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Janus and RG-interfaces in minimal 3d gauged supergravity

T0 review · 3 major / 5 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read This paper constructs Janus and RG-flow interface solutions in the simplest three-dimensional gauged supergravity and shows they obey the proposed inequality chain $0 \le c_{LR} \le c_{\rm eff} \le \min(c_L,c_R)$.

desk verdict 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. read the letter →

arxiv 2412.16749 v1 pith:GF3ULVZD submitted 2024-12-21 hep-th

Michael Gutperle , Charlie Hultgreen-Mena This is my paper · ORCID
classification hep-th
keywords JanussolutionsRG-flowinterfacesgaugedsupergravityholographicentanglemententropyeffectivecentralchargetransmissioncoefficientAdS/CFTtopological
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 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.

What carries the argument

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 $c_{LR}/c=(c_{\rm eff}/c)^2$.

What would settle it

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.

Watch

Extended reading notes

Core claim

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].

Load-bearing premise

The result rests on a transmission formula derived for a stack of thick branes and applied without proof to the thin single-interface solutions constructed here, and if that application fails the inequality check collapses.

Editorial extensions

If this is right

  • The strict inequality $c_{LR}<c_{\rm eff}<\min(c_L,c_R)$ is a generic feature of non-trivial Janus and RG-flow interfaces in this model, with equality occurring only at the supersymmetric vacuum, i.e. for the trivial interface.
  • The relation $c_{LR}/c=(c_{\rm eff}/c)^2$ holds exactly for the half-BPS $N=8$ Janus solution, giving a three-dimensional analogue of the ten-dimensional super-Janus result of [36].
  • The model provides a simple numerical laboratory where the whole chain (4.14) can be scanned over a continuous family of initial conditions, so future proposals for interface inequalities can be tested cheaply.
  • Any interface CFT dual to these solutions must have a transmission coefficient bounded by the effective central charge, which constrains the amount of energy that can pass through the interface.

Reading between the lines

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

  • 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.
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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

3 major / 5 minor

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].

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 (3)
  1. [Section 3, numerical solutions] 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.
  2. [Section 3/4.3] 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.
  3. [Section 3] 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.
minor comments (5)
  1. [Section 4.3] The section title 'T ransmission and reflection coefficients' contains an extra space; please fix this typographical error.
  2. [Section 4.2] The Ryu-Takayanagi prescription is spelled as 'Ryu-Takanayagi' in the text; the correct spelling is 'Ryu-Takayanagi'.
  3. [Throughout] 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).
  4. [Section 2] 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.
  5. [Section 4.1] 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.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the numerical inequality checks and the exact N=8 relation are computed from the solutions rather than fitted or assumed.

full rationale

The paper's derivation chain is self-contained and does not reduce to its own inputs. The numerical Janus and RG-flow solutions are obtained by integrating the equations of motion (3.3)-(3.4) from initial conditions at the turning point, with no parameter fitted to the target observables. The effective central charge c_eff is computed from the warp factor at the minimum, c_eff = (3/(2G_N)) e^{B(0)}, while c_LR is computed from the independent holographic transport formula (4.12) using sigma = integral (phi')^2 du; the inequality chain (4.14) is imported from the external paper [1] and checked, not derived by construction. The exact N=8 calculation similarly evaluates c_eff/c = 1/cosh q and c_LR/c = 1/cosh^2 q from the explicit solution of [37], so the relation (5.9) is a computed consequence rather than an assumed input. The only notable concern is whether the thick-brane continuum formula (4.12) from [53] is valid for the single thin numerical interfaces considered here; that is a regime-applicability question, not a circularity, because applying the formula does not make the resulting c_LR equal by definition to c_eff or to the inequality being tested. Self-citations such as [37], [49], and [50] supply explicit solutions and standard holographic formulas with stated assumptions, and none is invoked as an unverified uniqueness theorem to forbid alternatives. No fitted input is relabeled as a prediction, and no known result is merely renamed. Therefore the circularity score is 0.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The free parameters are the model parameter a, the shooting initial conditions for numerical solutions, and the integration constants of the exact N=8 solution; none are fitted to data. The axioms are standard holographic formulas and two domain assumptions about the applicability of the c_LR formula and the N=8 solution. No invented entities are introduced.

free parameters (3)
  • a (model parameter) = 3/4 for representative plots; scanned in regimes a < 1/sqrt(2), 1/sqrt(2) < a < 1, a > 1
    The scalar potential and the number of vacua depend on a; it is a theory input, not fitted to data, but it determines which interface solutions exist.
  • Initial conditions phi(0), phi'(0) = varies, see Figure 4
    Numerical solutions are generated by shooting from the turning point u=0; the inequality check is performed on representative families, not the full parameter space.
  • N=8 solution parameters p, q = arbitrary real; plots use q = 3/2 and q = 1/5
    The exact half-BPS solution of [37] depends on two integration constants p and q; the derived relation (5.9) is independent of p and holds for all q.
assumptions (5)
  • standard math Brown-Henneaux relation c = 3l/(2G_N) connects central charge to AdS radius, used for c_L and c_R in (4.6).
    Standard holographic dictionary result; invoked in Section 4.1.
  • standard math Ryu-Takayanagi formula (4.1) computes entanglement entropy from geodesic length.
    Standard holographic prescription; used throughout Section 4.
  • domain assumption The truncation theta = A_mu = 0 reduces the N=2 action (2.8) to gravity plus a real scalar with potential (2.9).
    Stated in Section 2; allows the simpler analysis. It is a consistency requirement of the truncation.
  • domain assumption The holographic formula (4.12) for c_LR, derived in [53] for thick-brane arrays, applies to the thin numerical interface solutions.
    Crucial for the transmission coefficient; the paper does not justify its extension to these thin interfaces.
  • domain assumption The N=8 solution of [37] describes an interface with equal AdS radii l_L = l_R = 1 on both sides.
    Used in Section 5 to compute c_LR; stated implicitly by setting l_R = l_L = 1 in (4.12).

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Pith. "Pith review of Janus and RG-interfaces in minimal 3d gauged supergravity." pith.science (2026). https://pith.science/paper/GF3ULVZD

@misc{pith2026241216749,
  author       = {Pith},
  title        = {Pith review of: Janus and RG-interfaces in minimal 3d gauged supergravity},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/GF3ULVZD}},
  note         = {Machine review of arXiv:2412.16749}
}
abstract

In this paper we find solutions of minimal $d=3,N=2$ gauged supergravity corresponding to Janus and RG-flow interfaces. We use holography to calculate symmetric and interface entanglement entropy as well as reflection coefficients and confirm that a recently proposed [1] inequality involving these quantities is satisfied for the solutions found here.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Entanglement C-functions of defects and interfaces in $\mathcal{N}=4$ supersymmetric Yang-Mills theory

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    A probe-D5 holographic calculation gives analytic defect/interface entanglement entropy for massive D3/D5 intersections and shows the entropic C-function is monotonic but not always a finite degree-of-freedom count.

Reference graph

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