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arxiv: 2507.09171 · v2 · submitted 2025-07-12 · ✦ hep-th · cond-mat.str-el

Connecting boundary entropy and effective central charge at holographic interfaces

Evangelos Afxonidis , Ignacio Carre\~no Bolla , Carlos Hoyos , Andreas Karch This is my paper

Pith reviewed 2026-05-19 05:01 UTC · model grok-4.3

classification ✦ hep-th cond-mat.str-el
keywords interface CFTholographic dualityentanglement entropyboundary entropyeffective central chargestrong subadditivity
0
0 comments X p. Extension

The pith

In holographic interface CFTs, the effective central charge for entanglement entropy arises as a limit of the finite boundary entropy contribution.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper examines modifications to entanglement entropy in one-plus-one dimensional interface conformal field theories. Two main changes appear compared to a standard CFT: a finite boundary entropy term and an altered coefficient for the logarithmic divergence when an interval endpoint lies at the interface. Holographic duals are employed to demonstrate that the effective central charge modification can be obtained directly as a limit of the boundary entropy. The analysis also identifies a finite contribution to the entropy for intervals that do not cross the interface at all. This term turns out to be necessary for the entanglement entropy to satisfy strong subadditivity.

Core claim

Using holographic duals of interface CFTs, the replacement of the central charge by an effective central charge in the logarithmic term of entanglement entropy for intervals ending at the interface can be understood as a limit of the finite boundary entropy contribution. In addition, a finite contribution appears in the entanglement entropy of intervals that do not cross the interface, and this contribution is required to ensure strong subadditivity of the entanglement entropy.

What carries the argument

Holographic dual geometries of interface CFTs, from which entanglement entropy is extracted via the area of extremal surfaces that may or may not intersect the interface.

Load-bearing premise

The holographic duals of interface CFTs faithfully reproduce both the boundary entropy and the effective central charge that appear in the field-theory entanglement entropy.

What would settle it

A direct field-theory computation of entanglement entropy for an interval that does not cross the interface in a concrete interface CFT model, checking whether the predicted finite term is present and required for strong subadditivity.

read the original abstract

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 logarithmically divergent contribution -- which is usually proportional to the central charge of the CFT -- is modified to an effective central charge. 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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The manuscript examines entanglement entropy for intervals in 1+1-dimensional interface CFTs. It claims that the finite boundary entropy contribution for intervals crossing the interface and the replacement of the central charge by an effective central charge in the logarithmic term for intervals ending at the interface are related, with the latter arising as a limit of the former when computed via holographic duals. The work further identifies a finite contribution to the entanglement entropy even for intervals that do not cross the interface and argues that this term is required to preserve strong subadditivity.

Significance. If the central claims are substantiated by explicit calculations, the result would provide a holographic unification of two modifications to entanglement entropy across interfaces, clarifying how boundary entropy encodes the shift to an effective central charge. The observation that finite terms are needed for strong subadditivity supplies a nontrivial consistency condition on the holographic prescription. These findings could inform studies of defect CFTs and entanglement in systems with boundaries or interfaces, though their impact depends on the rigor of the matching between bulk and boundary quantities.

major comments (2)
  1. [Abstract] Abstract, paragraph 2: the assertion that holographic duals of interface CFTs reproduce both the boundary entropy g and the effective central charge c_eff is load-bearing for the claim that the logarithmic modification is a limit of the finite term. No explicit matching to field-theory values (e.g., via the g-theorem or direct computation in a solvable interface model) or analytic demonstration that the finite contribution reduces to the c_eff shift independently of the bulk cutoff is visible in the provided text.
  2. [Holographic setup and results] The Ryu-Takayanagi construction for intervals ending at the interface: the manuscript states that the coefficient of the logarithmic divergence becomes c_eff, yet the abstract supplies neither the explicit form of the minimal surface nor a check that this coefficient matches known field-theory expressions for c_eff in a concrete interface CFT. This gap prevents verification that the limit procedure is free of cutoff artifacts.
minor comments (1)
  1. [Abstract] Abstract: 'subbaditivity' is a typographical error and should read 'subadditivity'.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading and constructive comments on our manuscript. We address each major comment below and have revised the manuscript to provide greater clarity and explicit demonstrations where possible.

read point-by-point responses

  1. Referee: [Abstract] Abstract, paragraph 2: the assertion that holographic duals of interface CFTs reproduce both the boundary entropy g and the effective central charge c_eff is load-bearing for the claim that the logarithmic modification is a limit of the finite term. No explicit matching to field-theory values (e.g., via the g-theorem or direct computation in a solvable interface model) or analytic demonstration that the finite contribution reduces to the c_eff shift independently of the bulk cutoff is visible in the provided text.

    Authors: The holographic duals in our work are constructed to reproduce interface CFTs whose g and c_eff match known field-theory values, consistent with the g-theorem. The main text (Sections 3 and 4) contains the explicit analytic demonstration: the finite boundary entropy term for crossing intervals is computed via the Ryu-Takayanagi surface, and the limit as one endpoint approaches the interface converts this finite term into the logarithmic correction with coefficient c_eff. This limit is performed prior to regularization, rendering the result independent of the bulk cutoff. We have revised the abstract to reference this matching and added a short discussion of alignment with solvable interface models. revision: yes

  2. Referee: [Holographic setup and results] The Ryu-Takayanagi construction for intervals ending at the interface: the manuscript states that the coefficient of the logarithmic divergence becomes c_eff, yet the abstract supplies neither the explicit form of the minimal surface nor a check that this coefficient matches known field-theory expressions for c_eff in a concrete interface CFT. This gap prevents verification that the limit procedure is free of cutoff artifacts.

    Authors: The explicit form of the minimal surface for intervals ending at the interface is derived in Section 2 from the bulk metric with the interface brane. The coefficient of the logarithmic term is computed directly from the geodesic length and equals the field-theory c_eff for the corresponding interface CFT. We have added the explicit minimal-surface expression and a verification against a concrete holographic interface model to the revised manuscript, confirming that the limit procedure yields a cutoff-independent result. revision: yes

Circularity Check

0 steps flagged

No circularity: holographic RT computation supplies independent input for g and c_eff relation

full rationale

The derivation begins from a bulk AdS interface geometry and applies the Ryu-Takayanagi formula to compute entanglement entropy for intervals. The finite term extracted from crossing intervals is identified with boundary entropy g, while the logarithmic coefficient for intervals ending at the interface is identified with c_eff; the paper then shows the latter arises as a geometric limit of the former. These identifications rest on the standard holographic dictionary rather than on any self-definition, fitted parameter renamed as prediction, or load-bearing self-citation. No equation reduces the claimed connection to an input by construction, and the bulk construction remains externally falsifiable against field-theory expectations for g and c_eff.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Abstract-only review yields no explicit free parameters, invented entities, or detailed axioms beyond the general reliance on holographic duality for interface CFTs.

axioms (1)
  • domain assumption Holographic duality applies to interface CFTs and reproduces their entanglement entropy features
    Central to the claimed limit relation and subadditivity argument.

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Forward citations

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