String theory and gravity

A.M. Polyakov; T. Damour

REVIEW

String theory and gravity

T. Damour, A.M. Polyakov

General Relativity and Quantum Cosmology · Submitted 29 Nov 1994 · 6 references

Pith's verdict: The valuable part is not the attractor, which is Damour–Nordtvedt 1993, but the steep B(Φ) dependence of hadron masses, which makes the residual dilaton coupling tiny and gives equivalence-principle tests a concrete composition-dependent target.

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arXiv IDgr-qc/9411069 (version 1)

Pith IDPMTCAKYO, Pith's permanent record of this paper and its review

CitationA.M. Polyakov, T. Damour. "String theory and gravity." arXiv:gr-qc/9411069 (1994). https://pith.science/paper/PMTCAKYO

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Editor's note

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Short version: the useful content here is not the attractor itself — that is Damour–Nordtvedt 1993, and the paper says so — it is the observation that the dilaton's matter coupling runs through B(Φ) so steeply, via Λ_QCD ∼ B^{-1/2} exp(−8π²b₃^{-1}k₃B), that the same attractor relaxes the dilaton to a decoupling point with a residual coupling small enough to have escaped notice. That reframing is worth the read, and Eq. (14) — the composition-dependent EP violation with its C_B, C_D, C_E coefficients — is the part that actually gave experimentalists something to aim at. Uranium versus hydrogen is a real target, not a slogan. What the paper does well: the toy action is explicit, the frame transformation is done cleanly, and the authors are honest about what they do not know. They say outright that little is known about the global behaviour of B(Φ) and that the mechanism needs a universality condition. The rms estimates in Eqs. (7) and (15) are not dressed up as predictions; the random-phase approximation is stated as such. Soft spots, in order of weight. First, the universality condition is the whole ballgame and it is assumed. The stress-test point lands: a Z₂ symmetry Φ → −Φ gives B_i′(0) = 0, a common extremum, not a common maximum. The attractor needs κ > 0. Nothing in the paper fixes the sign of B_i″(0), and getting a maximum at all requires the loop terms c₁e^{2Φ} + … to overcome the monotonic tree-level e^{−2Φ}, which puts the maximum at g_s ∼ O(1) where the genus expansion defining B(Φ) is not controlled. The hedge “may be all what is needed” is honest but thin. Second, and minor for an essay: the 1.36 × 10^{−18} in Eq. (15) is a scaling law, not a number, since κ and Δφ are free. The experimental target is the composition dependence, not the magnitude. Who should read it: anyone working on equivalence-principle tests or dilaton and moduli phenomenology. It is a pointer to Ref. [1] and should be read that way. Recommendation: yes, send it out. The mechanism is well posed, the predictions are falsifiable, and the load-bearing assumption is stated in the open where a referee can attack it.

Referee report

Significance

The paper's strengths are real and should be named. It writes down an explicit, if toy, effective action (Eq. (1)) and carries the chain from the string-frame coupling function through the Einstein-frame gauge coupling (Eq. (3)) to the phi-dependence of the QCD scale (Eq. (4)) and of hadron masses (Eq. (5)) without inserting free functions along the way. The resulting observational signatures are falsifiable and specific: a definite scaling of the equivalence-principle violation with kappa and Delta phi (Eq. (15)), a definite composition dependence through the coefficients C_B, C_D, C_E in Eq. (14), and correlated post-Newtonian and drift signals in Eqs. (9)-(12). The prediction that the residual violation is small but nonzero, rather than zero, is the kind of statement an experimental program can target, and the suggestion that measuring the ratios C_B/C_E and C_D/C_E would probe the Higgs sector and coupling unification is a concrete, if ambitious, claim. The attractor mechanism itself -- relaxation toward a common maximum of the coupling functions -- is a genuine idea, and its relation to the earlier metric-scalar attractor of Ref. [6] is worth stating explicitly.

Major objections (2)

[Universality condition following Eq. (2); Eq. (6)] The authors are explicit that the attractor requires all B_i(Phi) to admit a local maximum at a common Phi_m, and they propose that a discrete symmetry such as S-duality (Phi -> -Phi, g_s -> 1/g_s) 'may be all what is needed to ensure the minimal required universality.' That proposal delivers less than the mechanism needs. A Z_2 symmetry implies B_i(Phi) = B_i(-Phi), hence B_i'(0) = 0, i.e. a common extremum at the self-dual point, but it does not fix the sign of B_i''(0). The attractor requires a maximum, kappa > 0 in Eq. (6); if the symmetric point is a minimum, the cosmological evolution drives phi away from it and the decoupling scenario fails. The sign is set by the string-loop coefficients, e.g. c_1 in Eq. (2), which the essay does not exhibit. A related control issue deserves a sentence: for B to have a maximum, the loop terms must overcome the monotonic tree-level e^{-2Phi}, which places the extremum at g_s of order one, where the genus expansion defining B(Phi) in Eq. (2) is not under parametric control. The concrete test is to state the sign of the curvature at the symmetric point (or point to where Ref. [1] establishes it) and to say whether the maximum lies in a regime where the expansion of Eq. (2) is meaningful. This is a correctness risk for the central claim, not merely a presentational gap, although it can likely be addressed by a short clarifying paragraph plus a pointer to Ref. [1].
[Eqs. (7) and (15)] The headline number of Eq. (15), (Delta a/a)_max^rms = 1.36 x 10^{-18} kappa^{-4} Omega_75^{-3/2} (Delta phi)^2, is presented as the prediction of the scenario, but it is not parameter-free: it scales as kappa^{-4} and as the square of Delta phi, the deviation of the dilaton from Phi_m at the beginning of the classical radiation era, which is not determined anywhere in the essay. Over the stated range kappa >~ 0.5 the prefactor alone moves by more than an order of magnitude, and Delta phi is effectively unconstrained. The paper should present Eq. (15) as a scaling law with an explicit plausible range rather than as a single number, and should say what range of Delta phi is natural in the scenario. The same applies to Eq. (7), whose rms estimate rests on the random-phase approximation for the roughly ten relaxation oscillations; that assumption should be stated where the number is quoted, together with the scaling with the number of mass thresholds, so that a reader can see how the 10^{-9} factor is assembled.

Minor objections (6)

[Eq. (4)] As printed, the exponent in Eq. (4) is difficult to parse (the factors around b_3^{-1} and k B(phi) are ambiguous), and the same is true of the definition of omega following Eq. (12). These should be checked carefully at proof stage, since Eqs. (4) and (11)-(12) are the quantitative core of the paper.
[Eq. (8)] The coefficient beta_3 = 40.8 kappa is quoted without indication of its origin. A one-line derivation from Eq. (4), showing the two contributions from the prefactor B^{-1/2} and from the exponential, would let the reader verify the number and see why the dependence on B is steep.
[Paragraph preceding Eq. (3); abstract] The abstract and introduction state that the dilaton stays massless, but the essay never says why the attractor does not generate a mass for it. One sentence would suffice: at the maximum of B the matter-induced mass vanishes because dm_A/dphi = 0 there, leaving only a curvature of order the Hubble scale, so the field is cosmologically light. This is the mechanism, and it deserves to be stated rather than left implicit.
[Eq. (14) and following paragraph] Only C_E is estimated; C_B and C_D are left undetermined. The claim that measuring the ratios C_B/C_E and C_D/C_E would probe the Higgs sector and coupling unification should be softened accordingly, or accompanied by a statement of what would be needed to compute C_B and C_D.
[Penultimate paragraph] The statement that the model contains 'no small parameters' sits awkwardly with kappa and Delta phi being free inputs and with the smallness of the residual coming from the large number of relaxation e-folds (the Z_0^{-3/4} factor and the roughly ten threshold events). Rewording to say that the smallness follows from the amount of cosmological relaxation, rather than from the absence of small parameters, would be more accurate.
[Throughout; Ref. [1]] The essay would benefit from one explicit sentence distinguishing results derived here from results quoted from Ref. [1], particularly for the attractor dynamics and the numerical coefficients in Eqs. (7)-(8). The relation to the metric-scalar attractor of Ref. [6] should also be stated in one line: what is new here is the string-loop origin of the common maximum, not the attractor mechanism itself.

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The paper

The paper claims

String-loop corrections may let the dilaton stay exactly massless by driving it, through cosmic expansion, to a field value where it almost stops coupling to matter, leaving only tiny, structured deviations from general relativity.

The reading

String theory pairs the graviton with a scalar partner, the dilaton, and any ordinary matter coupling of that scalar would show up as a violation of the equivalence principle — which is why most discussions assume the dilaton must acquire a Planck-scale mass. This paper argues that string-loop corrections can preserve the dilaton's masslessness instead: if the various dilaton coupling functions all peak at the same field value, cosmological expansion acts as an attractor that drags the dilaton to that peak and holds it there. At the peak every particle mass sits at a local minimum with respect to the dilaton, so the dilaton's coupling to matter is nearly zero today, though not exactly zero. The payoff is a model with no small parameters that predicts a specific, tiny pattern of deviations from general relativity: a residual composition-dependent fifth force, post-Newtonian corrections, and slow drifts of the coupling constants. The authors present this as a reason to push equivalence-principle tests several orders of magnitude further, since such tests would become low-energy windows on string-scale physics.

What carries the argument

The load-bearing object is the common coupling function $B(φ)$: a single dilaton-dependent factor in front of the entire effective action, whose local maximum at $φ_m$ is the attractor point. Its curvature, $ln B(φ) ≃ const. - ½ κ(φ - φ_m)^2$, controls how fast the cosmological relaxation converges, and the steep exponential dependence of $Λ_{QCD}$ on $B$ (Eq. 4) is what makes each mass threshold a strong kick. The machinery converts a statement about string-loop topology — genus-$n$ worldsheets contributing powers of $g_s^2 = e^{2Φ}$ — into quantitative predictions for $Δa/a$, $1-γ_{Edd}$, $β_{Edd}-1$, $dot{α}/α$ and $dot{G}/G$.

Extended reading notes

Core claim

The central claim is that the dilaton need not be given a large mass to escape experimental bounds; cosmological evolution can do that job instead. The authors take the effective four-dimensional action of the string massless modes, in which a single function $B(Φ)$ multiplies the whole Lagrangian, with the tree-level term $e^{-2Φ}$ followed by string-loop terms $c_0 + c_1 e^{2Φ} + c_2 e^{4Φ} + …$. Because the gauge coupling is $g^{-2} = kB(φ)$ and the QCD scale depends steeply on it, every particle mass becomes a function of the dilaton alone, $m_A(φ) = m_A[B(φ)]$. The dilaton is then dynamically driven toward the field value where $B$ has a local maximum — equivalently, where all masses are locally minimized — and each mass threshold during the radiation era, plus the matter era afterwards, ratchets it closer to that point. The residual displacement $(φ_0 - φ_m)$ sets every observable deviation, and it enters squared, which is why the predicted effects are small enough to have escaped detection while remaining nonzero.

Load-bearing premise

Everything rests on the universality condition the authors state explicitly after Eq. (2): all the separate dilaton coupling functions must have a local maximum at the same field value, an assumption they motivate with S-duality or a $Φ → -Φ$ symmetry but do not derive from string theory.

Editorial extensions

If this is right

The dilaton remains exactly massless, so it would not appear as a new particle produced at accelerators; its presence would register only as a weak, composition-dependent fifth force.
Post-Newtonian deviations from general relativity are predicted at the level $1-γ_{Edd} ≃ 2β_3^2(φ_0-φ_m)^2$ and $β_{Edd}-1 ≃ ½β_3^3(φ_0-φ_m)^2$, small but in principle measurable.
The fine-structure constant and Newton's constant should drift slowly, at rates given by Eqs. (11) and (12), each suppressed by $(φ_0-φ_m)^2 H_0$.
Measuring the ratios $C_B/C_E$ and $C_D/C_E$ in the equivalence-principle violation would probe the Higgs sector and the unification of coupling constants.
If the same attractor mechanism applies to a modulus field rather than the dilaton, the deviations from general relativity should be numerically larger, because masses depend less steeply on a modulus.

Reading between the lines

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

The attractor logic is not specific to string theory: any light scalar whose contribution to all masses peaks at a common field value will be driven toward decoupling, so the argument works as a general filter that any massless scalar must pass.
Because the residual coupling scales as the square of the displacement from the maximum, the scenario is self-protecting: a modest improvement in experimental bounds translates into a much weaker constraint on the initial displacement $Δφ$, which is why a massless dilaton can survive despite the tightness of equivalence-principle tests.
The predicted violation grows with the square of the dilaton's displacement at the start of the radiation era, so early-universe physics — inflation, reheating, and the initial conditions of $φ$ — becomes indirectly observable in tabletop free-fall experiments.
If a discrete symmetry such as S-duality is what enforces the required universality, the same argument should protect other $g_s → 1/g_s$ symmetric scalars, suggesting a broader class of hidden light fields than the dilaton alone.

Original abstract

It is pointed out that string-loop effects may generate matter couplings for the dilaton allowing this scalar partner of the tensorial graviton to stay massless while contributing to macroscopic gravity in a way naturally compatible with existing experimental data. Under a certain assumption of universality of the dilaton coupling functions (possibly realized through a discrete symmetry such as S-duality), the cosmological evolution drives the dilaton towards values where it decouples from matter. At the present cosmological epoch, the coupling to matter of the dilaton should be very small, but non zero. This provides a new motivation for improving the experimental tests of Einstein's Equivalence Principle.

The compiled record

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The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; show every role.

It is pointed out that string-loop effects may generate matter couplings for the dilaton allowing this scalar partner of the tensorial graviton to stay massless while contributing to macroscopic gravity in a way naturally compatible with existing experimental data. Under a certain assumption of universality of the dilaton coupling functions (possibly realized through a discrete symmetry such as S-duality), the cosmological evolution drives the dilaton towards values where it decouples from matter. At the present cosmological epoch, the coupling to matter of the dilaton should be very small, but non zero. This provides a new motivation for improving the experimental tests of Einstein's Equivalence Principle.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	It is pointed out that string-loop effects may generate matter couplings for the dilaton allowing this scalar partner of the tensorial graviton to stay massless while contributing to macroscopic gravity in a way naturally compatible with existing experimental data.	result 0.71	0.44	0.57	hedged possibility 1.00
s1	Under a certain assumption of universality of the dilaton coupling functions (possibly realized through a discrete symmetry such as S-duality), the cosmological evolution drives the dilaton towards values where it decouples from matter.	result 0.86	0.36	0.11	hedged possibility 0.71
s2	At the present cosmological epoch, the coupling to matter of the dilaton should be very small, but non zero.	result 0.84	0.40	0.27	asserted 0.73
s3	This provides a new motivation for improving the experimental tests of Einstein's Equivalence Principle.	future work 0.62	0.13	0.16	asserted 0.89

What kind of paper the classifier reports this is: theoretical result 0.92 · evidence from argument 0.87.

What was examined, and what was not

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arXiv listing abstract v1

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full text
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relations to other papers

levels run

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

References

Works cited (6)

[1]

T. Damour and A.M. Polyakov, Nucl. Phys. B. 423,532 (1994)

View on Pith 1994
[6]

T. Damour and K. Nordtvedt, Phys. Rev. Lett. 70, 2217 (1993); Phys. Rev. D 48, 3436 (1993)

View on Pith 1993
[2]

E.S. Fradkin and A.A. Tseytlin, Phys. Lett. B 158, 316 (1985)

View on Pith 1985
[3]

C.G. Callan, D. Friedan, E.J. Martinec and M.J. Perry, Nu cl. Phys. B 262, 593 (1985)

View on Pith 1985
[4]

C.G. Callan, I.R. Klebanov and M.J. Perry, Nucl. Phys. B 278, 78 (1986)

View on Pith 1986
[5]

V.S. Kaplunovsky, Nucl. Phys. B 307, 145 (1988)

View on Pith 1988

Forward citations

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How the literature uses it

51 arXiv papers cite this in 125 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 75 sentences without a confident label

Contests it 3 papers

In the present communication we demonstrate that the field equations used by [ref] are incomplete.

On the cosmic convergence mechanism of the massless dilaton · Introduction · contest 0.93
Therefore, it shows that the parameter $Υ$ is missing in the formula for the $γ$ parameter given in [ref] .

The \gamma\ parameter in Brans-Dicke-like (light-)Scalar-Tensor theory with a universal scalar/matter coupling · Rescaling of the scalar-field, and correction of Damour and Polyakov's equation for $γ$ · contest 0.88
The existence of this important fermion coupling is overlooked in the work of [ref] .

Constraints on extended Jordan-Brans-Dicke gravity · How to introduce standard model in eJBD gravity · contest 0.88

Uses its method or tool 1 paper

Following [ref] , the action can be reformulated in the so-called Einstein representation[Also know as Einstein frame.].

On the cosmic convergence mechanism of the massless dilaton · Introduction · 0.88

Compares with it 6 papers

In order to compare with [ref] , let us write: [equation] with [equation] Therefore, as suggested in section [ref], the coupling strength $α_2$ is in general different from $α_0=∂lnA / ∂φ|_Φ_0$.

The \gamma\ parameter in Brans-Dicke-like (light-)Scalar-Tensor theory with a universal scalar/matter coupling · Rescaling of the scalar-field, and correction of Damour and Polyakov's equation for $γ$ · 0.91
In previous work on the phenomenological consequences of dilaton couplings [ref] it was suggested that the EP signal would be essentially proportional to $Z^2A^-4/3$, i.e. related to the Coulomb energy term $∝d_e$ in the results above.

Equivalence Principle Violations and Couplings of a Light Dilaton · Relation to theoretical expectations · 0.87
We recover the usual forms of the temporal variation and evolution of the fine-structure coupling, in Refs. [ref] , in the absence of disformal couplings.

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Cites it as background 24 papers

As commented earlier, the authors of Refs. [ref] investigated cosmological signatures of modified gravity theories when there is the presence of a scalar field with a non minimal multiplicative coupling to the electromagnetic Lagrangian (see also [ref] ).

Galaxy clusters and a possible variation of the fine structure constant · Theoretical Model · 0.96
The post-Newtonian phenomenology of theories with scalar/matter coupling has partially been studied, notably in [ref] .

The \gamma\ parameter in Brans-Dicke-like (light-)Scalar-Tensor theory with a universal scalar/matter coupling · Introduction · 0.83
.— In perturbative string theory, the effective action of gravitation is not general relativity but a scalar-tensor theory with non-minimal coupling between the scalar-field (called dilaton) and both the Ricci scalar and the material part of the Lagrangian [ref] .

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Discussion

Disagree with the review, or know something it missed? Leave a comment, highlight any passage above to comment on it, or challenge this review formally.

[1] [1]

T. Damour and A.M. Polyakov, Nucl. Phys. B. 423,532 (1994)

View on Pith 1994

[2] [6]

T. Damour and K. Nordtvedt, Phys. Rev. Lett. 70, 2217 (1993); Phys. Rev. D 48, 3436 (1993)

View on Pith 1993

[3] [2]

E.S. Fradkin and A.A. Tseytlin, Phys. Lett. B 158, 316 (1985)

View on Pith 1985

[4] [3]

C.G. Callan, D. Friedan, E.J. Martinec and M.J. Perry, Nu cl. Phys. B 262, 593 (1985)

View on Pith 1985

[5] [4]

C.G. Callan, I.R. Klebanov and M.J. Perry, Nucl. Phys. B 278, 78 (1986)

View on Pith 1986

[6] [5]

V.S. Kaplunovsky, Nucl. Phys. B 307, 145 (1988)

View on Pith 1988