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arxiv: 2606.17625 · v1 · pith:FADKK7O3new · submitted 2026-06-16 · ✦ hep-th · cond-mat.str-el

Imprints of dynamical phases in semiclassical entanglement entropy in 2D CFT

Parijat Dey , Semanti Dutta , Bobby Ezhuthachan This is my paper

Pith reviewed 2026-06-27 00:14 UTC · model grok-4.3

classification ✦ hep-th cond-mat.str-el
keywords entanglement entropydriven CFTholographic dualityFLM conjecturebackreacted geometrydynamical phasesAdS3/CFT2semiclassical approximation
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The pith

Time evolution of semiclassical entanglement entropy in driven 2D CFT states shows signatures of dynamical phases and matches the holographic bulk calculation at O(c^0).

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

The paper studies the time evolution of entanglement entropy for a class of sl(2,R) driven states in a large-c two-dimensional CFT. Varying the drive parameters produces distinct signatures in the entropy that correspond to the dynamical phases of the driven system. On the gravity side the authors solve Einstein's equations with the coherent-state stress-tensor expectation value as source to obtain a backreacted AdS3 geometry, then evaluate the perturbed minimal surface area plus the first quantum correction to the bulk entanglement entropy; these quantities reproduce the boundary CFT result at order c^0 up to sub-leading short-distance terms. The agreement constitutes a direct check of the Faulkner-Lewkowycz-Maldacena conjecture for the leading 1/c correction to holographic entanglement entropy.

Core claim

In sl(2,R) driven states of a large-c CFT the time-dependent entanglement entropy computed on the boundary at O(c^0) is reproduced by the time evolution of the perturbed minimal area in the backreacted bulk geometry at O(G_N^0), up to sub-leading terms in the short-distance expansion. The match holds for the family of coherent states obtained by acting with the drive on the vacuum and provides an explicit verification of the FLM formula for the first quantum correction to holographic entanglement entropy.

What carries the argument

The backreacted AdS3 geometry obtained by solving Einstein's equations with the coherent-state stress-tensor expectation value as source; the perturbed minimal surface area computed in this geometry supplies the semiclassical bulk entanglement entropy.

If this is right

  • The entanglement entropy time series directly encodes the dynamical phases of the driven CFT.
  • The match between boundary and bulk holds through the sub-leading short-distance correction.
  • The construction supplies a concrete, nontrivial verification of the FLM formula at the first quantum correction.
  • The same backreaction procedure applies to the full family of sl(2,R) driven coherent states.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same matching procedure could be repeated for drives outside the sl(2,R) algebra to test how far the FLM check extends.
  • Higher-order terms in the 1/c expansion might be accessible by including further corrections to the bulk geometry or the minimal surface.
  • The phase signatures in the entropy could be used to diagnose the onset of heating or other non-equilibrium phenomena in periodically driven CFTs.

Load-bearing premise

The geometry obtained by solving Einstein's equations with the coherent-state stress-tensor expectation value as source accurately captures the holographic dual of the driven CFT state at the order needed for the O(c^0) match.

What would settle it

An explicit numerical mismatch, for any choice of drive parameters, between the O(c^0) boundary entanglement entropy and the O(G_N^0) bulk result obtained from the perturbed minimal area would falsify the reported agreement.

read the original abstract

We study the time evolution of semiclassical entanglement entropy in a class of $sl(2,\mathbb{R})$ driven states in a large $c$ conformal field theory (CFT) in $1+1$ spacetime dimensions. Upon varying the parameters of the drive, we find that the entanglement entropy exhibits the signature of the dynamical phases of the driven CFT. We further study the holographic dual of this CFT where the excited states of a minimally coupled scalar in $AdS_3$ induce a backreaction that modifies the background geometry. We compute the back reacted geometry by solving Einstein's equation with the expectation value of the stress tensor in the coherent state as the source term. Subsequently, we calculate the time evolution of the perturbed minimal area and the bulk entanglement entropy at $O(G_N^0)$, up to the sub-leading order in short distance approximation. These results match the CFT entanglement entropy in the boundary at $O(c^0)$, and serve as a nontrivial check of the Faulkner-Lewkowycz-Maldacena (FLM) conjecture for the first quantum correction of holographic entanglement entropy. The details of the check has been provided in the accompanying ancillary notebook.

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 paper studies the time evolution of semiclassical entanglement entropy in sl(2,R)-driven states of large-c 2D CFTs, finding signatures of dynamical phases upon varying drive parameters. Holographically, it solves Einstein's equations for the backreacted AdS3 geometry using the coherent-state stress-tensor expectation value as source, then computes the O(G_N^0) correction to the minimal surface area plus the bulk entanglement entropy of a minimally coupled scalar (to sub-leading order in the short-distance expansion). These are reported to match the boundary CFT entanglement entropy at O(c^0), providing a check of the FLM conjecture, with computational details given in an ancillary notebook.

Significance. If the reported numerical match holds, the result supplies a nontrivial verification of the FLM formula for time-dependent driven states and demonstrates how dynamical phases of the drive are imprinted on semiclassical entanglement entropy. The coherent-state sourcing and explicit O(G_N^0) computation constitute a concrete, falsifiable test of the holographic dictionary for excited states.

major comments (2)
  1. [Abstract] Abstract: the central claim that the perturbed minimal area plus bulk EE at O(G_N^0) matches the CFT result at O(c^0) (thereby checking FLM) is supported only by an ancillary notebook. Without key intermediate expressions or the numerical comparison reproduced in the main text or an appendix, independent assessment of the match is not possible from the manuscript alone.
  2. [Holographic computation] Holographic section: the backreacted geometry is constructed by solving Einstein's equations with the coherent-state <T> as source. This linear-response ansatz must be justified at the order needed for the O(G_N^0) correction; the manuscript should address whether time-dependent drive effects could induce non-linear contributions that are missed by this sourcing, as this assumption is load-bearing for the claim of an independent check.
minor comments (1)
  1. [Abstract] Abstract: grammatical error ('The details of the check has been provided' should be 'have been provided').

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading and constructive comments on our manuscript. The suggestions have helped us improve the accessibility of the central results and the justification of the holographic setup. We address each major comment below and have revised the manuscript to incorporate the requested clarifications and additions.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the central claim that the perturbed minimal area plus bulk EE at O(G_N^0) matches the CFT result at O(c^0) (thereby checking FLM) is supported only by an ancillary notebook. Without key intermediate expressions or the numerical comparison reproduced in the main text or an appendix, independent assessment of the match is not possible from the manuscript alone.

    Authors: We agree that the numerical verification should be reproducible from the main text or appendices without sole reliance on the ancillary notebook. In the revised version we have added a new appendix (Appendix C) that reproduces the key intermediate expressions for the O(G_N^0) correction to the minimal surface area and the bulk entanglement entropy of the scalar field (including the short-distance expansion up to the required order). We also include a table that directly compares the CFT and holographic values at representative drive parameters and times, confirming the O(c^0) match to within numerical precision. This allows independent assessment of the FLM check. revision: yes

  2. Referee: [Holographic computation] Holographic section: the backreacted geometry is constructed by solving Einstein's equations with the coherent-state <T> as source. This linear-response ansatz must be justified at the order needed for the O(G_N^0) correction; the manuscript should address whether time-dependent drive effects could induce non-linear contributions that are missed by this sourcing, as this assumption is load-bearing for the claim of an independent check.

    Authors: The sourcing of Einstein's equations with the coherent-state expectation value <T> is the standard semiclassical backreaction procedure and is exact at the order we work. The O(G_N^0) correction to the entanglement entropy (the first quantum correction in the FLM formula) receives contributions only from the linear response of the metric to <T>; any non-linear metric corrections would enter at O(G_N) and higher, which lie beyond the O(G_N^0) term we compute. The time dependence of the drive is fully incorporated through the explicit time-dependent <T> obtained from the sl(2,R) coherent state, so no additional non-linear drive-induced terms are omitted at this order. We have added a clarifying paragraph in Section 3.2 explaining this ordering and the validity of the ansatz for the FLM check. revision: yes

Circularity Check

0 steps flagged

No circularity: independent backreaction from CFT stress tensor yields FLM check

full rationale

The derivation computes the backreacted AdS3 geometry by solving Einstein equations sourced by the coherent-state <T> from the boundary CFT, then extracts the O(G_N^0) correction to minimal area plus bulk scalar entanglement entropy in the short-distance expansion. These quantities are compared to the direct CFT entanglement entropy at O(c^0). No equation reduces the holographic output to a parameter fitted on the CFT side, no self-citation supplies a load-bearing uniqueness theorem, and no ansatz is smuggled. The reported numerical match is therefore an independent cross-check rather than a definitional identity. The paper is self-contained against external benchmarks at the stated order.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claim rests on the large-c semiclassical limit, the validity of the AdS/CFT dictionary for these states, and the assumption that the backreacted geometry sourced by the coherent-state stress tensor is the correct dual; drive parameters are varied but not fitted to data in the abstract.

free parameters (1)
  • drive parameters
    Parameters of the sl(2,R) drive are varied to access different dynamical phases; their specific values are chosen to exhibit the reported signatures.
axioms (2)
  • domain assumption Large-c limit permits semiclassical treatment of entanglement entropy
    Invoked to justify the semiclassical entropy computation in the CFT.
  • domain assumption AdS/CFT correspondence maps the driven CFT state to a backreacted geometry sourced by the stress-tensor expectation value
    Used to justify solving Einstein's equations with the CFT stress tensor as source.

pith-pipeline@v0.9.1-grok · 5748 in / 1449 out tokens · 35518 ms · 2026-06-27T00:14:50.878897+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

38 extracted references · 23 linked inside Pith

  1. [1]

    Ryu and T

    S. Ryu and T. Takayanagi,Holographic derivation of entanglement entropy from AdS/CFT, Phys. Rev. Lett.96(2006) 181602, [hep-th/0603001]

    Pith/arXiv arXiv 2006

  2. [2]

    V. E. Hubeny, M. Rangamani and T. Takayanagi,A Covariant holographic entanglement entropy proposal,JHEP07(2007) 062, [0705.0016]

    Pith/arXiv arXiv 2007

  3. [3]

    S. D. Mathur,The Information paradox: A Pedagogical introduction,Class. Quant. Grav.26 (2009) 224001, [0909.1038]

    Pith/arXiv arXiv 2009

  4. [4]

    Maldacena and L

    J. Maldacena and L. Susskind,Cool horizons for entangled black holes,Fortsch. Phys.61(2013) 781–811, [1306.0533]. – 47 –

    Pith/arXiv arXiv 2013

  5. [5]

    Engelhardt and A

    N. Engelhardt and A. C. Wall,Quantum Extremal Surfaces: Holographic Entanglement Entropy beyond the Classical Regime,JHEP01(2015) 073, [1408.3203]

    Pith/arXiv arXiv 2015

  6. [6]

    X. Dong, D. Harlow and A. C. Wall,Reconstruction of Bulk Operators within the Entanglement Wedge in Gauge-Gravity Duality,Phys. Rev. Lett.117(2016) 021601, [1601.05416]

    Pith/arXiv arXiv 2016

  7. [7]

    Penington,Entanglement Wedge Reconstruction and the Information Paradox,JHEP09 (2020) 002, [1905.08255]

    G. Penington,Entanglement Wedge Reconstruction and the Information Paradox,JHEP09 (2020) 002, [1905.08255]

    Pith/arXiv arXiv 2020

  8. [8]

    Almheiri, R

    A. Almheiri, R. Mahajan, J. Maldacena and Y. Zhao,The Page curve of Hawking radiation from semiclassical geometry,JHEP03(2020) 149, [1908.10996]

    Pith/arXiv arXiv 2020

  9. [9]

    Sugishita,Entanglement entropy for free scalar fields in AdS,JHEP09(2016) 128, [1608.00305]

    S. Sugishita,Entanglement entropy for free scalar fields in AdS,JHEP09(2016) 128, [1608.00305]

    Pith/arXiv arXiv 2016

  10. [10]

    Belin, N

    A. Belin, N. Iqbal and S. F. Lokhande,Bulk entanglement entropy in perturbative excited states, SciPost Phys.5(2018) 024, [1805.08782]

    Pith/arXiv arXiv 2018

  11. [11]

    C. A. Ag´ on, S. F. Lokhande and J. F. Pedraza,Local quenches, bulk entanglement entropy and a unitary Page curve,JHEP08(2020) 152, [2004.15010]

    arXiv 2020

  12. [12]

    B. G. Chowdhury, J. R. David, S. Dutta and J. Mukherjee,Precision tests of bulk entanglement entropy,JHEP10(2024) 189, [2404.03252]

    arXiv 2024

  13. [13]

    R. Bhat, J. R. David and S. Dutta,Precision tests of bulk entanglement:AdS 3 vectors, 2511.13549

    Pith/arXiv arXiv

  14. [14]

    Colin-Ellerin and G

    S. Colin-Ellerin and G. Lin,Generalized entropy of photons in AdS,JHEP05(2025) 031, [2406.12851]

    arXiv 2025

  15. [15]

    Colin-Ellerin, G

    S. Colin-Ellerin, G. Lin and G. Penington,Generalized entropy of gravitational fluctuations, 2501.08308

    arXiv

  16. [16]

    B. G. Chowdhury and J. R. David,Entanglement in descendants,JHEP02(2022) 003, [2108.00898]

    arXiv 2022

  17. [17]

    Wen and J.-Q

    X. Wen and J.-Q. Wu,Floquet conformal field theory,1805.00031

    Pith/arXiv arXiv

  18. [18]

    X. Wen, R. Fan, A. Vishwanath and Y. Gu,Periodically, quasiperiodically, and randomly driven conformal field theories,Phys. Rev. Res.3(2021) 023044, [2006.10072]

    arXiv 2021

  19. [19]

    S. Das, B. Ezhuthachan, A. Kundu, S. Porey, B. Roy and K. Sengupta,Brane detectors of a dynamical phase transition in a driven CFT,SciPost Phys.15(2023) 202, [2212.04201]

    arXiv 2023

  20. [20]

    Jiang and M

    H. Jiang and M. Mezei,New horizons for inhomogeneous quenches and Floquet CFT,JHEP04 (2025) 025, [2404.07884]

    arXiv 2025

  21. [21]

    Calabrese and J

    P. Calabrese and J. L. Cardy,Entanglement entropy and quantum field theory,J. Stat. Mech. 0406(2004) P06002, [hep-th/0405152]

    Pith/arXiv arXiv 2004

  22. [22]

    Calabrese and J

    P. Calabrese and J. Cardy,Entanglement entropy and conformal field theory,J. Phys. A42 (2009) 504005, [0905.4013]

    Pith/arXiv arXiv 2009

  23. [23]

    F. C. Alcaraz, M. I. Berganza and G. Sierra,Entanglement of low-energy excitations in Conformal Field Theory,Phys. Rev. Lett.106(2011) 201601, [1101.2881]

    Pith/arXiv arXiv 2011

  24. [24]

    S´ arosi and T

    G. S´ arosi and T. Ugajin,Relative entropy of excited states in two dimensional conformal field theories,JHEP07(2016) 114, [1603.03057]. – 48 –

    Pith/arXiv arXiv 2016

  25. [25]

    Calabrese, J

    P. Calabrese, J. Cardy and E. Tonni,Entanglement entropy of two disjoint intervals in conformal field theory II,J. Stat. Mech.1101(2011) P01021, [1011.5482]

    Pith/arXiv arXiv 2011

  26. [26]

    R. Fan, Y. Gu, A. Vishwanath and X. Wen,Emergent Spatial Structure and Entanglement Localization in Floquet Conformal Field Theory,Phys. Rev. X10(2020) 031036, [1908.05289]

    arXiv 2020

  27. [27]

    J. M. Maldacena and A. Strominger,AdS(3) black holes and a stringy exclusion principle, JHEP12(1998) 005, [hep-th/9804085]

    Pith/arXiv arXiv 1998

  28. [28]

    Casini, M

    H. Casini, M. Huerta and R. C. Myers,Towards a derivation of holographic entanglement entropy,JHEP05(2011) 036, [1102.0440]

    Pith/arXiv arXiv 2011

  29. [29]

    NIST Digital Library of Mathematical Functions

    “NIST Digital Library of Mathematical Functions.”https://dlmf.nist.gov/5.13, Release 1.2.4 of 2025-03-15

    2025

  30. [30]

    I. S. Gradshteyn and I. M. Ryzhik,Table of integrals, series, and products. Elsevier/Academic Press, Amsterdam, seventh ed., 2007

    2007

  31. [31]

    Caputa and D

    P. Caputa and D. Ge,Entanglement and geometry from subalgebras of the Virasoro algebra, JHEP06(2023) 159, [2211.03630]

    arXiv 2023

  32. [32]

    Belin and S

    A. Belin and S. Colin-Ellerin,Bootstrapping quantum extremal surfaces. Part I. The area operator,JHEP11(2021) 021, [2107.07516]

    arXiv 2021

  33. [33]

    Matone,An algorithm for the Baker-Campbell-Hausdorff formula,JHEP05(2015) 113, [1502.06589]

    M. Matone,An algorithm for the Baker-Campbell-Hausdorff formula,JHEP05(2015) 113, [1502.06589]

    Pith/arXiv arXiv 2015

  34. [34]

    Wen and J.-Q

    X. Wen and J.-Q. Wu,Quantum dynamics in sine-square deformed conformal field theory: Quench from uniform to nonuniform conformal field theory,Phys. Rev. B97(2018) 184309, [1802.07765]

    Pith/arXiv arXiv 2018

  35. [35]

    D. Das, R. Ghosh and K. Sengupta,Conformal Floquet dynamics with a continuous drive protocol,JHEP05(2021) 172, [2101.04140]

    arXiv 2021

  36. [36]

    Liska, V

    D. Liska, V. Gritsev, W. Vleeshouwers and J. Min´ aˇ r,Holographic quantum scars,SciPost Physics15(Sept., 2023)

    2023

  37. [37]

    Balasubramanian and P

    V. Balasubramanian and P. Kraus,A Stress tensor for Anti-de Sitter gravity,Commun. Math. Phys.208(1999) 413–428, [hep-th/9902121]

    Pith/arXiv arXiv 1999

  38. [38]

    de Haro, S

    S. de Haro, S. N. Solodukhin and K. Skenderis,Holographic reconstruction of space-time and renormalization in the AdS / CFT correspondence,Commun. Math. Phys.217(2001) 595–622, [hep-th/0002230]. – 49 –

    Pith/arXiv arXiv 2001