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Holographic Timelike Entanglement Entropy in Non-relativistic Theories

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Pith's one-line read Holographic timelike entanglement entropy is shown to encode both the stability of non-relativistic theories and the presence of Fermi surfaces through a logarithmic real part and a constant imaginary part.

desk verdict The Fermi-surface signature and all quantitative prefactors rest on displayed EOMs that are the reciprocals of those following from the paper's own action; treat the numbers as unverified until the integrals are redone. read the letter →

arxiv 2411.18514 v1 pith:2AOW5YFZ submitted 2024-11-27 hep-th

Mir Afrasiar , Jaydeep Kumar Basak , Dimitrios Giataganas This is my paper · ORCID
classification hep-th
keywords timelikeentanglemententropyhyperscalingviolationLifshitzholographyFermisurfacepseudoentropynullenergyconditiontemporalholographic
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

This paper tries to establish that timelike entanglement entropy (tEE), a complex-valued information measure defined holographically by combining spacelike and timelike extremal surfaces, is a sharp probe of non-relativistic physics. In theories with Lifshitz-like anisotropy or hyperscaling violation, both the real and imaginary parts of tEE depend on the symmetry-breaking exponents $z$ and $\theta$ in a calculable way. The paper derives closed-form expressions for these parts and shows that they encode whether the theory is stable: demanding natural behavior of the tEE restricts the parameter space to almost exactly the region allowed by the null energy condition and thermodynamic stability. It also proposes a Fermi-surface diagnosis: at $\theta=d-2$ the real part violates the area law logarithmically, with coefficient $2/z$, and the imaginary part becomes the constant $i\pi/z$. If correct, this gives a holographic observable that can flag both stability and the presence of Fermi surfaces, and it gives the imaginary part of tEE a physical meaning beyond its role in conformal theories.

What carries the argument

The load-bearing object is the conjectured holographic identification of tEE with the area of the union of one spacelike and one timelike extremal surface that are homologous to a timelike boundary interval of length $T$; the finite interval itself is defined as $T = T_{Im} - T_{Re}$ after removing the common IR divergence. The technical tools are the equation of motion for the embedding function $t(r)$, the gradient normal vector field whose squared norm and orthogonality measures $|I_1|^2$ and $|I_2|^2$ decide where surfaces are spacelike, timelike, or null, and a parameter-space classification of which surface types occur as $z$ and $\theta$ vary. These tools let the authors compute both components of tEE analytically and correlate the conformal-like surface behavior with the null energy condition and thermodynamic stability.

What would settle it

Compute the transition-matrix pseudoentropy directly in a (1+1)-dimensional Lifshitz scalar theory with $\theta=d-2$: the holographic prediction is $\mathrm{Re}(S)=(2/z)\log(zT/\epsilon)$ and $\mathrm{Im}(S)=i\pi/z$. Any independent field-theoretic or lattice result with a different log coefficient or imaginary constant would falsify the identification, while agreement would support it.

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Extended reading notes

Core claim

For a strip-like timelike interval of length $T$ in a hyperscaling-violating bulk, the paper claims the finite tEE is $$\frac{4G_N}{$L^{{d-2}}$}\hat S^T_{Re} = -f(\gamma)\sec(\pi\gamma)\, $z^{{-\frac{d-2+z-\theta}}${z}}\left(\frac{1}{T}\right)^{\frac{d-2-\$\theta$}{z}}, \qquad \frac{4G_N}{$L^{{d-2}}$}\hat S^T_{Im} = i f(\gamma)\, $z^{{-\frac{d-2+z-\theta}}${z}}\left(\frac{1}{T}\right)^{\frac{d-2-\$\theta$}{z}},$$ with $\gamma = z/[2(d-2+z-\theta)]$ and a constant $f(\gamma)$ fixed by the dimension and exponents; the two parts are related by $\hat S_{Re}=i\sec(\pi\gamma)\hat S_{Im}$. When $\theta=d-2$ these formulas must be treated separately, and the paper obtains $$\frac{4G_N}{$L^{{d-2}}$}\tilde S^T_{Re} = \frac{2}{z}\log\left(\frac{zT}{\tilde\epsilon}\right), \qquad \frac{4G_N}{$L^{{d-2}}$}\tilde S^T_{Im} = \frac{i\pi}{z},$$ which it reads as the tEE signature of a Fermi surface. Throughout, the sign of $d-2+z-\theta$ controls whether the timelike extremal surface extends to the deep IR or back to the boundary, and the paper shows that the parameter regions where the tEE surfaces look like conformal ones coincide with the NEC-plus-stability region. It further claims that in the large-dimension limit the real and imaginary parts become equal in magnitude, and that the temporal entanglement entropy, the Euclidean-signature cousin, shows the same logarithmic Fermi-surface behavior.

Load-bearing premise

The load-bearing premise is that the holographic area formula for timelike entanglement entropy, the union of spacelike and timelike extremal surfaces, actually computes the quantity; this equality has been confirmed only in (2+1)-dimensional theories, so the higher-dimensional results, including the Fermi-surface signatures, rest on an unproven equivalence.

Editorial extensions

If this is right

  • For hyperscaling-violating theories, tEE scales as $T^{-(d-2-\theta)/z}$; at $\theta=d-2$ the real part obeys a logarithmic area-law violation while the imaginary part is the constant $i\pi/z$, giving two independent Fermi-surface signatures.
  • Requiring the tEE to decrease monotonically with the interval and its surfaces to behave like conformal ones restricts $(z,\theta)$ to almost exactly the parameter region fixed by the NEC and thermodynamic stability, so tEE doubles as a stability diagnostic.
  • In spatially anisotropic Lifshitz-like theories, both parts of tEE depend on which spatial direction the strip is localized along, with exponents $d-3+1/z$ versus $d-2$, making tEE more sensitive to Lorentz breaking than entanglement entropy.
  • In the large-dimension limit the real and imaginary parts of tEE become equal in magnitude in all the theories studied, a property the paper argues is universal.
  • The Euclidean temporal entanglement entropy reproduces the same Fermi-surface logarithmic law at $\theta=d-2$ and equals the real part of tEE there, providing a consistency check.

Reading between the lines

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

  • Editorial inference: if the holographic tEE conjecture holds beyond (2+1) dimensions, the constant imaginary part $i\pi/z$ becomes a practical diagnostic: a finite imaginary pseudoentropy in a system with Lifshitz scaling would indicate a Fermi surface without needing to resolve the Fermi surface itself.
  • Editorial inference: the same $\theta=d-2$ computation could be tested in free-fermion lattice models with anisotropic hopping, where the transition-matrix pseudoentropy can be computed directly; agreement with $(2/z)\log(zT/\epsilon)$ would support the conjecture, while disagreement would localize where it breaks.
  • Editorial inference: the near-identity between natural tEE surfaces and the NEC-plus-stability region suggests tEE could serve as a cheap holographic screening criterion for proposed gravity duals of condensed-matter systems, since an extremal-surface calculation is easier than solving the full field equations.
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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 / 4 minor

Summary. The paper studies holographic timelike entanglement entropy (tEE) in non-relativistic holographic theories with Lifshitz-like spatial anisotropy and hyperscaling violation. The authors derive extremal-surface equations for spacelike and timelike surfaces, classify surface behavior, compute analytic expressions for the real and imaginary parts of tEE, and propose that tEE can probe stability, naturalness, and the presence of Fermi surfaces. They also compute temporal entanglement entropy in the Euclidean continuation. The claimed results include explicit scaling forms in Eqs. (4.22) and (4.24), a logarithmic Fermi-surface signature Re(S)=(2/z)log(zT/epsilon) and constant imaginary part i pi/z at theta=d-2, and analogous results for anisotropic Lifshitz theories.

Significance. If correct, the paper would provide a systematic holographic characterization of timelike entanglement entropy outside Lorentz-invariant settings, with concrete parameter dependence on the Lifshitz exponent z and hyperscaling-violation exponent theta. It would also give a new Fermi-surface diagnostic through the imaginary part of tEE. The manuscript contains extensive analytic formulas, consistency checks against known AdS results, and a detailed surface classification. However, the main quantitative results are derived from displayed equations of motion that are internally inconsistent with the stated surface properties; as submitted, the central numbers are not supported.

major comments (3)
  1. [§4.1.1, Eq. (4.5)] Equation (4.5) is not the EOM following from the generic expression (2.3) for the hyperscaling-violating metric (4.1). Substituting (4.1) into (2.3) for a strip with one x-direction fixed gives t'^2 = r^{2(z-1)}/[1+s(r0/r)^{2ν}] with ν=d-2+z-theta, whereas (4.5) gives t'^2 = r^{2(z-1)}[1+s(r0/r)^{2ν}]. These are reciprocals. In particular, for s=-1 the displayed form gives t'_Im(r0)=0, while §2.1 and the Figure 5 caption require t'_Im(r0)=∞. Since Eqs. (4.18)-(4.24) are obtained by integrating (4.5), the quantitative results (4.22), (4.24), and the Fermi-surface limit (4.29) are unverified.
  2. [§3.1.1, Eq. (3.3)] The same reciprocal error appears in the y-localized anisotropic Lifshitz computation. For the metric (3.1), substituting into (2.3) places the factor [1+s(r0/r)^{2(d-1)z}] in the denominator of t'^2, whereas (3.3) has it in the numerator. The displayed t'_Im(r0)=0 contradicts the boundary condition t'_Im(r0)=∞ stated for timelike surfaces in §2.1. Consequently, the subsystem lengths (3.11)-(3.12) and the areas (3.15)-(3.16) are derived from the wrong equation of motion; although the final AdS-equivalence result may be independently true by symmetry, the printed derivation does not establish it.
  3. [§3.2.1, Eq. (3.19)] For the x1-localized strip there is an additional exponent error beyond the reciprocal issue. With the conventions of §2 and the metric (3.1), the transverse factor for a strip with one x-direction fixed is gxx^{d-3} (the y direction is unwarped), so gtt gxx^{d-3} = -r^{-2z(d-2)}. Equation (2.3) then gives t'^2 = r^{2z-2}/[1+s(r0/r)^{2z(d-2)}], not the expression in (3.19) with exponent 2(d-2)z+2. As a result, the parameter β below (3.25), the scaling law (3.24), and all formulas (3.27)-(3.31) are not consequences of the stated metric and need to be recalculated.
minor comments (4)
  1. [§2.1, Eq. (2.3)] The constant c^2 is introduced before C^2 is defined; reordering these definitions would improve readability.
  2. [§3.1.3, Eqs. (3.11)-(3.12)] The cutoff ϵ1 is introduced as an IR regulator, but the explicit divergent terms are not displayed; please state the cutoff prescription used to obtain the quoted finite parts.
  3. [§4.1.1, around Eq. (4.9)] The text repeatedly refers to a 'monotonically decreasing norm' of tEE, but tEE is complex; please specify whether the statement concerns Re(S), |S|, or some other quantity.
  4. [Appendix A, Eq. (A.5)] The text has a typo: 'were k(r) := d1A1(r)+d2A2(r)' should read 'where k(r) := ...'.

Circularity Check

0 steps flagged · score 2.0 of 10

No circular reduction identified: the tEE results are analytic integrals of the stated area functional, and the few self-citations serve as conventions or consistency checks rather than load-bearing inputs.

full rationale

The central quantities in this paper are obtained by solving the Euler–Lagrange equations (2.3) derived from the area functional (2.2) for the hyperscaling-violating metric (4.1) and the anisotropic Lifshitz metric (3.1), then subtracting the disconnected IR-divergent pieces as described in Section 2.1. The finite-interval prescription T = T_Im − T_Re is introduced as a definition following [21,23] and is stated as such ('As in [23], at the IR region r → ∞, the extremal surfaces contributing to the real and imaginary parts of the tEE satisfies t′_Re(∞) = t′_Im(∞)... then the total subsystem length at the boundary r → 0 is T = TIm − TRe'); this is a convention adopted from the tEE framework, not a quantity fitted to the paper's own outputs, and the same prescription appears in the external reference [21]. The Fermi-surface analysis in Section 4.1.4 applies an established area-law log-violation criterion to the computed Re(S) and derives Im(S) = iπ/z as an integral result; it does not define the theory parameters in terms of the conclusion. The self-citations to [23] (subtraction scheme) and [36] (Lifshitz field-theory comparison) are used as consistency checks and are not load-bearing: the final expressions (4.22), (4.24), and (4.29) are analytic integrals of the displayed equations of motion with no fitted parameters. The paper also explicitly flags the main limitation: the holographic tEE conjecture 'has been confirmed in (2 + 1)-dimensional theories [21]', so the higher-dimensional results are conditional on that conjecture; this is an acknowledged external assumption rather than a circular step. No equation is defined in terms of the claimed prediction, and no fitted quantity is renamed as a prediction, so no circular step is identified.

Assumptions & free parameters 0 free parameters · 6 assumptions · 0 invented entities

The paper introduces no fitted free parameters or invented entities. Its central claims rely on the holographic tEE conjecture, the T_Im - T_Re subtraction, the NEC/stability definition of naturalness, and the area-law criterion for Fermi surfaces. z and theta are inputs of the backgrounds, not fit parameters.

assumptions (6)
  • domain assumption Timelike entanglement entropy is given by the holographic area of the union of spacelike and timelike extremal surfaces homologous to the boundary interval.
    Section 2.1 states this prescription and cites [21]; it is a conjecture in higher dimensions and confirmed only in (2+1)-dimensional theories.
  • domain assumption The finite boundary interval is T = T_Im - T_Re, with contributions from the timelike and spacelike surfaces regulated by an IR cutoff.
    Section 2.1 and Eq. (3.13), taken from the authors' prior work [23]; no independent derivation is given for non-relativistic backgrounds.
  • domain assumption The null energy condition and the thermodynamic stability condition d-theta-1 > 0 define the 'natural' parametric region of a holographic theory.
    Sections 4 and Appendix A, citing [18,26]; used as the benchmark for the tEE stability claim.
  • domain assumption Logarithmic violation of the entanglement area law signals a Fermi surface in the dual theory.
    Section 4.1.4 introduces this criterion, following the holographic Fermi-surface literature [13,14,19]; the paper uses it to interpret the theta=d-2 result.
  • domain assumption Wick rotation t=i tau defines the temporal entanglement entropy as a distinct but related quantity.
    Section 2.2 defines temporal entanglement entropy in Euclidean signature following [21,22]; used to compute Section 4.2.
  • domain assumption The metrics (3.1) and (4.1) are valid holographic duals of Lifshitz-like anisotropic and hyperscaling-violating field theories.
    Sections 3 and 4, citing [18,45]; the paper does not derive these backgrounds.

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Pith. "Pith review of Holographic Timelike Entanglement Entropy in Non-relativistic Theories." pith.science (2026). https://pith.science/paper/2AOW5YFZ

@misc{pith2026241118514,
  author       = {Pith},
  title        = {Pith review of: Holographic Timelike Entanglement Entropy in Non-relativistic Theories},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/2AOW5YFZ}},
  note         = {Machine review of arXiv:2411.18514}
}
read the original abstract

Timelike entanglement entropy is a complex measure of information that is holographically realized by an appropriate combination of spacelike and timelike extremal surfaces. This measure is highly sensitive to Lorentz invariance breaking. In this work, we study the timelike entanglement entropy in non-relativistic theories, focusing on theories with hyperscaling violation and Lifshitz-like spatial anisotropy. The properties of the extremal surfaces, as well as the timelike entanglement entropy itself, depend heavily on the symmetry-breaking parameters of the theory. Consequently, we show that timelike entanglement can encode, to a large extent, the stability and naturalness of the theory. Furthermore, we find that timelike entanglement entropy identifies Fermi surfaces either through the logarithmic behavior of its real part or, alternatively, via its constant imaginary part, with this constant value depending on the theory's Lifshitz exponent. This provides a novel interpretation for the imaginary component of this pseudoentropy. Additionally, we examine temporal entanglement entropy, an extension of timelike entanglement entropy to Euclidean space, and provide a comprehensive discussion of its properties in these theories.

Figures

Figures reproduced from arXiv: 2411.18514 by the authors.

Figure 1
Figure 1. The tEE surfaces for z > 1 corre￾sponding to A2 of (3.22). The boundary of the theory is at r → 0. The equation of mo￾tion for the spacelike hypersurfaces ΣRe fol￾lows the boundary conditions t ′ Re|r→0 = 0 and t ′ Re|r→∞ = ∞, whereas for the timelike sur￾face ΣIm, the boundary conditions are given by t ′ Im|r→r0 = ∞ and t ′ Im|r→∞ = ∞. We plot the timelike surfaces with red color and the space￾like ones with green.… view at source ↗
Figure 4
Figure 4. The hypersurfaces for z < −(d − 2)−1 described by B of (3.23). gxx and g −1 yy diverge at r → ∞. There are two discrete sets of surfaces for z = −4/5 with solid lines and and z = −3/5 plotted with dashed. For both the cases, ΣRe follow the same boundary conditions given by t ′ Re|r→0 = ∞ and t ′ Re|r→∞ = 0, while ΣIm sat￾isfies t ′ Im|r→r0 = ∞ and t ′ Im|r→0 = ∞. 3.2.2 Computation of the Timelike Entanglement Entrop… view at source ↗
Figure 5
Figure 5. This surface corresponds to the case A0, (4.11). The equation of motion for the spacelike hypersurfaces ΣRe follow the bound￾ary conditions t ′ Re|r→0 = 0 and t ′ Re|r→∞ = ∞, whereas for the timelike hypersurface ΣIm, the boundary conditions are given by t ′ Im|r→r0 = ∞ and t ′ Im|r→∞ = ∞. The red curve in the plot describes the timelike surfaces and the green curves are for spacelike ones. We choose d = 4 and the t… view at source ↗
Figures from the paper (3 more)
Figure 7
Figure 7. Figure 7: This surface corresponds to the case A2 of (4.11). The equation of motion for ΣRe follows the boundary conditions t ′ Re|r→0 = ∞ and t ′ Re|r→∞ = 0, whereas for ΣIm, the bound￾ary conditions are given by t ′ Im|r→r0 = ∞ and t ′ Im|r→∞ = 0. Here we have z = 1/10 and θ =…
Figure 9
Figure 9. Figure 9: This surface corresponds to the case C of (4.14). The boundary of the geometry here is at r = ∞ fixed by θ > d−1. The equation of motion for ΣRe follows the boundary conditions t ′ Re|r→0 = ∞ and t ′ Re|r→∞ = 0. For ΣIm, the boundary conditions are given by t ′ Im|r→r0…
Figure 10
Figure 10. Figure 10: The NEC (4.3) for the hyperscal￾ing violation theory together with the thermo￾dynamic stability conditions (4.4) are shaded with light green. The stability conditions ex￾clude an additional minor regime compared to NEC and result to two disconnected regimes. The blue …

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Reference graph

Works this paper leans on

54 extracted references · 20 canonical work pages · cited by 9 Pith papers

  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]

    arXiv 2006

  2. [2]

    Aharonov, D.Z

    Y. Aharonov, D.Z. Albert and L. Vaidman, How the result of a measurement of a 36 component of the spin of a spin-1/2 particle can turn out to be 100 , Phys. Rev. Lett. 60 (1988) 1351

    work page 1988

  3. [3]

    Dressel, M

    J. Dressel, M. Malik, F.M. Miatto, A.N. Jordan and R.W. Boyd, Colloquium: Understanding quantum weak values: Basics and applications , Rev. Mod. Phys. 86 (2014) 307

    work page 2014

  4. [4]

    Mollabashi, N

    A. Mollabashi, N. Shiba, T. Takayanagi, K. Tamaoka and Z. Wei, Pseudo Entropy in Free Quantum Field Theories , Phys. Rev. Lett. 126 (2021) 081601 [ 2011.09648]

    arXiv 2021

  5. [5]

    Mollabashi, N

    A. Mollabashi, N. Shiba, T. Takayanagi, K. Tamaoka and Z. Wei, Aspects of pseudoentropy in field theories , Phys. Rev. Res. 3 (2021) 033254 [ 2106.03118]

    arXiv 2021

  6. [6]

    Fisher, Scaling and critical slowing down in random-field ising systems , Phys

    D.S. Fisher, Scaling and critical slowing down in random-field ising systems , Phys. Rev. Lett. 56 (1986) 416

    work page 1986

  7. [7]

    Henley, Relaxation time for a dimer covering with height representation , Journal of Statistical Physics 89 (1997) 483–507

    C.L. Henley, Relaxation time for a dimer covering with height representation , Journal of Statistical Physics 89 (1997) 483–507

    work page 1997

  8. [8]

    Ardonne, P

    E. Ardonne, P. Fendley and E. Fradkin, Topological order and conformal quantum critical points, Annals Phys. 310 (2004) 493 [ cond-mat/0311466]

    arXiv 2004

Show all 54 references
  1. [9]

    Fradkin, D.A

    E. Fradkin, D.A. Huse, R. Moessner, V. Oganesyan and S.L. Sondhi, Bipartite rokhsar–kivelson points and cantor deconfinement , Physical Review B 69 (2004)

    2004

  2. [10]

    Vishwanath, L

    A. Vishwanath, L. Balents and T. Senthil, Quantum criticality and deconfinement in phase transitions between valence bond solids , Physical Review B 69 (2004)

    2004

  3. [11]

    Ghaemi, A

    P. Ghaemi, A. Vishwanath and T. Senthil, Finite-temperature properties of quantum lifshitz transitions between valence-bond solid phases: An example of local quantum criticality, Physical Review B 72 (2005)

    2005

  4. [12]

    Yang, Ferromagnetic transition in one-dimensional itinerant electron systems , Phys

    K. Yang, Ferromagnetic transition in one-dimensional itinerant electron systems , Phys. Rev. Lett. 93 (2004) 066401

    2004

  5. [13]

    Wolf, Violation of the entropic area law for Fermions , Phys

    M.M. Wolf, Violation of the entropic area law for Fermions , Phys. Rev. Lett. 96 (2006) 010404 [quant-ph/0503219]

    2006 arXiv

  6. [14]

    Gioev and I

    D. Gioev and I. Klich, Entanglement Entropy of Fermions in Any Dimension and the Widom Conjecture, Phys. Rev. Lett. 96 (2006) 100503 [ quant-ph/0504151]

    2006 arXiv

  7. [15]

    Swingle, Conformal Field Theory on the Fermi Surface , Phys

    B. Swingle, Conformal Field Theory on the Fermi Surface , Phys. Rev. B 86 (2012) 035116 [1002.4635]. 37

    2012 arXiv

  8. [16]

    Zhang, T

    Y. Zhang, T. Grover and A. Vishwanath, Entanglement entropy of critical spin liquids , Phys. Rev. Lett. 107 (2011) 067202

    2011

  9. [17]

    Kachru, X

    S. Kachru, X. Liu and M. Mulligan, Gravity duals of Lifshitz-like fixed points , Phys. Rev. D 78 (2008) 106005 [ 0808.1725]

    2008 arXiv

  10. [18]

    X. Dong, S. Harrison, S. Kachru, G. Torroba and H. Wang, Aspects of holography for theories with hyperscaling violation , JHEP 06 (2012) 041 [ 1201.1905]

    2012 arXiv

  11. [19]

    Ogawa, T

    N. Ogawa, T. Takayanagi and T. Ugajin, Holographic Fermi Surfaces and Entanglement Entropy, JHEP 01 (2012) 125 [ 1111.1023]

    2012 arXiv

  12. [20]

    Huijse, S

    L. Huijse, S. Sachdev and B. Swingle, Hidden Fermi surfaces in compressible states of gauge-gravity duality, Phys. Rev. B 85 (2012) 035121 [ 1112.0573]

    2012 arXiv

  13. [21]

    K. Doi, J. Harper, A. Mollabashi, T. Takayanagi and Y. Taki, Timelike entanglement entropy, JHEP 05 (2023) 052 [ 2302.11695]

    2023 arXiv

  14. [22]

    Grieninger, K

    S. Grieninger, K. Ikeda and D.E. Kharzeev, Temporal entanglement entropy as a probe of renormalization group flow , JHEP 05 (2024) 030 [ 2312.08534]

    2024 arXiv

  15. [23]

    Afrasiar, J.K

    M. Afrasiar, J.K. Basak and D. Giataganas, Timelike entanglement entropy and phase transitions in non-conformal theories , JHEP 07 (2024) 243 [ 2404.01393]

    2024 arXiv

  16. [24]

    Chu and H

    C.-S. Chu and H. Parihar, Time-like entanglement entropy in AdS/BCFT , JHEP 06 (2023) 173 [ 2304.10907]

    2023 arXiv

  17. [25]

    Caputa, S

    P. Caputa, S. Purkayastha, A. Saha and P. Su lkowski, Musings on SVD and pseudo entanglement entropies, 2408.06791

    arXiv

  18. [26]

    Chu and D

    C.-S. Chu and D. Giataganas, c-Theorem for Anisotropic RG Flows from Holographic Entanglement Entropy, Phys. Rev. D 101 (2020) 046007 [ 1906.09620]

    2020 arXiv

  19. [27]

    Hoyos, N

    C. Hoyos, N. Jokela, J.M. Pen ´ ın, A.V. Ramallo and J. Tarr ´ ıo,Risking your NEC , JHEP 10 (2021) 112 [ 2104.11749]

    2021 arXiv

  20. [28]

    Wald, General relativity, Chicago Univ

    R.M. Wald, General relativity, Chicago Univ. Press, Chicago, IL (1984)

    1984

  21. [29]

    Giataganas, Probing strongly coupled anisotropic plasma , JHEP 07 (2012) 031 [1202.4436]

    D. Giataganas, Probing strongly coupled anisotropic plasma , JHEP 07 (2012) 031 [1202.4436]

    2012 arXiv

  22. [30]

    Narayan, de Sitter space, extremal surfaces, and time entanglement , Phys

    K. Narayan, de Sitter space, extremal surfaces, and time entanglement , Phys. Rev. D 107 (2023) 126004 [ 2210.12963]. 38

    2023 arXiv

  23. [31]

    Li, Z.-Q

    Z. Li, Z.-Q. Xiao and R.-Q. Yang, On holographic time-like entanglement entropy , JHEP 04 (2023) 004 [ 2211.14883]

    2023 arXiv

  24. [32]

    Narayan, Further remarks on de Sitter space, extremal surfaces, and time entanglement, Phys

    K. Narayan, Further remarks on de Sitter space, extremal surfaces, and time entanglement, Phys. Rev. D 109 (2024) 086009 [ 2310.00320]

    2024 arXiv

  25. [33]

    Jiang, P

    X. Jiang, P. Wang, H. Wu and H. Yang, Timelike entanglement entropy in dS 3/CFT2, JHEP 08 (2023) 216 [ 2304.10376]

    2023 arXiv

  26. [34]

    Guo, Y.-z

    W.-z. Guo, Y.-z. Jiang and J. Xu, Pseudoentropy sum rule by analytical continuation of the superposition parameter, 2405.09745

    arXiv

  27. [35]

    Jena and S

    S.S. Jena and S. Mahapatra, A note on the holographic time-like entanglement entropy in Lifshitz theory, 2410.00384

    arXiv

  28. [36]

    Basak, A

    J.K. Basak, A. Chakraborty, C.-S. Chu, D. Giataganas and H. Parihar, Massless Lifshitz field theory for arbitrary z , JHEP 05 (2024) 284 [ 2312.16284]

    2024 arXiv

  29. [37]

    K. Doi, J. Harper, A. Mollabashi, T. Takayanagi and Y. Taki, Pseudoentropy in dS/CFT and Timelike Entanglement Entropy , Phys. Rev. Lett. 130 (2023) 031601 [ 2210.09457]

    2023 arXiv

  30. [38]

    Kanda, T

    H. Kanda, T. Kawamoto, Y.-k. Suzuki, T. Takayanagi, K. Tasuki and Z. Wei, Entanglement phase transition in holographic pseudo entropy , JHEP 03 (2024) 060 [2311.13201]

    2024 arXiv

  31. [39]

    Caputa, B

    P. Caputa, B. Chen, T. Takayanagi and T. Tsuda, Thermal Pseudo-Entropy, 2411.08948

    arXiv

  32. [40]

    He, P.H.C

    S. He, P.H.C. Lau and L. Zhao, Detecting quantum chaos via pseudo-entropy and negativity, 2403.05875

  33. [41]

    Jiang, P

    X. Jiang, P. Wang, H. Wu and H. Yang, Timelike entanglement entropy and T T deformation, Phys. Rev. D 108 (2023) 046004 [ 2302.13872]

    2023 arXiv

  34. [42]

    W.-z. Guo, S. He and Y.-X. Zhang, Relation between timelike and spacelike entanglement entropy, 2402.00268

  35. [43]

    Heller, F

    M.P. Heller, F. Ori and A. Serantes, Geometric interpretation of timelike entanglement entropy, 2408.15752

    arXiv

  36. [44]

    Azeyanagi, W

    T. Azeyanagi, W. Li and T. Takayanagi, On String Theory Duals of Lifshitz-like Fixed Points, JHEP 06 (2009) 084 [ 0905.0688]. 39

    2009 arXiv

  37. [45]

    Giataganas, U

    D. Giataganas, U. G¨ ursoy and J.F. Pedraza,Strongly-coupled anisotropic gauge theories and holography, Phys. Rev. Lett. 121 (2018) 121601 [ 1708.05691]

    2018 arXiv

  38. [46]

    Giataganas, N

    D. Giataganas, N. Pappas and N. Toumbas, Holographic observables at large d , Phys. Rev. D 105 (2022) 026016 [ 2110.14606]

    2022 arXiv

  39. [47]

    Rokhsar and S.A

    D.S. Rokhsar and S.A. Kivelson, Superconductivity and the quantum hard-core dimer gas , Phys. Rev. Lett. 61 (1988) 2376

    1988

  40. [48]

    Burkov, M.D

    A.A. Burkov, M.D. Hook and L. Balents, Topological nodal semimetals, Phys. Rev. B 84 (2011) 235126

    2011

  41. [49]

    Burkov and L

    A.A. Burkov and L. Balents, Weyl semimetal in a topological insulator multilayer , Phys. Rev. Lett. 107 (2011) 127205

    2011

  42. [50]

    Wan, A.M

    X. Wan, A.M. Turner, A. Vishwanath and S.Y. Savrasov, Topological semimetal and fermi-arc surface states in the electronic structure of pyrochlore iridates , Phys. Rev. B 83 (2011) 205101

    2011

  43. [51]

    Landsteiner, Y

    K. Landsteiner, Y. Liu and Y.-W. Sun, Quantum phase transition between a topological and a trivial semimetal from holography , Phys. Rev. Lett. 116 (2016) 081602 [1511.05505]

    2016 arXiv

  44. [52]

    Rodgers, E

    R. Rodgers, E. Mauri, U. G¨ ursoy and H.T.C. Stoof, Thermodynamics and transport of holographic nodal line semimetals , JHEP 11 (2021) 191 [ 2109.07187]

    2021 arXiv

  45. [53]

    Baggioli and D

    M. Baggioli and D. Giataganas, Detecting Topological Quantum Phase Transitions via the c-Function, Phys. Rev. D 103 (2021) 026009 [ 2007.07273]

    2021 arXiv

  46. [54]

    Hoyos and P

    C. Hoyos and P. Koroteev, On the Null Energy Condition and Causality in Lifshitz Holography, Phys. Rev. D 82 (2010) 084002 [ 1007.1428]. 40

    2010 arXiv

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