{"id":"b812f221-eb9c-42dd-a5be-64e3cdbcd206","arxiv_id":"2507.17862","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"Under asymptotically safe quantum gravity, photon and scalar propagators acquire Källén-Lehmann spectral functions that are non-normalizable and change sign in the ultraviolet.","lead":"Researchers computed how quantum gravitational fluctuations change the way photons and scalar particles propagate, using a Lorentzian-signature functional renormalisation group within the asymptotic safety scenario. The resulting spectral functions are non-normalizable and turn negative at Planckian energies, which challenges the interpretation of light and matter particles as ordinary physical observables in quantum gravity.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The claimed KL representation is assumed by the spectral ansatz (16), and the UV sign flip sits in a regime where the neglected continuum feedback is unquantified; the deep-IR check does not constrain it.","rationale":"I read the paper as an honest, technically demanding computation whose main result is conditional: given the Callan-Symanzik spectral RG and the stated truncation, it produces matter spectral functions with the displayed properties. The reader's weakest_assumption identifies the precise soft spot: the KL representation is assumed in the ansatz (16) and the flow is solved without continuum feedback. This is not an internal inconsistency, and the paper is transparent about the approximation; but it means the advertised result that the propagators 'possess a KL spectral representation' is not demonstrated in the sense of excluding other analytic structures. The statement in Sec. VI B that complex conjugate poles are not observed is circular, since the ansatz excludes them. The IR comparison in Sec. VI C provides genuine anchor and credit is due for that check, but it validates only the low-energy part of the spectral function, not the UV sign flip or the non-normalizable tail. The stability test in Sec. VI C is useful but treats η*_h as a free parameter; it does not bound the neglected feedback of the continua. The concrete test I propose directly addresses both weaknesses: include the continuum feedback in the flow and then inspect the analytic structure of the resulting propagator. If the sign flip and KL property survive that test, the CONDITIONAL verdict is justified; if not, the central claim would need to be weakened. My agreement with the reader is full: the same assumption is the load-bearing one. Therefore the verdict should remain CONDITIONAL, i.e. unchanged from the reader's assessment, pending this check.","tokens_in":25929,"tokens_out":3268,"duration_ms":40527,"concrete_test":"Modify the supplementary Mathematica notebook to retain the multi-particle continua on the right-hand side of the spectral flow (14), instead of projecting only the delta peak: at each scale k, feed the current f_Φ,grav and f_Φ,ferm back into the diagrammatic kernels, iterate to convergence, and recompute ρ_A and ρ_ϕ at k = 0. Then check two things: (i) whether the sign flip near λ ∼ M_Pl survives; (ii) whether the resulting propagator G_Φ(p) is analytic off the real timelike axis, e.g. by numerically searching for zeros or poles on the second Riemann sheet. If the sign flip disappears or complex conjugate poles emerge, the claimed KL representation and the UV negativity are truncation artifacts rather than robust predictions.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim—that gauge and scalar propagators admit a KL spectral representation and that their spectral functions turn negative in the UV—rests on the spectral ansatz (16) together with the delta-peak-only projection used in the flow. Both are inputs, not outputs. Equation (16) fixes the analytic structure to an on-shell delta plus two multi-particle continua with thresholds; complex conjugate poles, additional branch cuts, or momentum-dependent residues are excluded by construction. The paper's statement in Sec. VI B that 'we do not observe such behaviour' is therefore not an actual test of the KL property: the ansatz cannot see competing singularities. Likewise, the neglect of continuum feedback (Sec. IV) turns an integro-differential flow into an ODE. The only quantitative validation is the deep-IR comparison in Sec. VI C (a relative shift of about 8.4% for the gauge field). That comparison probes low-energy physics, whereas the sign flip and the asymptotic scaling ∝ λ^{η*_Φ−2} occur around and above the Planck scale, where no independent check is given. The stability analysis in Sec. VI C (positivity of the gauge spectral function would require η*_h ≲ 0.3, against the computed η*_h ≈ 0.96) shows how sensitive the sign flip is, but it treats η*_h as a free parameter and does not quantify the truncation error. Because the central qualitative results live in the unvalidated UV region, the KL representation and the negative, non-normalizable spectral functions are conditional on a truncation whose effect there is unknown.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper develops a spectral renormalisation-group framework in Lorentzian signature with a Callan-Symanzik regulator and applies it to a gravity-matter system containing a U(1) gauge field, an uncharged scalar, and a fermion with Yukawa coupling. The authors compute the photon and scalar two-point functions, extract their spectral functions under the ansatz of Eq. (16), and obtain UV-IR trajectories with an interacting fixed point. They report that both matter spectral functions are non-normalisable, turn negative around the Planck scale, and depend on the gravity gauge-fixing parameters, with the fermion-loop contribution universal and positive below the Planck scale. They also translate the spectral functions into effective-action form factors and discuss implications for unitarity and scattering amplitudes.","tokens_in":26369,"tokens_out":2711,"duration_ms":33926,"significance":"If the central result held, it would be an important step in understanding whether matter fields coupled to asymptotically safe quantum gravity admit Källén-Lehmann representations and whether photons and uncharged scalars remain physical observables above the Planck scale. The paper is careful in several respects: the deep-IR comparison against one-loop effective field theory (Sec. VI C) is a concrete, quantitative check; the authors explicitly list their approximations in Sec. IV; they state the gauge-dependence of the matter spectral functions; and they provide the flow equations and a supplementary Mathematica notebook, which aids reproducibility. The qualitative message, however, is currently stronger than the evidence: the KL representation is assumed rather than derived, and the UV sign flip is not independently validated beyond the specific delta-peak projection. If the authors can reframe the claim and quantify the truncation error, the paper would be a valuable contribution; as it stands, the headline result is partly circular.","major_comments":[{"comment":"The central claim that the photon and scalar propagators possess a Källén-Lehmann spectral representation is not a derived output. Equation (7) is assumed for the full propagator factors, and Eq. (16) further restricts the spectral function to an on-shell delta peak plus two multi-particle continua with fixed thresholds. Consequently, the statement in Sec. VI B that the authors 'do not observe' complex conjugate poles or other non-analyticities is true only by construction: such structures are excluded by the ansatz. To make the KL claim non-circular, the authors need either to derive the absence of competing singularities from the flow equations or to test an enlarged ansatz that allows complex poles/branch cuts and show that they are not generated.","section":"Sec. III A, Sec. III C, Eq. (16), Sec. VI B"},{"comment":"The approximation of keeping only the delta-peak contribution on the right-hand side of the spectral flow (Sec. IV) turns an integro-differential equation into an ODE, but its error is only quantified in the deep IR. The comparison between Eqs. (39) and (38) gives a relative shift of 8.4% for the gauge field, yet this probes spectral values below the fermion threshold, whereas the sign flip and the asymptotic scaling \\rho \\propto \\lambda^{\\eta^*_\\Phi - 2} occur around and above the Planck scale (Fig. 4). No analogous check constrains the UV region. The authors should either include the continuous parts of the spectral functions in the flow at least at leading order, or provide another estimate of the UV truncation error; without this, the sign flip and non-normalisability are not established beyond the specific projection used.","section":"Sec. IV, Sec. VI C, Eq. (14)"},{"comment":"The stability analysis with \\eta_h^* treated as a free parameter is informative but incomplete as stated. The bounds \\eta_h^*|_{\\rm gauge} \\lesssim 0.3 and \\eta_h^*|_{\\rm scalar} \\lesssim -54 show that positivity of the scalar spectral function is far from the computed value \\eta_h^* \\approx 0.96, but the sentence that 'extended approximations are not expected to induce quantitatively significant changes in anomalous dimensions' is an assertion, not an estimate. The authors should provide a concrete error estimate for \\eta_h^* (for example from the difference between the Lorentzian and Euclidean extractions, or from the dependence on the regulator) before claiming that the sign change is 'hard-wired' for the scalar.","section":"Sec. VI C, Eqs. (40)-(41)"}],"minor_comments":[{"comment":"The symbol \\beta is used both for the beta functions of the Yukawa and gauge couplings and for the gravitational gauge-fixing parameter in Eq. (37); this notational clash should be resolved, for instance by renaming the gauge-fixing parameter.","section":"Sec. IV, Eq. (23), Sec. VI C, Eq. (37)"},{"comment":"The text describes the fermion mass as 'm_\\psi = 10^{-2} M_{\\rm Pl}' but the figure caption says '10^{-2}M_{\\rm Pl}'; the units and the illustrative nature of the value should be stated consistently in both places.","section":"Sec. VI A, Fig. 4"},{"comment":"The phrase 'we show that both possess a Källén-Lehmann spectral representation' should be softened to reflect that the representation is imposed by the ansatz in Eq. (16) and then found to be consistent with the projected flow; otherwise the abstract overstates the logical status of the result.","section":"Abstract and Sec. VII"},{"comment":"The trajectory for the fermion mass parameter \\mu_\\psi is an input rather than a result, and the claim that c_1 has 'strongly sub-leading influence' is only checked for the particular ranges shown; this should be stated explicitly in the main text near Eq. (21).","section":"Sec. IV, Eq. (21)"}],"recommendation":"major_revision","confidential_remarks":"The paper comes from a group with a strong track record in asymptotically safe gravity, and the supplementary notebook and explicit flow equations are assets. The main risk for the journal is that the advertised claim of a KL representation is circular given the ansatz in Eq. (16), and that the central UV sign flip is only tested in the deep IR. If the authors reframe the central claim as 'consistency with a KL ansatz under a truncated flow' and add a quantitative UV truncation-error estimate, the paper could become suitable for publication. I would not recommend rejection, because the computations and the IR checks are valuable, and the limitations are at least partially acknowledged in the text."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Here's my take. The genuinely new thing is the first computation of photon and scalar spectral functions in Lorentzian asymptotically safe quantum gravity, including gauge dependence and the translation into form factors. That is a real step beyond the graviton spectral function of [35], and the paper is honest about what it does and doesn't do. The deep-IR comparison, with an 8.4% relative error for the gauge field, is a useful anchor, and the stability analysis in Sec. VI C is a good-faith attempt to estimate how robust the sign flip is. Credit where due: this is technically demanding work, the flow equations are not hidden, and the supplementary notebook is a reasonable gesture.\n\nThat said, the central claim—that the propagators possess a KL representation and that the spectral functions turn negative in the UV—is weaker than the abstract lets on. The KL representation is built into the ansatz in Eq. (16); the flow cannot see competing singularities like complex conjugate poles. The paper's statement in Sec. VI B that 'we do not observe such behaviour' is therefore not a test of the KL property. Also, neglecting the feedback of the continua turns an integro-differential flow into an ODE, and the only quantitative validation (the IR comparison) probes deep-IR physics, not the Planck-scale-to-UV region where the sign flip lives. The stability analysis shows how sensitive the sign flip is to eta_h*, but it treats eta_h* as free and doesn't quantify the truncation error. So the headline qualitative results are conditional on truncations whose UV error is unknown. The reader's conditional verdict is fair.\n\nI should stress what is not a problem: using the gravity input from [35] by the same group is not a flaw, since it's the established method and the paper cites prior work widely. The gauge-dependence analysis is actually a plus, not a defect. The paper's own limitation sections are candid.\n\nWho is this for? People working in asymptotic safety who want to know what Lorentzian spectral methods can currently say about matter propagators, and people interested in unitarity constraints on quantum gravity. It deserves a serious referee: the question is important, the method is sound in outline, and the limitations are declared rather than buried. I would send it to peer review with a request for either an auditable notebook or an explicit error estimate in the UV, and let the authors respond to the KL-ansatz concern. My own verdict would be conditional acceptance, not rejection.","headline":"A serious, technically demanding first computation of matter spectral functions in Lorentzian asymptotically safe gravity, but the KL representation and UV sign flip are assumed rather than demonstrated.","tokens_in":26800,"tokens_out":1874,"would_cite":true,"duration_ms":20938,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"In asymptotically safe quantum gravity, photon and scalar propagators keep a Källén–Lehmann form, but their spectral functions turn negative and non-normalisable in the ultraviolet.","keywords":["asymptotic safety","quantum gravity","Källén–Lehmann spectral representation","spectral functions","functional renormalisation group","Lorentzian signature","photon propagator","scalar propagator"],"falsifier":"Re-solve the flow equations (14) with the multi-particle continua $f_{\\Phi,\\mathrm{grav}}$ and $f_{\\Phi,\\mathrm{ferm}}$ kept on the right-hand side; if the spectral functions at $k=0$ no longer turn negative for $\\lambda\\gtrsim M_{\\mathrm{Pl}}$, the ultraviolet sign flip is an artifact of the delta-peak-only truncation. A complementary check is to compute the scattering spectral function of $G_{A,\\mathrm{scat}}$ in Eq. (47) with quantum-corrected vertices and test whether it is positive semi-definite.","tokens_in":25711,"feed_emoji":"🌌","tokens_out":9486,"duration_ms":90171,"temperature":0.7,"pith_summary":"This paper asks what happens to ordinary matter propagators—photons and uncharged scalars—once gravity is quantised and offers an asymptotically safe ultraviolet completion. Using a spectral renormalisation group adapted to Lorentzian signature, it finds that both propagators still admit a Källén–Lehmann spectral representation, made of an on-shell delta peak and two multi-particle continua. The gravitational continua are gauge-dependent and dominate in the deep ultraviolet, where the spectral functions turn negative and become non-normalisable. The paper concludes that, with quantum gravity present, the photon and the uncharged scalar are no longer physical observables above the Planck scale, even though they remain effectively positive and universal below it. This matters because it decides which states can appear in a unitary scattering theory of asymptotically safe gravity with matter.","feed_headline":"Photon and scalar spectra turn negative above the Planck scale","feed_subtitle":"Gravity-induced spectral functions become gauge-dependent and negative at high energies while staying positive in the infrared.","key_machinery":"The machinery is the spectral renormalisation group: the functional renormalisation group flow (11) with a Callan-Symanzik-type regulator $R_{k,\\Phi}=Z_\\Phi k^2$ for bosons and $R_{k,\\psi}=Z_\\psi k\\,\\mathbb{1}$ for fermions, which shifts masses by the cutoff $k$ without introducing cuts or poles in the complex momentum plane. The load-bearing ansatz is Eq. (16), which fixes each matter spectral function as an on-shell delta peak plus two continua with thresholds at $m_\\Phi+m_h$ and $2m_\\psi$. Internal propagators are replaced by their spectral representations, and the flow of the two-point function is projected on the delta-peak part only, turning the integro-differential spectral flow into ordinary differential equations for the mass parameters, anomalous dimensions, and continuum functions. UV divergences are handled by dimensional regularisation and momentum-independent counterterms renormalised at vanishing momentum. The anomalous dimensions extracted from the delta-peak projection set the ultraviolet scaling of the continua.","core_discovery":"The central claim is that in a Lorentzian gravity-matter system with an asymptotically safe fixed point, the full photon and scalar propagators each satisfy a Källén–Lehmann representation with spectral function $\\rho_\\Phi(\\lambda)=Z_\\Phi^{-1}[2\\pi\\delta(\\lambda^2-m_\\Phi^2)+\\theta(\\lambda^2-(m_\\Phi+m_h)^2)f_{\\Phi,\\mathrm{grav}}(\\lambda)+\\theta(\\lambda^2-4m_\\psi^2)f_{\\Phi,\\mathrm{ferm}}(\\lambda)]$. On the UV-safe trajectory the graviton and fermion loops generate continua whose ultraviolet scaling is $\\propto\\lambda^{\\eta_\\Phi^*-2}$; with fixed-point anomalous dimensions $\\eta_A^*\\approx 0.52$ and $\\eta_\\phi^*\\approx 0.045$, the spectral functions decay more slowly than a free propagator and are therefore non-normalisable. Around the Planck scale both $\\rho_A$ and $\\rho_\\phi$ change sign, driven by the graviton diagram with the matter regulator insertion, which is negative and dominates in the ultraviolet. The paper stresses that the persistence of a Källén–Lehmann form is itself non-trivial, since complex conjugate poles or other non-analyticities could have destroyed it; no such behaviour is seen. The associated form factors inherit the branch cut structure and diverge and turn negative above the Planck scale, which the authors read as a signal that classical vertices cannot be used for amplitudes in that regime.","pith_inferences":["A consequence the authors leave implicit is that the negative, non-normalisable scalar spectral function, if confirmed beyond the quenched approximation, would forbid uncharged elementary scalars from appearing as asymptotic states in the deep ultraviolet of any asymptotically safe theory.","The gauge-independent scattering propagator $G_{A,\\mathrm{scat}}$ of Eq. (47) offers a sharper falsifier than the propagator itself: once quantum-corrected vertices are computed, its spectral function must be positive semi-definite if the theory is unitary.","The same spectral-RG computation could be repeated with the multi-particle continuum fed back into the flow; in the deep infrared this changes the gauge-field spectral function by about 8.4%, and the interesting question is whether the Planck-scale sign flip shifts or disappears under that feedback.","Since the Planck-scale peak is tied to the complex-conjugate critical exponents of the Newton coupling, the sign flip may also appear in other observables that couple to the graviton spectral function near the Planck scale, such as the $e^+e^-\\to\\mu^+\\mu^-$ cross section computed with the same methods."],"forward_implications":["Photons and uncharged scalars lose their status as physical observables above the Planck scale: their spectral functions become gauge-dependent, non-normalisable, and partly negative.","Below the Planck scale and above the fermion threshold, the universal fermion-loop contribution dominates and is positive, so matter spectral functions remain effectively physical in the infrared.","The form factors $f_{FF}(p^2)$ and $f_{\\phi\\phi}(p^2)$ diverge and become negative around the Planck scale, so scattering amplitudes built from these propagators and classical vertices are not trustworthy in the ultraviolet.","An asymptotically safe fixed point with $g_Y^*=0.455$ and $y_t^*=0.462$ provides a UV completion for the U(1) and Yukawa couplings if the gravitational coefficients $f_g$ and $f_y$ are positive as assumed.","The sign flip in the scalar spectral function is robust (positivity would require $\\eta_h^*\\lesssim -54$), while the photon case is marginal (positivity requires $\\eta_h^*\\lesssim 0.3$), so the photon prediction is the more easily tested one."],"supporting_citations":[{"why":"Establishes the spectral renormalisation group with a Callan-Symanzik mass cutoff and the healthy graviton spectral function that the present computation extends to matter.","marker":"[35]"},{"why":"Provides the reconstructed graviton spectral function used for comparison of the Planck-scale peak structure.","marker":"[34]"},{"why":"Defines the Källén–Lehmann spectral representation for propagators, which the paper assumes for every field.","marker":"[110]"},{"why":"Provides the companion derivation of the spectral representation and its normalisation properties.","marker":"[111]"},{"why":"Introduces momentum-independent mass regulators for gauge-invariant Wilsonian flows, the idea behind the cutoff used here.","marker":"[102]"},{"why":"Applies the mass-type regulator to non-perturbative thermal flows, supporting the choice that avoids spurious cuts and poles.","marker":"[103]"},{"why":"Shows the gravity contribution coefficient $f_g$ for the U(1) beta function is non-negative, underpinning the UV completion of the gauge sector.","marker":"[54]"},{"why":"Supplies the leading-order gravitational contribution to the Yukawa beta function that the paper models with the coefficient $f_y$.","marker":"[55]"},{"why":"Computes the graviton-mediated $e^+e^-\\to\\mu^+\\mu^-$ amplitude with the same spectral functions, the scattering context the paper uses to argue for gauge-independent amplitudes.","marker":"[88]"}],"fun_headline_variants":["Gravity flips photon and scalar spectra negative at Planck scale","Planck-scale gravity drives matter spectral functions to negative values","Negative photon spectral function emerges from asymptotically safe gravity","Gauge and scalar spectral functions turn non-normalizable near Planck scale","Planck-scale gravity makes photon and scalar spectral functions negative"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The computation assumes from the outset that every propagator has a Källén–Lehmann form with one delta peak and two smooth continua, and it neglects the feedback of those continua into the flow equations, so the spectral representation is an input rather than something the calculation itself could disprove.","fun_headline_variants_meta":{"raw":{"variants":["Gravity flips photon and scalar spectra negative at Planck scale","Planck-scale gravity drives matter spectral functions to negative values","Negative photon spectral function emerges from asymptotically safe gravity","Gauge and scalar spectral functions turn non-normalizable near Planck scale","Planck-scale gravity makes photon and scalar spectral functions negative"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000679,"raw_usage":{"total_tokens":3104,"prompt_tokens":984,"completion_tokens":2120,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":600,"completion_tokens_details":{"reasoning_tokens":2037}},"tokens_in":600,"tokens_out":2120,"duration_ms":15617,"temperature":1.0,"reasoning_tokens":2037,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-06T14:38:47.254701+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Re-solve the flow equations (14) with the multi-particle continua $f_{\\Phi,\\mathrm{grav}}$ and $f_{\\Phi,\\mathrm{ferm}}$ kept on the right-hand side; if the spectral functions at $k=0$ no longer turn negative for $\\lambda\\gtrsim M_{\\mathrm{Pl}}$, the ultraviolet sign flip is an artifact of the delta-peak-only truncation. A complementary check is to compute the scattering spectral function of $G_{A,\\mathrm{scat}}$ in Eq. (47) with quantum-corrected vertices and test whether it is positive semi-definite.","supporting_citations":[],"review_version":1}