REVIEW
Ultraviolet dissipation and defect OPE in bottom-up holographic interfaces
High Energy Physics - Theory · Submitted 2 Oct 2026 · 56 references
Pith's verdict: The central reduction of c_UV, BOPE coefficients, and the defect spectrum to the optical length ρ is real and the algebra checks out, but the paper stands on one step it does not fully control: the projection from the full double-trace mode matrix to a single-channel equation, with the off-diagonal channel mixing unestimated.
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Referee report
The paper
The paper claims
For a broad class of bottom-up holographic interfaces, a single geometric quantity — the optical length $\rho$ of the AdS$_2$-sliced bulk — simultaneously fixes the ultraviolet dissipation rate $c_{\mathrm{UV}}$, the large-dimension…
The reading
What carries the argument
The optical coordinate $u(x)=\int^x dx'/A(x')$ and optical length $L=\int_{-\infty}^{\infty} dx/A(x)$ with normalized density $\rho = L/\pi$. The warpfactor $A(x)$ of the bottom-up metric $ds^2=dx^2 + A(x)^2 ds^2_{\mathrm{AdS}_2}$ is subject to an endpoint regularity condition, $A(y)=y^{-1}(1+\varepsilon(y))$ with $\varepsilon(y)=O(y^2)$, $\partial_y\varepsilon=O(y)$, $\partial_y^2\varepsilon=O(1)$ in inward optical distance $y$; this keeps the Liouville remainder $W_\nu = V_\Delta - V_0$ bounded relative to a reference potential $V_0 = (\nu^2-\tfrac14)(\pi/L)^2\csc^2(\pi u/L)$, so the min-max bound (2.16) forces the Weyl spectral density $\rho = L/\pi$ and the identification $c_{\mathrm{UV}}=c/\rho$. The dissipation rate itself is obtained from the projected double-trace equation $1 - h_R^2 G^{\mathrm{proj}}_{R,k} G^{B,\mathrm{eff}}_{R,k}=0$, whose WKB poles shift to $\omega^{\mathrm{open}}_{n,k}-\Omega_{n,k} = \frac{1}{2\pi i\rho}\log\frac{1+g}{1+g e^{2\pi i\nu}}$, giving a positive limiting dissipation $\gamma_\infty = \frac{1}{2\pi\rho}\log\frac{1+g}{|1+g e^{2\pi i\nu}|}$.
Extended reading notes
Core claim
The paper establishes that in the radial WKB regime of fixed descendant level, three seemingly distinct interface observables all reduce to one geometric datum, the optical length $\rho = L/\pi$: the asymptotic density of the defect-primary tower ($\lim_{\omega\to\infty} N_k(\omega)/\omega = \rho$), the ratio of BOPE coefficients ($\lim_{d\to\infty} b_I^2(d)/b_{AdS}^2(d) = 1/\rho$), and the ultraviolet dissipation ratio ($c_{\mathrm{UV}}/c = 1/\rho = \pi/L$). Using $c/c_{\mathrm{UV}} = L/\pi$ together with the null energy condition on the warpfactor, the paper proves the new lower bound $c_{\mathrm{LR}} \ge 2c_{\mathrm{eff}}/(2+\pi(c/c_{\mathrm{UV}}-1))$, which brackets transmission from below and complements the upper bound $c_{\mathrm{LR}} \le c_{\mathrm{eff}}$. The bound saturates exactly on a family of two vacuum AdS$_3$ caps joined by an AdS$_2\times\mathbb{R}$ throat, and the paper verifies the results against pure AdS$_3$, BPS-Janus, and non-BPS Janus examples.
Load-bearing premise
The load-bearing premise is the endpoint regularity condition on the warpfactor, that in inward optical distance $A(y)=y^{-1}(1+\varepsilon(y))$ with $\varepsilon(y)=O(y^2)$, which keeps the Liouville remainder bounded and forces the Weyl spectral density $\rho=L/\pi$ and the identification $c_{\mathrm{UV}}=c/\rho$; the author acknowledges this condition fails for some smooth supergravity Janus examples, leaving the main relations and the $c_{\mathrm{UV}}$-form of the bound unestablished there.
Editorial extensions
If this is right
- For any warpfactor in the stated regularity class, the ratio $c_{\mathrm{UV}}/c$ is fixed by the bulk optical length, making the projected dissipation rate computable from geometry without solving the full quasinormal spectrum.
- The same $1/\rho$ governs BOPE coefficients at large defect dimension, so the defect OPE data and the open-system dissipation rate are determined by one geometric parameter.
- The new bound $c_{\mathrm{LR}} \ge 2c_{\mathrm{eff}}/(2+\pi(c/c_{\mathrm{UV}}-1))$ closes the window on energy transmission from below, complementing $c_{\mathrm{LR}} \le c_{\mathrm{eff}}$.
- Saturation of the bound selects a specific throat geometry, providing a target for holographic and bootstrap checks.
- The equality $c_{\mathrm{UV}} = c_{\mathrm{eff}}$ seen in BPS-Janus is shown to be special, not general, for holographic interfaces.
Reading between the lines
- The optical length $\rho$ is exactly the Weyl density of the defect-primary tower, which suggests a field-theoretic reading of $c_{\mathrm{UV}}$ as the open-system analogue of $c_{\mathrm{eff}}$, governed by the spectral density of defect states rather than by entanglement — a conjecture beyond this paper.
- One could test the universality at the massless point $\nu=1$, where the dissipation rate decays only logarithmically (per the companion massless analysis here and the earlier BPS-Janus result); that regime likely has a separate scaling structure worth probing.
- If the same $1/\rho$ identification holds beyond holography, the new bound would become a constraint on any conformal interface whose defect spectral density is known, allowing crossing-symmetry bootstrap bounds at large defect dimension to be compared with the geometric prediction.
Original abstract
We study the radial ultraviolet dissipation quantity $c_{UV}$ defined in arXiv:2601.16888v3 and defect OPE data in bottom-up holographic interfaces. We relate $c_{UV}$ along with the defect primary spectrum and BOPE coefficients in the large defect dimension limit to the optical length $\rho$ in the holographic bulk. In addition, we prove a new holographic bound for conformal interfaces relating entanglement entropy, energy transmission and UV dissipation: \[ c_{LR}\geq \frac{2c_{\mathrm{eff}}}{2+\pi(c/c_{\mathrm{UV}}-1)}. \] This compliments the upper bound of $c_{LR}$ by $c_\text{eff}$ proved in arXiv:2404.01515.
The compiled record
The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.
The abstract, sentence by sentence
We study the radial ultraviolet dissipation quantity $c_{UV}$ defined in arXiv:2601.16888v3 and defect OPE data in bottom-up holographic interfaces. We relate $c_{UV}$ along with the defect primary spectrum and BOPE coefficients in the large defect dimension limit to the optical length $\rho$ in the holographic bulk. In addition, we prove a new holographic bound for conformal interfaces relating entanglement entropy, energy transmission and UV dissipation: \[ c_{LR}\geq \frac{2c_{\mathrm{eff}}}{2+\pi(c/c_{\mathrm{UV}}-1)}. \] This compliments the upper bound of $c_{LR}$ by $c_\text{eff}$ proved in arXiv:2404.01515.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We study the radial ultraviolet dissipation quantity $c_{UV}$ defined in arXiv:2601.16888v3 and defect OPE data in bottom-up holographic interfaces. | contribution 0.95 | 0.70 | 0.06 | asserted 0.90 |
| s1 | We relate $c_{UV}$ along with the defect primary spectrum and BOPE coefficients in the large defect dimension limit to the optical length $\rho$ in the holographic bulk. | result 0.56 | 0.89 | 0.19 | asserted 1.00 |
| s2 | In addition, we prove a new holographic bound for conformal interfaces relating entanglement entropy, energy transmission and UV dissipation: \[ c_{LR}\geq \frac{2c_{\mathrm{eff}}}{2+\pi(c/c_{\mathrm{UV}}-1)}. | result 0.90 | 0.94 | 0.61 | asserted 1.00 |
| s3 | \] This compliments the upper bound of $c_{LR}$ by $c_\text{eff}$ proved in arXiv:2404.01515. | background 0.49 | 0.15 | 0.09 | asserted 0.98 |
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References
Discussion
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