. B. Green and M. J. Perry, “Instantons and seven- branes in type IIB superstring theory,” Phys. Lett. B370(1996),37-44 DOI:10.1016/0370-2693(95)01565-5[hep-th/9511080[hep-th]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1016/0370-2693(95)01565-5 1996

  64. [64]

    Gravity and Strings

    T. Ortín, “Gravity and Strings”,2nd edition, Cambridge University Press,2015

    2015

  65. [65]

    Covariant generalized conserved charges of General Relativity,

    C. Gómez-Fayrén, P . Meessen and T. Ortín, “Covariant generalized conserved charges of General Relativity,” JHEP09(2023),174DOI:10.1007/JHEP09(2023)174 [arXiv:2307.04041[gr-qc]]

    work page doi:10.1007/jhep09(2023)174 2023

  66. [66]

    Conserved charges for gravity with locally AdS asymptotics

    R. Aros, M. Contreras, R. Olea, R. Troncoso and J. Zanelli, “Conserved charges for gravity with locally AdS asymptotics,” Phys. Rev. Lett.84(2000),1647-1650 DOI:10.1103/PhysRevLett.84.1647[gr-qc/9909015[gr-qc]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevlett.84.1647 2000

  67. [67]

    Mass, Angular Momentum and Thermodynamics in Four-Dimensional Kerr-AdS Black Holes

    R. Olea, “Mass, angular momentum and thermodynamics in four-dimensional Kerr-AdS black holes,” JHEP06(2005),023DOI:10.1088/1126-6708/2005/06/023 [hep-th/0504233[hep-th]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1088/1126-6708/2005/06/023 2005

  68. [68]

    Counterterms, Koun- terterms, and the variational problem in AdS gravity,

    G. Anastasiou, O. Miskovic, R. Olea and I. Papadimitriou, “Counterterms, Koun- terterms, and the variational problem in AdS gravity,” JHEP08(2020),061 DOI:10.1007/JHEP08(2020)061[arXiv:2003.06425[hep-th]]

    work page doi:10.1007/jhep08(2020)061 2020

  69. [69]

    Topological regularization and self-duality in four-dimensional anti-de Sitter gravity

    O. Miskovic and R. Olea, “Topological regularization and self-duality in four-dimensional anti-de Sitter gravity,” Phys. Rev. D79(2009),124020 DOI:10.1103/PhysRevD.79.124020[arXiv:0902.2082[hep-th]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevd.79.124020 2009

  70. [70]

    Magnetic Mass in 4D AdS Gravity

    R. Araneda, R. Aros, O. Miskovic and R. Olea, “Magnetic Mass in4D AdS Gravity,” Phys. Rev. D93(2016) no.8,084022DOI:10.1103/PhysRevD.93.084022 [arXiv:1602.07975[hep-th]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevd.93.084022 2016

  71. [71]

    Electric-magnetic duality of dyonic Kerr- Newman-NUT-AdS spacetimes,

    C. Corral and R. Olea, “Electric-magnetic duality of dyonic Kerr- Newman-NUT-AdS spacetimes,” Phys. Rev. D110(2024) no.10,104021 DOI:10.1103/PhysRevD.110.104021[arXiv:2408.03901[hep-th]]. 30

    work page doi:10.1103/physrevd.110.104021 2024

  72. [72]

    Magnetic Monopoles in Kaluza-Klein Theories,

    D. J. Gross and M. J. Perry, “Magnetic Monopoles in Kaluza-Klein Theories,” Nucl. Phys. B226(1983),29-48DOI:10.1016/0550-3213(83)90462-5

    work page doi:10.1016/0550-3213(83)90462-5 1983

  73. [73]

    Kaluza-Klein Monopole,

    R. D. Sorkin, “Kaluza-Klein Monopole,” Phys. Rev. Lett.51(1983),87-90 DOI:10.1103/PhysRevLett.51.87

    work page doi:10.1103/physrevlett.51.87 1983

  74. [74]

    Equivalence of Eguchi–Hanson metric to two- center Gibbons–Hawking metric,

    M. K. Prasad, “Equivalence of Eguchi–Hanson metric to two- center Gibbons–Hawking metric,” Phys. Lett. B83(1979),310-310 DOI:10.1016/0370-2693(79)91114-6

    work page doi:10.1016/0370-2693(79)91114-6 1979

  75. [75]

    Eguchi–Hanson metrics with cosmological constant,

    H. Pedersen, “Eguchi–Hanson metrics with cosmological constant,” Class. and Quan. Gravity2(1985),579DOI:10.1088/0264-9381/2/4/022

    work page doi:10.1088/0264-9381/2/4/022 1985

  76. [76]

    Eguchi-Hanson Solitons in Odd Dimensions

    R. Clarkson and R. B. Mann, “Eguchi–Hanson solitons in odd dimensions,” Class. Quant. Grav.23(2006),1507-1524DOI:10.1088/0264-9381/23/5/005 [hep-th/0508200[hep-th]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1088/0264-9381/23/5/005 2006

  77. [77]

    Soliton Solutions to the Einstein Equations in Five Dimensions

    R. Clarkson and R. B. Mann, “Soliton solutions to the Einstein equations in five dimensions,” Phys. Rev. Lett.96(2006),051104 DOI:10.1103/PhysRevLett.96.051104[hep-th/0508109[hep-th]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevlett.96.051104 2006

  78. [78]

    Accelerating Taub-NUT and Eguchi-Hanson solitons in four dimensions

    B. Chng, R. B. Mann and C. Stelea, “Accelerating Taub–NUT and Eguchi– Hanson solitons in four dimensions,” Phys. Rev. D74(2006),084031 DOI:10.1103/PhysRevD.74.084031[gr-qc/0608092[gr-qc]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevd.74.084031 2006

  79. [79]

    Five-Dimensional Eguchi-Hanson Solitons in Einstein-Gauss-Bonnet Gravity

    A. W. C. Wong and R. B. Mann, “Five-Dimensional Eguchi–Hanson Soli- tons in Einstein-Gauss-Bonnet Gravity,” Phys. Rev. D85(2012),046010 DOI:10.1103/PhysRevD.85.046010[arXiv:1112.2229[hep-th]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevd.85.046010 2012

  80. [80]

    Phase tran- sitions and stability of Eguchi–Hanson-AdS solitons,

    T. Durgut, R. A. Hennigar, H. K. Kunduri and R. B. Mann, “Phase tran- sitions and stability of Eguchi–Hanson-AdS solitons,” JHEP03(2023),114 DOI:10.1007/JHEP03(2023)114[arXiv:2212.12685[gr-qc]]

    work page doi:10.1007/jhep03(2023)114 2023

Showing first 80 references.