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REVIEW 4 major objections 5 minor 27 references

Instanton Moduli, Topology and the Bosonic/Heterotic String Origins

T0 review · 4 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read The paper shows that 't Hooft instanton moduli can change the NS(-1)-brane metric topology from a smooth space to a bolt without altering the conserved magnetic flux.

desk verdict The advertised 4D Killing spinor fails the printed supersymmetry variations, taking down the BPS claim, though the bosonic topology story is worth a look. read the letter →

arxiv 2507.05351 v1 pith:EVEK7IAT submitted 2025-07-07 hep-th

Liang Ma , H. Lu This is my paper
classification hep-th
keywords NS(-1)-brane'tHooftinstantonbosonic/heteroticdualityBPSsolutionsmodulibolttopologyKillingspinorsSalam-Sezginmodel
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

The paper constructs new supersymmetric NS(-1)-brane solutions in ${\cal N}=1$, $D=4$ supergravity with two copies of $SU(2)$ Yang-Mills fields, where 't Hooft instantons supply the source for the magnetic NS-NS 3-form flux. The central claim is that the instanton moduli are not part of the flux data: the charge $Q=2/g^2$ is fixed by the Bianchi identity, yet changing the instanton size changes the string-frame metric topology from smooth $\mathbb R^4$ to an $\mathbb R\times S^3$ bolt. On this basis the authors argue that brane creation can occur as a purely geometric effect when an instanton shrinks to zero size, and that the same solutions, uplifted to $D=10$, give evidence for the proposed bosonic/heterotic duality. This gives a concrete geometric origin for the otherwise auxiliary Yang-Mills instantons in four-dimensional supergravity.

What carries the argument

The load-bearing object is the modified Bianchi identity $dH_{(3)} = \frac14(F^I\wedge F^I + \tilde F^{\tilde I}\wedge \tilde F^{\tilde I})$, combined with self-dual $SU(2)\times SU(2)$ 't Hooft instantons, which supply a smooth source for the NS-NS 3-form flux. The solutions are organised by a harmonic function $H$ on Euclidean $\mathbb R^4$ (e.g. (7), (17), (22)); all fields, including the Killing spinors, enter through $H$. The uplift to $D=10$ uses the consistent warped $R\times T^{1,1}$ reduction of the heterotic theory and the $S^3\times S^3$ reduction of the bosonic string, so that the instanton moduli appear as geometric parameters of the internal fibre spaces.

What would settle it

A direct check would be to compute curvature invariants of the string-frame metric (26) at $r=0$ for the single-instanton solution (7) as $a\to 0$, and to verify independently whether the integral of $dB_{(2)}$ over a small sphere enclosing the origin stays exactly $2/g^2$ in both the finite-$a$ and $a=0$ cases; if the flux changes or the $r=0$ region is singular rather than a bolt $\mathbb R\times S^3$, the central topology-change claim would fail.

Watch

Extended reading notes

Core claim

The paper claims that the single-instanton NS(-1)-brane solution (7), with finite sizes $a$ and $\tilde a$, is a smooth $\mathbb R^4$ configuration, while taking $a=0$ or $\tilde a=0$ removes the corresponding Yang-Mills instanton but leaves the conserved charge $Q=2/g^2$ untouched; the metric then becomes the NS(-1)-brane with $q=1/g$ and bolt topology $\mathbb R\times S^3$. The mechanism is the modified Bianchi identity $dH_{(3)} = \frac14(F^I_{(2)}\wedge F^I_{(2)} + \tilde F^{\tilde I}_{(2)}\wedge \tilde F^{\tilde I}_{(2)})$, which gives the instantons a topological role: the flux integral is independent of the instanton size, so the transition is a topology change of the string-frame metric without loss of charge. Uplifting to the bosonic and heterotic strings makes the moduli parameters of pure geometry in the internal $S^3\times S^3$ or $R\times T^{1,1}$ fibre spaces, and the Killing spinors of both sides transform in a way consistent with the recently proposed bosonic/heterotic duality.

Load-bearing premise

The entire construction rests on the validity of the recently proposed bosonic/heterotic duality and of the consistent $R\times T^{1,1}$ and $S^3\times S^3$ reduction ansatz from the authors' earlier work; if that duality or the reduction ansatz is not correct, the $D=10$ uplifted solutions and the Killing-spinor interpretation lose their grounding.

Editorial extensions

If this is right

  • The magnetic 3-form charge $Q=2/g^2$ is conserved when instanton moduli vary, so the transition from $\mathbb R^4$ to $\mathbb R\times S^3$ is a genuine topology change without flux violation.
  • Shrinking an instanton to zero, or letting two instantons coalesce, creates an NS(-1)-brane with bolt geometry, giving a purely geometric mechanism for brane creation.
  • In the $D=10$ uplifts, the Yang-Mills instanton moduli are reinterpreted as fibre parameters of the internal $S^3\times S^3$ or $R\times T^{1,1}$ spaces, so the four-dimensional gauge data is encoded in geometry.
  • The Killing spinors on both the bosonic and heterotic sides, together with the chirality projection $\Gamma_{11}\hat\epsilon = \pm i\hat\epsilon$, provide a concrete test point for the proposed bosonic/heterotic duality.
  • The same technique yields new BPS solutions of the $D=6$ Salam-Sezgin model via an $S^2$ reduction from the four-dimensional single-$SU(2)$ case.

Reading between the lines

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

  • A natural extension the paper does not pursue is to compute the Euclidean action difference between the $\mathbb R^4$ and $\mathbb R\times S^3$ saddles as $a$ is tuned; a finite, finite-action interpolation would sharpen the statement that the topology change is a physical transition rather than a modulus convention.
  • The construction suggests a general recipe: whenever a gauged supergravity has a Chern-Simons or Bianchi term, instanton moduli can act as geometric moduli that interpolate between smooth spaces and bolt spaces, so analogous transitions may exist in other dimensions and other sphere reductions.
  • The bosonic side already had pseudo-supersymmetry Killing spinors, so the new evidence lies in the explicit map through the bridging coordinate $\chi_2$; deriving the full spinor bilinear dictionary could turn the 'consistent with' statement into a quantitative duality check.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 5 minor

Summary. This paper constructs Euclidean NS(-1)-brane solutions in N=1, D=4 supergravity coupled to a tensor multiplet and two SU(2) Yang-Mills multiplets, with the gauge fields claimed to be 't Hooft instantons. The authors propose a single-center solution (7), assert a Killing spinor (12), and argue that the string-frame metric changes topology from R^4 to an R x S^3 bolt when the instanton size parameters vanish, while the 3-form flux is conserved. They then uplift the solution to the noncritical bosonic string and to the heterotic string using the reduction ansatz of their earlier papers [15,16], claim Killing spinors exist in both ten-dimensional theories, and interpret the result as support for the bosonic/heterotic duality. A separate D=6 Salam-Sezgin solution is also proposed. The bosonic field content is written out explicitly, but the supersymmetry checks are not displayed, and direct substitution into the printed equations shows that the central 4D Killing-spinor claim and the self-duality claim are both inconsistent as written.

Significance. If the central equations were correct, the paper would provide new smooth BPS Euclidean brane solutions, a geometric realization of brane creation through instanton moduli, and new examples of topology change in string-frame metrics, while also giving a concrete testing ground for the proposed bosonic/heterotic duality. The explicit metrics, gauge fields, H-flux, charge formula, and topology arguments are a strength: they are checkable and would be valuable. However, the BPS property is the load-bearing novelty, and the printed equations do not support it. The significance of the paper is therefore contingent on repairing the algebraic inconsistencies identified below.

major comments (4)
  1. [§2.1, Eqs. (6), (7), (11), (12)] Direct substitution contradicts the claimed Killing spinor. With ϵ = H^{-1/4}ϵ_0, Γ^{0123}ϵ_0 = ϵ_0, and H_{123} = -H' from (11), the dilatino variation in (6) gives δχ = (1/2 - 1/12)(H'/H)Γ^0ϵ = (5/12)(H'/H)Γ^0ϵ, using Γ^{123}ϵ = Γ^0ϵ. Similarly, ∇_0ϵ = -(1/4)(H'/H)ϵ and [Γ^{123},Γ_0]ϵ = -2ϵ, so δψ_0 = (-1/4 + 1/24)(H'/H)ϵ = -(5/24)(H'/H)ϵ. Neither expression vanishes for the solution (7). Since the 4D BPS property is the basis for the Killing-spinor map in Section 3 and for the claimed evidence for bosonic/heterotic duality, the authors must correct either the solution, the spinor, or the supersymmetry variations, and display the full substitution.
  2. [§2.1, Eq. (11)] The fields (7) are not self-dual as stated. From the frame components in (11), self-duality F^I = *F^I requires r f' = f(gf-1). Substituting f = a^2/(r^2+ga^2), the left-hand side equals -2a^2 r^2/(r^2+ga^2)^2 while the right-hand side equals -a^2 r^2/(r^2+ga^2)^2. The two sides agree only at a=0 or r=0. Thus the solution is not supported by 't Hooft instantons in the claimed sense, and the H(3) given through (7) and (11) cannot be sourced by the Bianchi identity (4) in the advertised way. This is a load-bearing error for the paper's central construction.
  3. [§2.2, Eqs. (16), (17)] The multi-center ansatz is not connected to the explicit single-center solution. Equation (16) states that f = -(1/g) log f' with □f'=0. For the single-center f in (7), this would require f' = exp(-g a^2/(r^2+ga^2)), which is not harmonic on Euclidean R^4. Consequently the multi-center H in (17) is not a generalization of (7), and the multi-instanton topology and brane-creation analysis in §2.3 does not follow from the explicit single-instanton solution. A consistent multi-center ansatz must be supplied or the claims must be restricted to the single-instanton case.
  4. [§3, Eqs. (24), (27), (34), (42)] The ten-dimensional Killing-spinor checks are asserted without showing the substitution, despite the nontrivial form of the vielbeine and fluxes in (32)-(33) and (39)-(41). Moreover, the uplift ansatz (24) and (37) is taken from the reduction framework of [15,16], whose validity is precisely the bosonic/heterotic duality that the paper purports to test. As presented, the existence of 10D Killing spinors demonstrates consistency of the authors' ansatz, not an independent test of the duality. The authors should verify the reduction from first principles or explicitly weaken the claim to consistency within their previously proposed framework.
minor comments (5)
  1. [§2.3, Eqs. (9), (21)] Equation (9) and the charge formula (21) are numerically inconsistent: with B(2) = -(1/(2g^2)) cosθ dφ∧dψ, one finds ∫_{S^3} dB = 4π^2/g^2, giving Q = 1/g^2 rather than 2/g^2.
  2. [§2.2, Eq. (16)] The notation is confusing because f' denotes a harmonic function in (16) but a derivative in (11). The two uses should be distinguished, for example by using Π or Φ for the harmonic function.
  3. [§2.3, near Eq. (18)] The text says an NS(-1)-brane with q=1/g is created when one instanton size vanishes, but equations (7) and (18) give q=1/g^2 for one vanishing center and q=2/g^2 when both vanish. Please check the dimensions and factors.
  4. [General presentation] There are several typos and infelicities: 'T-dualty' in the Introduction, 'workout' for 'work out' in Section 3, and 'the space middle' in Section 2.3.
  5. [§3.1, Eqs. (35) and (43)] The projection conditions imposed on the constant spinors are stated without derivation, and at least one non-trivial component of the Killing-spinor equations should be shown so that the reader can verify the claimed existence of spinors.

Circularity Check

2 steps flagged · score 6.0 of 10

The D=10 'duality test' is inherited from the authors' own papers [15,16]: the reduction ansatz and the χ2 bridging-coordinate role are taken from [15,16], so the claimed consistency with the bosonic/heterotic duality is built in rather than independently tested; the D=4 solution, charge, and topology arguments are explicit and not circular.

  1. ansatz smuggled in via citation [Section 3.1, around Eqs. (24), (26), (34)-(35)]
    "Employing the procedure outlined in [15], we obtain the D = 10 solution ... (24). ... This consistent reduction ansatz was obtained by virtue of the recently proposed bosonic/heterotic duality ... [15, 16]. ... The Killing spinor takes the same form as that in [16], where the Yang-Mills fields were turned off. All the Yang-Mills contribution to the Killing spinors enters solely through the function H."

    The D=10 metric (24) is not an independent construction: it is the [15] reduction ansatz evaluated on the D=4 solution, with the gauge fields entering through h^I = σ^I − gA^I. The paper's advertised result that instanton moduli 'become parameters of pure geometry' is therefore a restatement of that ansatz, and the statement that χ2 is the 'bridging coordinate' (hence that ϵ̌2,± do not survive) is taken from [16]. Inserting the authors' own duality ansatz and then finding Killing-spinor behavior 'consistent with the duality' is a self-referential check, not a test against an external prediction.

  2. self citation load bearing [Section 3.2, after Eq. (37), and Section 5]
    "Following the reduction ansatz of [15], we find that the instanton/wormhole solution of D = 4 becomes (37). ... As was discussed in [16], χ2 plays a role of bridging coordinate in the bosonic/heterotic duality. Consequently, the Killing spinors ˇϵ2,± will not survive the duality map."

    The paper's central conclusion that the Killing-spinor map 'is consistent with the recently proposed bosonic/heterotic string duality' is justified by citing [15,16], papers whose authors include the present authors. The duality itself and the χ2 bridging role are the load-bearing premise; this paper contributes no independent derivation or external check of that premise. Without [15,16], the Section 3 interpretation that the D=10 solutions and spinor projections constitute evidence for the duality has no support.

full rationale

The D=4 core of the paper is written out concretely: the solution (7), the Killing spinor ansatz (12), the charge integral (21), and the topology statements in Section 2.3 are explicit and can be checked by substitution, so they do not reduce by construction to a fit or to a definition. The brane-creation phenomenon is credited to the same-author papers [22,23], but the charge/topology computation here is displayed, so that is self-citation rather than a defining circularity. The main circularity is in Section 3: the D=10 'origins' and the purported test of the bosonic/heterotic duality use the reduction ansatz and the χ2 bridging-coordinate role from the authors' own prior papers [15,16]. Consequently, the conclusions that the instanton moduli become geometric fibre parameters and that the Killing-spinor transformation is consistent with the duality are built into the adopted ansatz; they are restatements of the cited construction rather than independent predictions. Separately, the paper does not display the substitution of (7), (11), and (12) into the Killing spinor equations (6); a reader checking this may find nonzero variations. If so, the supersymmetry claim would be incorrect, but that is a correctness risk, not a circularity, and it is outside the scope of this pass. Overall score reflects partial circularity: the D=10 duality evidence reduces to the authors' self-citation chain, while the D=4 solution and its bosonic charge/topology content remain independently checkable.

Assumptions & free parameters 5 free parameters · 5 assumptions · 0 invented entities

No new particles, forces, dimensions, or conserved quantities are introduced. The NS(-1)-brane is a naming choice for an existing Euclidean solution class, and the bosonic/heterotic duality is a framework imported from prior papers by the same authors.

free parameters (5)
  • a = arbitrary
    Instanton size modulus for the first SU(2); the topology-change claim studies a=0 versus a>0.
  • a_tilde = arbitrary
    Instanton size modulus for the second SU(2).
  • q = arbitrary
    NS(-1)-brane charge parameter in H=1+q/r^2 when instantons vanish; imported from [16].
  • h = arbitrary harmonic function
    Multi-center moduli function in the multi-instanton solution, eq. (17).
  • m = arbitrary
    Warp parameter in the heterotic uplift, eq. (37), from the R x T^{1,1} reduction ansatz.
assumptions (5)
  • domain assumption The N=1, D=4 supergravity with tensor multiplet and SU(2)xSU(2) Yang-Mills has the standard supersymmetry transformation rules leading to the Killing spinor equations (6).
    Section 2, equations (2)-(6); standard supersymmetric coupling not proven in this paper.
  • standard math The Bianchi identity dH = 1/4(F wedge F + F_tilde wedge F_tilde) gives a topological charge independent of instanton size.
    Section 2, eq. (4) and eq. (21); standard transgression mechanism cited from [9,11,22].
  • ad hoc to paper The D=10 uplift ansatz (24) is a consistent reduction following from [15].
    Section 3.1; consistency is asserted, not re-derived, and the ansatz is built from the bosonic/heterotic duality proposal.
  • ad hoc to paper The bosonic/heterotic duality of [15,16] is valid, including the mapping of Killing spinors from the bosonic side to the heterotic side.
    Section 3.2 and Section 5; the paper uses this duality as input while claiming to test it.
  • domain assumption The S2 Pauli reduction of the D=6 Salam-Sezgin model to the D=4 theory with one SU(2) is consistent.
    Section 4, eq. (48); imported from Gibbons-Pope [20].

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Cite this review

Pith. "Pith review of Instanton Moduli, Topology and the Bosonic/Heterotic String Origins." pith.science (2026). https://pith.science/paper/EVEK7IAT

@misc{pith2026250705351,
  author       = {Pith},
  title        = {Pith review of: Instanton Moduli, Topology and the Bosonic/Heterotic String Origins},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/EVEK7IAT}},
  note         = {Machine review of arXiv:2507.05351}
}
abstract

We construct new supersymmetric NS(-1)-branes supported by the $SU(2)\times SU(2)$ 't Hooft instantons in ${\cal N}=1$, $D=4$ supergravity. We show that although the magnetic 3-form string flux is invariant under the variation of instanton moduli, the string-frame metric can change topology, giving rise to either $\mathbb R^4$ or the new $\mathbb R\times S^3$ bolt topologies. We uplift the solutions to both heterotic and bosonic strings, where the instanton moduli become parameters of pure geometry. We find that the Killing spinors exist in both theories. The transformation of the Killing spinors from one theory to the other is consistent with the recently proposed bosonic/heterotic string duality. We further construct new BPS solutions in the $D=6$ Salam-Sezgin model, employing the technique developed in the paper.

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Works this paper leans on

27 extracted references · 12 canonical work pages

  1. [1]

    Duality and hydrodynamics,

    Y. Nambu, “Duality and hydrodynamics,” Lectures at the Copenhagen conference, 1970; T. Goto, “Relativistic quantum mechanics of one-dimensional mechanical continuum and subsidiary condition of dual resonance model,” Prog. Theor. Phys. 46, 1560-1569 (1971) doi:10.1143/PTP.46.1560

    doi:10.1143/ptp.46.1560 1971

  2. [2]

    Quantum geometry of bosonic strings,

    A.M. Polyakov, “Quantum geometry of bosonic strings,” Phys. Lett. B 103, 207-210 (1981) doi:10.1016/0370-2693(81)90743-7

    doi:10.1016/0370-2693(81)90743-7 1981

  3. [3]

    Superstrings and solitons,

    A. Dabholkar, G.W. Gibbons, J.A. Harvey and F. Ruiz Ruiz, “Superstrings and solitons,” Nucl. Phys. B 340, 33-55 (1990) doi:10.1016/0550-3213(90)90157-9

    doi:10.1016/0550-3213(90)90157-9 1990

  4. [4]

    String solitons,

    M.J. Duff, R.R. Khuri and J.X. Lu, “String solitons,” Phys. Rept. 259, 213-326 (1995) doi:10.1016/0370-1573(95)00002-X [arXiv:hep-th/9412184 [hep-th]]

    arXiv 1995

  5. [5]

    Gueven, Phys

    R. Gueven, Phys. Lett. B 276, 49-55 (1992) doi:10.1201/9781482268737-16

    work page doi:10.1201/9781482268737-16 1992

  6. [6]

    Black strings and p-branes,

    G.T. Horowitz and A. Strominger, “Black strings and p-branes,” Nucl. Phys. B 360, 197-209 (1991) doi:10.1016/0550-3213(91)90440-9

    doi:10.1016/0550-3213(91)90440-9 1991

  7. [7]

    The selfdual type IIB superthreebrane,

    M.J. Duff and J.X. Lu, “The selfdual type IIB superthreebrane,” Phys. Lett. B 273, 409-414 (1991) doi:10.1016/0370-2693(91)90290-7

    doi:10.1016/0370-2693(91)90290-7 1991

  8. [8]

    Higher dimensional resolution of dila- tonic black hole singularities,

    G.W. Gibbons, G.T. Horowitz and P.K. Townsend, “Higher dimensional resolution of dila- tonic black hole singularities,” Class. Quant. Grav. 12, 297-318 (1995) doi:10.1088/0264- 9381/12/2/004 [arXiv:hep-th/9410073 [hep-th]]

    arXiv 1995

Show all 27 references
  1. [9]

    Heterotic solitons,

    A. Strominger, “Heterotic solitons,” Nucl. Phys. B 343, 167-184 (1990) [erratum: Nucl. Phys. B 353, 565-565 (1991)] doi:10.1016/0550-3213(90)90599-9 16

    1990 doi

  2. [10]

    Heterotic phase transitions and singularities of the gauge dyonic string,

    M.J. Duff, H. L¨ u and C.N. Pope, “Heterotic phase transitions and singularities of the gauge dyonic string,” Phys. Lett. B 378, 101-106 (1996) doi:10.1016/0370-2693(96)00420- 0 [arXiv:hep-th/9603037 [hep-th]]

    1996 arXiv

  3. [11]

    Brane resolution through transgression,

    M. Cvetiˇ c, H. L¨ u and C.N. Pope, “Brane resolution through transgression,” Nucl. Phys. B 600, 103-132 (2001) doi:10.1016/S0550-3213(01)00050-5 [arXiv:hep-th/0011023 [hep-th]]

    2001 arXiv

  4. [12]

    Supergravity and a confining gauge theory: Du- ality cascades and χSB resolution of naked singularities,

    I.R. Klebanov and M.J. Strassler, “Supergravity and a confining gauge theory: Du- ality cascades and χSB resolution of naked singularities,” JHEP 08, 052 (2000) doi:10.1088/1126-6708/2000/08/052 [arXiv:hep-th/0007191 [hep-th]]

    2000 arXiv

  5. [13]

    Stringy cosmic strings and noncom- pact Calabi-Yau manifolds,

    B.R. Greene, A.D. Shapere, C. Vafa and S.T. Yau, “Stringy cosmic strings and noncom- pact Calabi-Yau manifolds,” Nucl. Phys. B 337, 1-36 (1990) doi:10.1016/0550-3213(90) 90248-C

    1990 doi

  6. [14]

    D-instantons and asymptotic geometries,

    E. Bergshoeff and K. Behrndt, “D-instantons and asymptotic geometries,” Class. Quant. Grav. 15, 1801-1813 (1998) doi:10.1088/0264-9381/15/7/002 [arXiv:hep-th/9803090 [hep- th]]

    1998 arXiv

  7. [15]

    Consistent warpedR × T1,1 reduction of heterotic supergravity,

    L. Ma and H. L¨ u, “Consistent warpedR × T1,1 reduction of heterotic supergravity,” JHEP 03, 203 (2025) doi:10.1007/JHEP03(2025)203 [arXiv:2501.04771 [hep-th]]

    2025 arXiv

  8. [16]

    New BPS States from bosonic/heterotic duality,

    K.P. Lu, H. L¨ u and L. Ma, “New BPS States from bosonic/heterotic duality,” to appear in JHEP. [arXiv:2505.21623 [hep-th]]

    arXiv

  9. [17]

    Pseudo-supersymmetry, consistent sphere reduc- tion and Killing spinors for the bosonic string,

    H. L¨ u, C.N. Pope and Z.L. Wang, “Pseudo-supersymmetry, consistent sphere reduc- tion and Killing spinors for the bosonic string,” Phys. Lett. B 702, 442-447 (2011) doi:10.1016/j.physletb.2011.07.041 [arXiv:1105.6114 [hep-th]]

    2011 arXiv

  10. [18]

    Killing Spinors for the bosonic string and the Kaluza-Klein theory with scalar potentials,

    H. Liu, H. L¨ u and Z.L. Wang, “Killing Spinors for the bosonic string and the Kaluza-Klein theory with scalar potentials,” Eur. Phys. J. C 72, 1853 (2012) doi:10.1140/epjc/s10052- 011-1853-5 [arXiv:1106.4566 [hep-th]]

    2012 arXiv

  11. [19]

    Pseudo-supergravity extension of the bosonic string,

    H. L¨ u, C.N. Pope and Z.L. Wang, “Pseudo-supergravity extension of the bosonic string,” Nucl. Phys. B 854, 293-305 (2012) doi:10.1016/j.nuclphysb.2011.09.002 [arXiv:1106.5794 [hep-th]]

    2012 arXiv

  12. [20]

    Consistent S2 Pauli reduction of six-dimensional chiral gauged Einstein-Maxwell supergravity,

    G.W. Gibbons and C.N. Pope, “Consistent S2 Pauli reduction of six-dimensional chiral gauged Einstein-Maxwell supergravity,” Nucl. Phys. B 697, 225-242 (2004) doi:10.1016/j.nuclphysb.2004.07.016 [arXiv:hep-th/0307052 [hep-th]]. 17

    2004 arXiv

  13. [21]

    Chiral compactification on Minkowski ×S2 of N = 2 Einstein- Maxwell supergravity in six dimensions,

    A. Salam and E. Sezgin, “Chiral compactification on Minkowski ×S2 of N = 2 Einstein- Maxwell supergravity in six dimensions,” Phys. Lett. B 147, 47 (1984) doi:10.1016/0370- 2693(84)90589-6

    1984 doi

  14. [22]

    Instanton moduli and brane creation,

    E. Lima, H. L¨ u, B.A. Ovrut and C.N. Pope, “Instanton moduli and brane creation,” Nucl. Phys. B 569 (2000), 247-261 doi:10.1016/S0550-3213(99)00478-2 [arXiv:hep-th/9903001 [hep-th]]

    2000 arXiv

  15. [23]

    Supercharges, Killing spinors and intersecting gauge five-branes,

    E. Lima, H. L¨ u, B.A. Ovrut and C.N. Pope, “Supercharges, Killing spinors and intersecting gauge five-branes,” Nucl. Phys. B572, 112-130 (2000) doi:10.1016/S0550-3213(99)00829-9 [arXiv:hep-th/9909184 [hep-th]]

    2000 arXiv

  16. [24]

    D = 7 SU (2) gauged supergravity from D = 10 supergravity,

    A. H. Chamseddine and W. A. Sabra, “ D = 7 SU (2) gauged supergravity from D = 10 supergravity,” Phys. Lett. B 476, 415-419 (2000) doi:10.1016/S0370-2693(00)00129-5 [arXiv:hep-th/9911180 [hep-th]]

    2000 arXiv

  17. [25]

    Consistent Kaluza-Klein sphere reductions,

    M. Cvetiˇ c, H. L¨ u and C.N. Pope, “Consistent Kaluza-Klein sphere reductions,” Phys. Rev. D 62, 064028 (2000) doi:10.1103/PhysRevD.62.064028 [arXiv:hep-th/0003286 [hep-th]]

    2000 arXiv

  18. [26]

    Gravitational multi-instantons,

    G.W. Gibbons and S.W. Hawking, “Gravitational multi-instantons,” Phys. Lett. B 78, 430 (1978) doi:10.1016/0370-2693(78)90478-1

    1978 doi

  19. [27]

    Gravitational instantons,

    S.W. Hawking, “Gravitational instantons,” Phys. Lett. A 60, 81 (1977) doi:10.1016/0375- 9601(77)90386-3 18

    1977 doi

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