Connecting boundary entropy and effective central charge at holographic interfaces

arXiv:2507.09171 · hep-th, cond-mat.str-el · Submitted 2025-07-12 · Read on arXiv

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Introduction to the show: ident: Quantum Radio. Generated commentary on the latest quantum physics and condensed matter papers.

Kai: I'm Kai, and with me are Mira and Lev, guest researcher.

Mira: Today's paper: "Connecting boundary entropy and effective central charge at holographic interfaces".

Kai: The study connects boundary entropy and effective central charge at holographic interfaces by showing that modifications to entanglement entropy in interface conformal field theories (ICFTs) can be understood as limits…

Mira: First, who's behind it and why it matters.

Title and authors: Kai: Now, looking at the actual summary of "Connecting boundary entropy and effective central charge at holographic interfaces," it lays out a pretty clear roadmap for understanding how entanglement entropy is modified in these interface CFTs compared to a standard CFT.

Mira: It boils down to two key modifications: first, there's this finite boundary entropy contribution that shows up even when the interval doesn't cross the interface, and second, when an endpoint of an interval sits right on that interface, the coefficient of the logarithmic divergence shifts from something like a standard central charge to this new effective central charge.

Lev: That distinction between crossing and non-crossing intervals seems crucial; it implies that for non-crossing ones, we need these finite contributions specifically to satisfy strong subadditivity, which is a known constraint in entanglement calculations.

Kai: Right, Lev, and Mira. They show this modification isn't just an arbitrary adjustment; they connect it by showing the effective central charge emerges as the limit of that boundary entropy function when one endpoint approaches zero distance from the interface.

Mira: I see how that connection works; it’s a formal bridge between a thermodynamic quantity—the boundary entropy number—and a geometric one derived from the holographic dual description of minimal surfaces, like those in RS braneworlds or Janus geometries.

Lev: If they can rigorously establish that this limit holds across different bulk geometries, it gives us confidence that these entropic relations are universal features of these interface systems.

The paper's summary: Kai: Shifting over to the suggested improvements in "Connecting boundary entropy and effective central charge at holographic interfaces," the authors propose ways to make this framework more practical for real-world applications.

Mira: They suggest developing a Geometric Entanglement Mapping module that takes input parameters from the bulk metric, like warp factors, and automatically derives that interface entropy function directly. This would be a huge step toward making the theory usable computationally.

Lev: If we can automate the derivation of g(two) from metric inputs, it means we could test how robust these entanglement relations are against different geometric deformations in our error correction models much faster than currently possible <ref:2507.09171#pg1>.

Kai: They also propose an Effective Central Charge Tracker that predicts c eff based on geometric ratios, specifically the ratio of endpoint distances like l A/l R, and they insist this must adhere to the bound where c eff at most (c L, c R).

Mira: I agree with that focus; enforcing those universal bounds is essential because it connects the specific holographic setup back to the underlying CFT physics we are trying to study.

Lev: And they propose an SSA Validator that uses geometric ratios derived from the duals to test if proposed entanglement calculations actually satisfy strong subadditivity, specifically flagging models where those finite contributions in non-crossing intervals might be missing.

The paper's improvements: Kai: Wrapping up on the conclusion of "Connecting boundary entropy and effective central charge at holographic interfaces," it seems they've successfully established that holographic entanglement entropy in interface CFTs has two intrinsically linked features: a finite boundary entropy contribution and this effective central charge.

Mira: They conclude that the interface entropy serves as a unified description of entanglement across all interval layouts, whether crossing or non-crossing, which is a significant achievement for characterizing defects in these systems.

Lev: For error correction research, the implication is that we now have a geometric tool to characterize how entanglement changes when you introduce spatial boundaries or interfaces into the system being simulated.

Kai: Precisely. The paper shows that this connection between boundary entropy and effective central charge is a key feature of these holographic systems, providing a unified way to look at them.

Mira: It suggests that understanding the precise nature of these interface effects might be necessary when trying to build more sophisticated topological phases in condensed matter.

Conclusion: Kai: So, to close out our discussion on "Connecting boundary entropy and effective central charge at holographic interfaces," we've seen how this framework provides a unified description of entanglement entropy across different interval layouts in interface CFTs.

Mira: The core message is that the finite boundary entropy contribution and the emergence of an effective central charge are fundamentally linked through holographic duals, offering a powerful tool for understanding boundaries and defects.

Lev: For us in error correction, this means we have a geometric quantity derived from bulk physics that relates directly to how entanglement evolves under specific constraints, which is something we need to explore further for hardware design.

Kai: I think the real impact here is providing a formal way to connect the geometry of the bulk spacetime—the warp factors and metrics—to universal entropic properties in the boundary theory.

Mira: That connection helps us understand how localized degrees of freedom manifest as quantifiable, measurable quantities in these complex systems.

Lev: I think the future work hinted at, looking for purely field-theoretic derivations for those boundary entropy limits, is where things get interesting for making this applicable to more general quantum many-body problems.

Department of Physics and Insituto de Ciencias y Tecnolog´ıas Especiales de Asturias (ICTEA), Universidad de Oviedo · Weinberg Institute, Department of Physics, University of Texas

hep-th, cond-mat.str-el

Submitted: 2025-07-12

Updated: 2026-10-07

Comments: 30 pages, 11 figures, v2: section 6.2 removed, finite contribution at infinity corrected, v3: new section 6.2 added, minor typos corrected

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Importance score: 86/100

The gist: The study connects boundary entropy and effective central charge at holographic interfaces by showing that modifications to entanglement entropy in interface conformal field theories (ICFTs) can be

Key concepts

Boundary Entropy: This is a finite contribution to entanglement entropy that exists even for intervals not crossing an interface. It is crucial for ensuring the strong subadditivity of entanglement entropy in these cases, indicating that interfaces introduce new physical degrees of freedom.
Effective Central Charge (ceff): When an interval endpoint lies at the interface, the coefficient of its logarithmic divergence in entanglement entropy changes to a value called ceff. This effective central charge is bounded by the original central charges and emerges as a limit of the interface entropy function.
Interface Entropy: This concept describes how entanglement entropy behaves differently for crossing versus non-crossing intervals, depending on whether they contain the interface. It provides a unified description of entanglement across various interval layouts in these systems.

Terminology

Entanglement — 53× in this paper · explained in 3 episodes
Entanglement Entropy — 41× in this paper · explained in 2 episodes
Generalization — 2× in this paper · explained in 13 episodes
Regularization — 2× in this paper · explained in 3 episodes
Consistency — 1× in this paper · explained in 3 episodes
Core — 1× in this paper · explained in 2 episodes
Degeneracy — 1× in this paper · explained in 3 episodes
Elias — 1× in this paper · explained in 2 episodes

Summary

The study connects boundary entropy and effective central charge at holographic interfaces by showing that modifications to entanglement entropy in interface conformal field theories (ICFTs) can be understood as limits of a finite boundary entropy contribution. This work is significant because it provides a unified description of entanglement entropy across different interval layouts and demonstrates how the effective central charge emerges from the limit of this interface entropy function.

Holographic Duals and Geodesics

The analysis utilizes holographic duals of ICFTs, specifically mentioning examples such as RS braneworlds, Janus solutions, and super Janus geometries. These dual geometries are typically described by three-dimensional metrics derived from ten-dimensional spacetimes involving compactification on a seven-dimensional internal manifold. The entanglement entropy is computed using the Ryu-Takayanagi prescription, which relates it to the area of minimal surfaces in the dual geometry, specifically length of geodesics ending at the interval endpoints on the boundary. The profile of these geodesics is determined by extremizing a functional involving a Lagrangian derived from the metric and warp factor.

Interface Entropy for Different Interval Types

The paper distinguishes between crossing intervals and non-crossing intervals based on whether they contain the interface. For crossing intervals, the entanglement entropy is given by an expression that includes terms proportional to log geff, which is identified as a finite contribution related to the boundary entropy number. For non-crossing intervals, a different form of interface entropy appears, necessary to ensure strong subadditivity of the entanglement entropy. The relationship between these two forms is established through the identity: log g(1) = log g(2) + c6 log 4lL/lR (1 + lL/lR) squared.

Effective Central Charge and Monotonicity

When an endpoint of an interval is at the interface, the coefficient of the logarithmic divergence is modified to an effective central charge ceff, which satisfies bounds like 0 ≤ cLR ≤ ceff ≤ min(cL, cR). The effective central charge emerges from a limit of the interface entropy function as one endpoint approaches zero distance from the interface. Furthermore, it is shown that this effective central charge and the interface entropy are directly related, with the latter emerging from a limit of the former.

Strong Subadditivity and C-Theorem

The Strong Subadditivity (SSA) condition for entanglement entropy requires a non-zero boundary entropy function even for intervals that do not cross the interface, implying that finite EE contributions are needed in these cases. The paper proves that log g(2) is a monotonically decreasing function of the ratio for both crossing and non-crossing intervals, which supports the entropic geff-theorem. This monotonicity is formalized by showing that Bg = d log g(2) / d log ρ is negative, leading to the conclusion that Ceff = -6Bg obeys a c-theorem, being a monotonically decreasing function of the ratio lL/lR.

Scheme-Independent Interface Entropy

The paper derives a scheme-independent definition of interface entropy by taking the difference between crossing and non-crossing interval EE in the limit where one endpoint hits the interface. This difference is found to be vanishing for Janus and super Janus geometries but non-zero for the RS braneworld construction, providing a scheme-independent definition of interface entropy. The final result shows that for crossing intervals, ceff = min(cL, cR), which is consistent with established bounds. For non-crossing intervals, the SSA condition requires that log g(2) must be monotonically decreasing with lL/lR faster than for crossing intervals.

Conclusion

The research demonstrates that holographic entanglement entropy in ICFTs possesses a finite boundary entropy contribution and an effective central charge, and these two features are intrinsically linked. The interface entropy provides a unified description of the EE across all interval layouts, serving as a key tool for characterizing defects and boundaries in these systems. The study also hints at future directions, such as finding purely field-theoretic derivations for boundary entropy limits and extending the concept of a c-theorem to RG flows at the interface.

The gist: The entanglement entropy of intervals in 1 + 1 interface CFTs is modified in two ways compared to a CFT without interface: there is a finite boundary entropy contribution, and, for an interval with an endpoint at the interface, the coefficient of the logarithmic divergent contribution-which is usually proportional to the central charge of the CFT- is modified to an effective central charge ceff. We show that the latter modification can be understood as a limit of the former using holographic duals of interface CFTs. Furthermore, we show that a finite contribution also appears in intervals that do not cross the interface and it is needed to ensure strong subbaditivity of the entanglement entropy.

How it works

Improvements for AI systems

As a fastidious and diligent researcher, I have analyzed this paper on holographic interfaces, entanglement entropy, and effective central charges in Interface Conformal Field Theories (ICFTs). The core contributions lie in providing a unified description of entanglement entropy across different interval configurations (crossing vs. non-crossing) and connecting the geometric properties of the bulk duals to universal quantities like the effective central charge.

Here are specific improvements for AI systems, categorized by capability:

)AI System Improvement Suggestions:

Capability Specific Improvement Detail

2.:---:---

Reasoning & Theory Integration (ICFT/Holography) Implement a Geometric Entanglement Mapping module that automatically derives the interface entropy function, log g(2), from input bulk metric parameters (e.g., warp factors, dilaton profiles). This system must be able to distinguish between crossing and non-crossing interval layouts based on the boundary conditions of the geodesic equations (3.4) and correctly apply the corresponding regularization schemes (3.9 vs 3.10).
Information Extraction & Universal Bounds Develop a Effective Central Charge Tracker that, given a CFT/ICFT description, can automatically calculate or predict the effective central charge, ceff, by analyzing the ratio of endpoint distances (lL/lR) and relating it to the minimal warp factor (eA∗). The system must enforce the hierarchy: ceff ≤ min(cL, cR), as derived in Section 5.1.
Strong Subadditivity Verification Create a SSA Validator that tests proposed entanglement entropy calculations against the SSA inequality (4.8) using the geometric ratios derived from holographic duals (e.g., comparing ρF′c and ρF′nc). This allows the system to automatically flag physical models where SSA is violated, specifically identifying when finite contributions in non-crossing intervals are necessary for consistency (4.5).
Limit Analysis & Scaling Behavior Implement a Limit Sensitivity Analyzer that specializes in the limits discussed in Section 5.1 and 5.2 (lL/lR → 0). This module must accurately predict the logarithmic divergence structure of the interface entropy, distinguishing between UV and IR contributions, and correctly calculate the scheme-independent finite contribution to the EE (log gi) using holographic examples like RS braneworlds where it is non-zero.
Model Comparison & Classification Build a Geometric Signature Classifier that uses the calculated scheme-independent interface entropy (log gi) as a diagnostic tool. This system can differentiate between physical duals:

:---:---

System Capabilities (Specific Outcomes) The improved AI system will be capable of:
Predictive Modeling for New Geometries Predicting the non-zero finite contribution to entanglement entropy (log gi) for novel holographic duals (e.g., specific Janus or super Janus parameterizations like those in Figures 7, 8, 9, 10) by calculating the integral in Section 5.20/5.23 and identifying geometric features like the minimal warp factor location (r∗).
RG Flow Characterization Developing a Ceff-Theorem Verifier that uses the derived relationship Ceff = -6Bg to characterize the evolution of entanglement entropy under geometric deformations (i.e., changes in lL/lR) within an ICFT, confirming its monotonicity against known constraints like Bg ≤ 0 (5.27).
Asymmetric Theory Handling Enabling the system to handle asymmetric ICFTs where cL ≠ cR by mapping the EE to a sum of BCFT contributions (6.1a/6.1b) and using the generalized geodesic equations (6.8a/b) that account for different AdS radii (RL, RR).

)Improved AI System Capabilities Summary:

The improved AI system will function as a specialized theoretical physics engine capable of:

Calculating entanglement entropy for ICFTs by mapping geometric bulk data to the interface entropy function, distinguishing between interval configurations.
Verifying physical consistency by checking Strong Subadditivity and predicting the necessity of finite contributions in non-crossing intervals.
Determining the effective central charge (ceff) based on geometric ratios and identifying its universal bounds against the bulk central charges.
Analyzing scaling limits (lL/lR → 0) to extract scheme-independent, finite entanglement entropy contributions that are absent in standard CFTs, providing a diagnostic tool for distinguishing between holographic duals (e.g., RS vs. Janus).
Characterizing the monotonicity of these entropic quantities using the pseudo-beta function Bg as a proxy for RG flow evolution within the ICFT context.