arxiv: 2510.07390 · v3 · submitted 2025-10-08 · ✦ hep-th · gr-qc· hep-ph

Heterotic Footprints in Classical Gravity: PM dynamics from On-Shell soft amplitudes at one loop

Arpan Bhattacharyya , Saptaswa Ghosh , Ankit Mishra , Sounak Pal This is my paper

Pith reviewed 2026-05-18 09:15 UTC · model grok-4.3

classification ✦ hep-th gr-qchep-ph

keywords Einstein-Maxwell-DilatonPost-Minkowskiansoft amplitudeseikonalblack hole scatteringinfrared finiteconservative potential

0

0 comments p. Extension

The pith

One-loop soft amplitudes extract the conservative two-body dynamics of charged black holes in EMD theory after IR subtraction.

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

The paper demonstrates that the classical conservative scattering of charged black holes in Einstein-Maxwell-Dilaton theory can be obtained by expanding one-loop amplitudes in the soft regime. It shows that these amplitudes are infrared finite when long-range interactions are treated with the Lippmann-Schwinger equation and IR subtraction. The scattering angle is derived from the eikonal exponentiation of the resulting amplitude. The approach separates the contributions from electromagnetic and dilatonic charges and recovers the general relativity results when those are turned off. This offers an amplitude-based method to study dynamics in modified gravity theories.

Core claim

We study classical scattering of charged black holes in Einstein-Maxwell-Dilaton theory. Working in the classical Post-Minkowskian regime, we extract the conservative two-body potential by expanding the one loop amplitudes in the soft regime. We show explicitly that the relevant soft amplitudes are infrared finite once the long-range interactions are consistently treated via Lippmann-Schwinger equation and the associated IR subtraction. The scattering angle is then obtained from the eikonal exponentiation of the soft amplitude. Our results track the separate roles of electromagnetic and dilatonic charges in both the conservative dynamics and the eikonal phase, and they reduce smoothly to the

What carries the argument

The soft expansion of one-loop amplitudes with Lippmann-Schwinger IR subtraction, which allows extraction of the conservative potential from on-shell data.

If this is right

The scattering angle follows from eikonal exponentiation of the IR finite soft amplitude.
Separate contributions of electromagnetic and dilatonic charges appear in the dynamics and phase.
Results agree with prior calculations in the literature.
These serve as building blocks for waveform modeling in beyond-GR scenarios.

Where Pith is reading between the lines

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

This method may extend to higher post-Minkowskian orders or other scalar-tensor theories.
The dilaton's role here hints at possible classical limits of heterotic string compactifications.
Amplitude techniques like this could inform numerical simulations of binary systems in alternative gravities.

Load-bearing premise

That the one-loop soft amplitudes capture the full classical conservative dynamics without needing further subtractions for radiation or higher loops.

What would settle it

Calculating the two-body scattering angle independently from the classical EMD equations of motion at one-loop PM order and finding a mismatch with the amplitude-derived result.

read the original abstract

We study classical scattering of charged black holes in Einstein-Maxwell-Dilaton (EMD) theory. Working in the classical (Post-Minkowskian) regime, we extract the conservative two-body potential by expanding the one loop amplitudes in the soft regime. We show explicitly that, as in GR, the relevant soft amplitudes are infrared (IR) finite once the long-range interactions are consistently treated via Lippmann-Schwinger equation and the associated IR subtraction. The scattering angle is then obtained from the eikonal exponentiation of the soft amplitude. Our results track the separate roles of electromagnetic and dilatonic charges in both the conservative dynamics and the eikonal phase, and they reduce smoothly to the GR limit when the charges and dilaton coupling are switched off. Where applicable, we compare with existing results in the literature and find agreement. These findings provide amplitude-based benchmarks for compact-object dynamics in EMD and furnish building blocks for waveform modeling in beyond-GR scenarios.

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

1 major / 2 minor

Summary. The paper computes the conservative Post-Minkowskian two-body dynamics of charged black holes in Einstein-Maxwell-Dilaton theory by expanding one-loop on-shell amplitudes in the soft regime. It shows that the relevant soft amplitudes become infrared finite after consistent treatment of long-range interactions via the Lippmann-Schwinger equation and associated subtraction, then extracts the scattering angle through eikonal exponentiation. Separate contributions from electromagnetic and dilatonic charges are tracked, the results reduce to the GR limit when charges vanish, and comparisons with existing literature are reported where possible.

Significance. If the central results hold, the work supplies amplitude-derived benchmarks for classical conservative dynamics in EMD theory, extending standard PM methods to include dilatonic and electromagnetic effects. This is useful for waveform modeling in beyond-GR scenarios and for isolating heterotic-inspired footprints in classical gravity. The explicit IR handling and charge separation constitute concrete strengths that align with existing eikonal and Lippmann-Schwinger techniques.

major comments (1)

The claim that the soft expansion of the one-loop amplitude fully captures the conservative dynamics (without radiation contamination) is load-bearing for the final scattering angle. An explicit demonstration that higher-order or radiation-reaction terms do not enter at the considered order would strengthen the result; this is not immediately visible from the abstract-level argument.

minor comments (2)

The notation distinguishing the soft limit from the classical limit could be made more uniform across sections to aid readability.
A short table summarizing the separate EM and dilaton contributions to the eikonal phase at each order would help readers track the results.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading and constructive feedback, as well as the recommendation for minor revision. We appreciate the recognition of the work's utility for beyond-GR waveform modeling and the strengths noted in IR handling and charge separation. We address the major comment below.

read point-by-point responses

Referee: The claim that the soft expansion of the one-loop amplitude fully captures the conservative dynamics (without radiation contamination) is load-bearing for the final scattering angle. An explicit demonstration that higher-order or radiation-reaction terms do not enter at the considered order would strengthen the result; this is not immediately visible from the abstract-level argument.

Authors: We agree that an explicit clarification would strengthen the manuscript. The conservative dynamics are isolated because the real part of the eikonal phase extracted from the soft one-loop amplitude encodes the conservative potential, while radiation-reaction contributions (arising from energy loss) are either encoded in the imaginary part or enter only at higher orders in the PM expansion, as is standard in the GR literature and extends directly to EMD by the separate tracking of electromagnetic and dilatonic charges. To address the referee's point, we will add a dedicated paragraph (or short subsection) providing this order-counting argument and referencing the relevant separation in the eikonal and Lippmann-Schwinger framework. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation relies on established external methods

full rationale

The paper extracts conservative two-body dynamics from one-loop soft amplitudes in EMD theory by applying Lippmann-Schwinger IR subtraction (standard for long-range interactions) followed by eikonal exponentiation to obtain the scattering angle. These techniques are invoked as in GR, with explicit reduction to the GR limit when charges vanish and direct comparisons to existing literature results showing agreement. No load-bearing steps reduce by construction to the paper's own fitted parameters, self-definitions, or unverified self-citations; the soft-regime focus and separate tracking of EM/dilaton roles remain independent of the target observables. The derivation is self-contained against external benchmarks in PM amplitude methods.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on standard assumptions of quantum field theory and gravitational scattering amplitudes; no new free parameters or invented entities are introduced in the abstract description.

axioms (2)

domain assumption Validity of the eikonal approximation to extract classical scattering angles from quantum amplitudes
Invoked to obtain the scattering angle from the soft amplitude.
standard math Standard infrared subtraction procedure using the Lippmann-Schwinger equation for long-range forces in gauge and gravity theories
Used to establish IR finiteness of the soft amplitudes.

pith-pipeline@v0.9.0 · 5718 in / 1157 out tokens · 41910 ms · 2026-05-18T09:15:10.592581+00:00 · methodology

discussion (0)

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Lean theorems connected to this paper

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IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

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Relation between the paper passage and the cited Recognition theorem.

We study classical scattering of charged black holes in Einstein-Maxwell-Dilaton (EMD) theory. Working in the classical (Post-Minkowskian) regime, we extract the conservative two-body potential by expanding the one loop amplitudes in the soft regime... The scattering angle is then obtained from the eikonal exponentiation of the soft amplitude.
IndisputableMonolith/Foundation/ArithmeticFromLogic.lean LogicNat recovery unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

After performing the appropriate EFT (Born) subtraction of long-range iterations, the momentum-space potential is infrared finite.

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matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

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Damour,Radiative contribution to classical gravitational scattering at the third order inG, Phys

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D. Bini, T. Damour, A. Geralico, S. Laporta and P. Mastrolia,Gravitational scattering at the seventh order inG: nonlocal contribution at the sixth post-Newtonian accuracy, Phys. Rev. D 103(2021), no. 4, 044038 [2012.12918]

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D. Bini, T. Damour and A. Geralico,Radiative contributions to gravitational scattering, Phys. Rev. D104(2021), no. 8, 084031 [2107.08896]

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D. Bini, T. Damour and A. Geralico,Radiated momentum and radiation reaction in gravitational two-body scattering including time-asymmetric effects, Phys. Rev. D107(2023), no. 2, 024012 [2210.07165]

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Damour and P

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P. Rettegno, G. Pratten, L. M. Thomas, P. Schmidt and T. Damour,Strong-field scattering of two spinning black holes: Numerical relativity versus post-Minkowskian gravity, Phys. Rev. D 108(2023), no. 12, 124016 [2307.06999]

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D. Bini, T. Damour and A. Geralico,Comparing one-loop gravitational bremsstrahlung amplitudes to the multipolar-post-Minkowskian waveform, Phys. Rev. D108(2023), no. 12, 124052 [2309.14925]

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