{"id":"d0ce887d-ee25-4ec7-98e7-d988a70f9c08","arxiv_id":"2412.16749","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"New numerical interface solutions in a minimal 3d supergravity model satisfy the proposed universal inequality between transmission and entanglement.","lead":"Researchers constructed numerical interface solutions in a simple three-dimensional supergravity model and tested a proposed inequality linking entanglement entropy and energy transmission across a quantum interface. The model provides a clean holographic testbed for universal properties of conformal interfaces.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The inequality check relies entirely on Eq. (4.12) for c_LR, a thick-brane continuum result imported from [53] without a direct derivation for these single numerical interfaces; a direct scattering computation is needed to know whether the check is meaningful.","rationale":"The central claim of the paper is that the holographic observables computed from the numerical Janus and RG-flow interfaces satisfy the inequality chain (4.14). Of the three quantities involved, c_LR is the only one obtained from an external formula rather than from a direct holographic computation in the constructed backgrounds. The formula (4.12) originates in a continuum-limit treatment of thick brane arrays, and the burden is on the authors to show that it applies to their single, non-supersymmetric domain walls. The exact N=8 calculation is a useful check, but it is a special configuration and cannot by itself establish the general applicability of (4.12) to the numerical solutions. This is not a claim of internal inconsistency; rather, it is an unverified external input on which the central numerical verification depends. The concrete test proposed above would settle the issue by computing c_LR directly from the linearized scattering equations. If the direct computation agrees with (4.12), the paper's verification stands; if it does not, the inequality check as presented would need to be revised. The reader's conditional verdict is therefore appropriate, and no change to that verdict is required by this stress-test pass.","tokens_in":12704,"tokens_out":7319,"duration_ms":70167,"concrete_test":"For one representative RG-flow solution (e.g., the a=3/4 solution along the blue line in Fig. 4) and one Janus solution, compute T directly: linearize Einstein's equations around the numerical background (3.2)-(3.5) for transverse traceless metric perturbations, reduce to a single ODE, solve with incoming and outgoing boundary conditions at u=±∞, extract the transmission amplitude, and form c_LR = (c_L + c_R) T. Compare the result to Eq. (4.12) using the same numerical profile. If the two disagree beyond numerical error, the claimed confirmation of (4.14) is not supported; if they agree, the formula is validated for these solutions.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Section 4.3 computes c_LR from Eq. (4.12), taken from [53]. That formula was derived for energy transport through a thick brane realized as a continuum limit of a periodic array of probe branes. The numerical Janus and RG-flow solutions of Section 3 are single, smooth domain walls whose width is comparable to the AdS scale, and the paper gives no argument that the continuum or effective-brane assumptions of [53] are satisfied in this regime. Since c_LR enters the claimed verification of (4.14) only through (4.12), an inapplicable formula would invalidate the main numerical check. The exact N=8 solution in Section 5 provides a consistency check, but it is a special supersymmetric case with equal AdS radii and does not test the non-supersymmetric, asymmetric RG-flow interfaces. The paper does not derive (4.12) from the equations of motion of the truncated theory, nor does it compare it with a direct scattering computation for these backgrounds.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper constructs numerical Janus and RG-flow interface solutions in minimal three-dimensional N=2 gauged supergravity, using an AdS2-slicing ansatz and a shooting method. The authors compute the symmetric interface entropy, the interface entanglement entropy (encoded in an effective central charge c_eff), and a transmission coefficient c_LR using the holographic formula (4.12) from [53]. They then check the inequality chain 0 ≤ c_LR ≤ c_eff ≤ min(c_L, c_R) proposed in [1] and report that strict inequality holds for all their solutions. In the second part, for an exact half-BPS Janus solution of N=8 three-dimensional gauged supergravity, they compute c_eff and c_LR analytically and obtain the quadratic relation c_LR/c = (c_eff/c)^2, matching the ten-dimensional result of [36].","tokens_in":12794,"tokens_out":4219,"duration_ms":38149,"significance":"If the numerical checks are reliable, the paper provides a useful low-dimensional holographic laboratory for testing recently proposed universal bounds on interface CFT data. The exact N=8 solution offers an analytic confirmation of a relation between transmission and entanglement, strengthening the universality of that relation. The paper is clearly written and the derivations from the truncated supergravity action to the ODE system are clean. The main weakness is that the central numerical verification relies on a formula for c_LR whose regime of validity is not established for the solutions constructed here.","major_comments":[{"comment":"The paper uses the holographic expression c_LR = (3/G_N)(1/l_R + 1/l_L + 8πG_N σ)^{-1}, attributed to [53], as the definition of c_LR for all numerical Janus and RG-flow interfaces. However, the text states that this formula was derived in [53] by taking a continuum limit of an array of probe branes, i.e., for a thick brane realized as a dense stack of thin branes. The single, smooth domain-wall solutions of Section 3 are not such an array, and the paper gives no argument—analytic or numerical—that the formula remains valid for these backgrounds. Since c_LR enters the verification of the inequality (4.14) exclusively through (4.12), the applicability of this formula is load-bearing for the paper's main claim. Please provide a direct derivation of (4.12) from the equations of motion of the truncated theory, or a comparison with a direct scattering computation for at least one representative interface, or a careful statement of the conditions under which [53]'s result applies and a check that these conditions are met by the numerical solutions.","section":"Section 3, numerical solutions"},{"comment":"The numerical solutions are obtained by a shooting method in Mathematica, but the manuscript gives no convergence checks, error estimates, or tolerances. The central claim that the strict inequality 0 < c_LR < c_eff < min(c_L, c_R) holds for all Janus and RG-flow solutions is based on these numerics, so it is important to demonstrate that the results are stable against numerical integration error and that the strict inequalities are not artifacts of the shooting procedure. Please include a quantitative error analysis (e.g., tolerance of the shooting parameters, step-size convergence, residual of the constraint (3.5) along the solutions) and state how the plotted curves in Figure 7 depend on these tolerances.","section":"Section 3/4.3"},{"comment":"The sentence 'It is straightforward to verify that the conditions (3.7) and (3.9) are inconsistent with the equations of motion (3.4) unless ϕ = ϕ(1) = 0' is stated without proof. This claim is used to conclude that all non-trivial AdS2-sliced solutions break all supersymmetries. Please provide the actual argument (e.g., combine (3.7) and (3.9) with the scalar equation (3.4) and the constraint (3.5) to show that ϕ' = 0 and ϕ = 0 is the only solution). This is a minor point for the main result, but it should be verifiable by the reader.","section":"Section 3"}],"minor_comments":[{"comment":"The section title 'T ransmission and reflection coefficients' contains an extra space; please fix this typographical error.","section":"Section 4.3"},{"comment":"The Ryu-Takayanagi prescription is spelled as 'Ryu-Takanayagi' in the text; the correct spelling is 'Ryu-Takayanagi'.","section":"Section 4.2"},{"comment":"The notation 'cef f' appears with a double space; the unified notation should be 'c_eff' everywhere, including in equations such as (4.10) and (4.14).","section":"Throughout"},{"comment":"The expression for Δ_±^{(1)} is written as Δ_±^{(1)} = 1 ± |1 - 2a^2|; for a = 1/√2 this gives a double root 1, but the text says this is valid for all a∈R. It may be worth a brief comment on the special case a = 1/√2 where the mass term in (2.13) vanishes and the operator dimension might need a more careful analysis.","section":"Section 2"},{"comment":"The derivation of ln g_A relies on a Fefferman-Graham coordinate transformation and the Brown-Henneaux formula. The relation between γ_L, γ_R and the central charges is clear, but it would be helpful to spell out the explicit expression for γ_L and γ_R in terms of the asymptotic behavior of B(u) to avoid ambiguity in the numerical fitting.","section":"Section 4.1"}],"recommendation":"major_revision","confidential_remarks":"The paper is within the scope of JHEP and presents a nice holographic check of the proposed inequality. The main issue is the unexamined use of the c_LR formula from [53] for the numerical interfaces; this is not a minor presentation point because without it the central verification is vacuous. In addition, the numerical reliability of the shooting solutions should be documented. I would be willing to reconsider after the authors address these points. I see no grounds for rejection, assuming the formula (4.12) is indeed applicable, as I expect it may be for this class of smooth domain walls, but the burden of proof lies with the authors."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"First thing to know: this is a solid, modest holography paper. It constructs the first Janus and RG-flow interface solutions in minimal d=3 N=2 gauged supergravity (one real scalar plus gravity), computes holographic observables, and checks the recent inequality 0 ≤ c_LR ≤ c_eff ≤ min(c_L, c_R) from [1]. The paper is honest, the derivations are standard, and the central claim holds up.\n\nWhat's genuinely new: the numerical solution families in Sec. 3, including the phase diagram separating Janus from fine-tuned RG-flow initial conditions, and the exact N=8 calculation in Sec. 5. That calculation is the strongest part: for the half-BPS Janus of [37], they derive c_eff/c = 1/cosh q and c_LR/c = 1/cosh^2 q, giving c_LR/c = (c_eff/c)^2, matching the ten-dimensional super-Janus result of [36]. It is clean, analytic, and independent.\n\nThe soft spots are real but not dealbreakers. The biggest is the use of Eq. (4.12) for c_LR, taken from a thick-brane continuum calculation in [53]. The paper does not justify applying it to these single, relatively thin domain walls. That is a fair criticism – the stress-test note is right about this – but it is not a knockout. The N=8 exact solution is itself a single interface, and the formula reproduces the expected relation, which suggests it has wider validity. Still, a one-paragraph justification or a direct scattering computation would have removed the doubt. Also, the numerical solutions have no convergence checks, no code or data release, and the claim that no supersymmetric solutions exist is stated as 'straightforward to verify' without the proof. These are minor-to-moderate issues, not load-bearing flaws.\n\nThe inequality check is a legitimate test of a recent conjecture in a new model. There is no circularity: c_eff comes from the geodesic at the interface, c_LR from the transmission formula, and the central charges from the asymptotic AdS radii.\n\nWho is this for? People working on holographic interfaces and the recent universal-bounds literature. A serious referee should see it. I would recommend accept after minor revision, with requests for a justification or caveat on (4.12), plus some numerical convergence data.","headline":"Solid, modest paper: new Janus/RG-flow solutions in minimal 3d N=2 gauged supergravity and a clean exact N=8 check; main caveat is the unexamined use of the thick-brane transmission formula.","tokens_in":13462,"tokens_out":3808,"would_cite":true,"duration_ms":30877,"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":"This paper constructs Janus and RG-flow interface solutions in the simplest three-dimensional gauged supergravity and shows they obey the proposed inequality chain $0 \\le c_{LR} \\le c_{\\rm eff} \\le \\min(c_L,c_R)$.","keywords":["Janus solutions","RG-flow interfaces","gauged supergravity","holographic entanglement entropy","effective central charge","transmission coefficient","AdS/CFT","topological interfaces"],"falsifier":"Take one of the numerical Janus or RG-flow interfaces with $a=3/4$ and compute the transmission coefficient directly from the two-point function of the boundary stress tensor by numerically solving the linearized fluctuation equations around the background, then compare the result with the value obtained from eq. (4.12); a mismatch for a non-trivial interface would show the assumed formula does not apply and would invalidate the verification of the inequality chain.","tokens_in":12383,"feed_emoji":"⚛️","tokens_out":7855,"duration_ms":60613,"temperature":0.7,"pith_summary":"The paper aims to show that minimal $d=3$, $N=2$ gauged supergravity, with only gravity, a single real scalar, and no supersymmetry preserved by the interfaces, is rich enough to contain both Janus interfaces (same CFT on both sides) and RG-flow interfaces (different CFTs on the two sides). Using these numerical solutions, it tests a recently proposed universal bound on interface entanglement: the transmission coefficient measured at the interface should lie between zero and the effective central charge of the interface, which in turn should not exceed the smaller of the two bulk central charges. The paper finds that every Janus and RG-flow solution it constructs satisfies the strict inequalities, with equality only for the trivial interface that is no interface at all. For an exact half-supersymmetric solution of the maximal $N=8$ theory, it derives the sharper relation $c_{LR}/c=(c_{\\rm eff}/c)^2$, matching a relation previously found for ten-dimensional supersymmetric Janus solutions. A sympathetic reader would care because these are among the first tests of the proposed inequality in a complete, albeit simplified, holographic setting.","feed_headline":"Minimal 3d supergravity interfaces obey proposed entanglement bound","feed_subtitle":"Numerical Janus and RG-flow interfaces satisfy c_LR ≤ c_eff ≤ min(c_L,c_R); only the trivial interface saturates it.","key_machinery":"The central object carrying the argument is the AdS$_2$-sliced metric ansatz $ds^2=du^2+e^{2B(u)}(dx^2-dt^2)/x^2$ with scalar $\\phi=\\phi(u)$; with this ansatz the equations of motion reduce to two second-order ODEs plus a constraint, and the constraint fixes $B(0)$ from the initial values $\\phi(0),\\phi'(0)$ at the turning point. The load-bearing identity is the holographic transmission formula $c_{LR}=(3/G_N)(1/l_R+1/l_L+8\\pi G_N\\sigma)^{-1}$ from [53], with $\\sigma=\\int(\\phi')^2du$ evaluated on the numerical solution; this turns the inequality chain (4.14) into a concrete numerical check. The exact half-supersymmetric $N=8$ solution of [37] supplies the sharper test: its warp factor $e^{2B}=\\mathrm{sech}^2 q\\,\\cosh^2 u$ gives $c_{\\rm eff}/c=\\mathrm{sech}\\,q$, and $\\sigma=2\\sinh^2 q$ yields $c_{LR}/c=\\mathrm{sech}^2 q$, establishing $c_{LR}/c=(c_{\\rm eff}/c)^2$.","core_discovery":"The central claim is that minimal $d=3$, $N=2$ gauged supergravity with the $\\theta=A_\\mu=0$ truncation admits families of AdS$_2$-sliced interface solutions that fall into three classes: Janus interfaces connecting the supersymmetric vacuum to itself, RG-flow interfaces connecting the supersymmetric vacuum to one of the non-supersymmetric vacua, and RG-flow interfaces connecting the two non-supersymmetric vacua. These solutions preserve no supersymmetry and are constructed numerically by shooting from the turning point of the warp factor. The paper then computes three holographic observables for these backgrounds: the $g$-factor from symmetric entanglement entropy, the effective central charge $c_{\\rm eff}$ from entanglement entropy ending at the interface, and the transmission coefficient $c_{LR}$ from the holographic formula of [53]. It verifies that the chain $0\\le c_{LR}\\le c_{\\rm eff}\\le \\min(c_L,c_R)$ holds with strict inequalities for all non-trivial solutions, and for the exact $N=8$ Janus solution of [37] it derives $c_{LR}/c=(c_{\\rm eff}/c)^2$, the same relation found for the ten-dimensional super-Janus of [36].","pith_inferences":["If the quadratic relation $c_{LR}/c=(c_{\\rm eff}/c)^2$ is a universal feature of half-BPS AdS$_3$ Janus solutions, then the transmission coefficient is determined entirely by the warp factor at the interface, giving a shortcut for computing transport properties of supersymmetric interfaces without solving the full fluctuation problem.","The numerical phase diagram in figure 4 suggests that fine-tuned RG-flow interfaces form codimension-one loci in initial-condition space while Janus solutions occupy open regions; a natural extension is to map the full space and identify the critical curves where singular solutions begin.","Because the dual CFTs of these numerical solutions are not known explicitly, the holographic check is currently the only handle on the inequality; a direct field-theoretic computation of $c_{LR}$ and $c_{\\rm eff}$ for a known interface CFT would provide an independent test of whether the bound is truly universal."],"forward_implications":["The strict inequality $c_{LR}