Pith. sign in

REVIEW 4 major objections 5 minor 2 cited by

In noncommutative Yang–Mills theory, a minimum length scale emerges that forces holographic subregion complexity through a behavioral transition and makes strong subadditivity fail at short distances.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

T0 review · deepseek-v4-flash

2026-08-02 23:11 UTC pith:2ZDXR7PY

load-bearing objection Plausible CV computation in NCYM, but the central claims rest on an unresolved choice between two extremal-surface branches, and the finite-T peak claim conflicts with its own Eq. (5.10). the 4 major comments →

arxiv 2602.14448 v2 pith:2ZDXR7PY submitted 2026-02-16 hep-th gr-qcmath-phmath.MP

Holographic Subregion Complexity and Fidelity Susceptibility in Noncommutative Yang--Mills Theory

Tadahito Nakajima This is my paper
classification hep-th gr-qcmath-phmath.MP
keywords holographic subregion complexitynoncommutative Yang-Mills theoryholographic fidelity susceptibilityminimum length scalestrong subadditivityAdS solitonCV conjectureUV/IR mixing
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The paper tries to establish that spatial noncommutativity — encoded in a Moyal-plane parameter a — changes the information-theoretic content of holographic subregion complexity in a qualitative way. It shows that the subregion's characteristic length has a minimum l_min ~ a, and as the subregion shrinks toward that scale the universal part of the complexity reverses character: negative and inverse-square in the commutative limit, positive and quartic in the noncommutative regime, with a lower bound. It further argues that strong subadditivity, a core information inequality, holds for this complexity in general but fails abruptly when the overlap of two subregions approaches l_min. The same framework yields a holographic fidelity susceptibility that grows monotonically with the noncommutativity parameter, and whose temperature and compactification dependence is computed. A reader would care because this links the nonlocality scale of the field theory to concrete, in-principle observable quantum information quantities.

Core claim

The central claim is that the CV-conjecture volume for a strip subregion in the holographic dual of noncommutative Yang–Mills theory has a cutoff-independent 'universal' part that is not a small deformation of the commutative answer. In the commutative limit C_A^(univ) is negative and proportional to -N^2 L^2 / l_C^2; in the large-noncommutativity limit it becomes positive and proportional to (27 N^2 L^2 / (2π^4 a^2)) (Γ(5/6)/Γ(1/3))^4 I (l/a)^4. Because the width l as a function of the extremal-surface turning point u_* has a minimum l_min ≃ 1.6a at u_* ≃ 0.79/a, the theory has a shortest relevant subregion scale: below it no RT-strip exists, and the paper interprets the resulting transitio

What carries the argument

The key machinery is the CV (complexity=volume) conjecture: holographic subregion complexity is the volume of the codimension-one bulk region enclosed by the Ryu–Takayanagi surface, with a string-frame dilaton factor. In the noncommutative D3-brane background the metric acquires the dressing factor h(u)=1/(1+a^4 u^4), and the strip width l(u_*) is double-valued with a minimum l_min ≃ 1.6a. This minimum is the mechanism behind the transition, the lower bound, and the SSA failure. The finite part is isolated with recursion relations for binomial integrals, and the cutoff-dependent part is identified with the fidelity susceptibility.

Load-bearing premise

The calculation assigns the physical HSC to one connected extremal surface even though the relation between subregion width and turning point is double-valued for l > l_min, and the two candidate surfaces are never compared; if the smaller-area branch is the physical one, the lower bound, the sign-reversal, and the SSA curve could change.

What would settle it

Evaluate the volume of the second RT-surface branch for l > l_min (or compute the full area/volume of both extremal surfaces) and check whether the smaller-area branch yields a positive HSC with the same lower bound and the same SSA failure near x = l_min; a different sign or no SSA violation would falsify the transition claim. A complementary check: measure the fidelity susceptibility of a NCYM ground state as a function of θ; if the divergent-part identification is right, it should grow monotonically with a and show the temperature-enhanced slope.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

If this is right

  • If the central claim is right, holographic subregion complexity in NCYM has a universal, cutoff-independent part in both regimes, so complexity can serve as a well-defined probe of noncommutativity.
  • The minimum length implies a finite lower bound on the universal complexity, and at finite temperature this lower bound rises with temperature, so thermal effects cannot remove the noncommutative signature.
  • Strong subadditivity of HSC fails only near l_min, meaning the noncommutativity scale acts as a sharp threshold where the holographic information structure ceases to be the usual one.
  • The holographic fidelity susceptibility increases monotonically with the noncommutativity parameter, and its slope is amplified by temperature, offering a quantitative handle on θ.
  • In the AdS soliton background, the sign change of HSC near l_min signals a connected/disconnected RT competition, analogous to a phase transition.

Where Pith is reading between the lines

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

  • A natural extension the paper leaves implicit: if the SSA violation is real, overlapping-strip entanglement measures in noncommutative lattice models should show the same violation when the overlap is of order sqrt(θ); this is testable in cold-atom or tensor-network simulations of Moyal-type interactions.
  • The paper never fixes which branch of the double-valued l(u_*) is physical; a reader could check whether the smaller-area branch removes the lower bound. If it does, the transition and SSA breakdown would be artifacts of branch choice.
  • Because the divergent part of HSC is identified with fidelity susceptibility only by conjecture, the monotonic growth of G_a with a would be a precise prediction for the response of the NCYM ground state to changes in θ — measurable in principle if the conjecture holds.
  • The soliton sign reversal suggests that HSC, not just entanglement entropy, can act as an order parameter for compactification/phase transitions; testing whether the same sign change appears in entanglement entropy would separate complexity-specific from generic geometric effects.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

4 major / 5 minor

Summary. The paper studies holographic subregion complexity (HSC) and holographic fidelity susceptibility (HFS) in the noncommutative Yang–Mills theory dual to the deformed AdS_5 background of Eq. (2.1). For an infinite strip of width l, the author derives a universal (cutoff-independent) part of the HSC, shows that the characteristic length has a minimum l_min ~ 1.6 a set by the noncommutativity scale, and claims that the HSC undergoes a behavioral transition near this scale, possesses a lower bound, and violates strong subadditivity only when the overlap width approaches l_min. The paper further analyzes finite-temperature and AdS-soliton deformations, claiming that temperature raises the lower bound and enhances the sensitivity of the regularized HFS to the noncommutativity parameter, while compactification suppresses that sensitivity.

Significance. If the central claims were established, the paper would provide an interesting holographic probe of nonlocality: it would show that a minimum length induced by noncommutativity produces qualitative changes in subregion complexity and a sharp information-theoretic breakdown near that scale. The author performs a substantial set of explicit numerical calculations across three backgrounds and carefully extracts finite parts via recursion relations, which is a strength. However, the main physical conclusions depend on a branch choice for the Ryu–Takayanagi surface that is never made, and one finite-temperature claim directly contradicts the paper's own formula. The HFS identification is also conjectural rather than derived. These issues make the current version unsuitable for publication without significant revision.

major comments (4)
  1. [Sec. 2, after Eq. (2.7)] The paper states that l(u_*) is double-valued for l > l_min, and Figures 1-2 plot both branches. But the HSC is defined using the *minimal* Ryu–Takayanagi surface (Eqs. (2.8)-(2.9)), so the physical HSC requires selecting the branch with smaller on-shell area (2.6). This comparison is never performed. The two branches are qualitatively different: the small-u_* branch connects to the negative commutative result (2.15), while the large-u_* branch gives the positive (l/a)^4 behavior (2.20). The abstract's claims of a 'behavioral transition', a lower bound, and the SSA breakdown in Sec. 4 are statements about the union of the two branches, not about a single well-defined physical quantity. The paper must identify the minimal-area branch and recompute the central results on that branch, or explain why the branch choice is irrelevant.
  2. [Sec. 5, Eq. (5.10) and Fig. 9] Eq. (5.10) gives G_aT = N^2/(12π^2) u_Λ^3 L^2 l_T. Since l_T is defined through X_T(u) in Eq. (5.3), whose integrand is decreased by increasing u_T, l_T is monotonically decreasing in u_T for fixed u_*. Therefore G_aT is monotonically decreasing in u_T and cannot exhibit a sharp peak at u_T ≈ u_*, contrary to the text and Fig. 9. The same contradiction appears in the conclusions. This is a load-bearing error: the claimed phase-transition-like peak in the finite-temperature HFS is an artifact of the plotting or interpretation. The definition and the figure must be reconciled, or the claim removed.
  3. [Sec. 4, Eq. (4.2) and Fig. 6] The strong-subadditivity test is performed using C_A^(univ)(l) from the two branches without first fixing the physical RT surface. Since the minimal-area branch is not identified, the reported SSA violation near l_min is branch-dependent. Moreover, the 'naive SSA-like property for complexity' is not guaranteed by the holographic proof for entanglement entropy (which applies to areas, not volumes), so the interpretation of DA|B as a test of strong subadditivity requires a derivation or at least a clear statement that this is a conjecture. Without the branch selection, the claim of an abrupt SSA violation at x=l_min is not supported.
  4. [Sec. 3, Eqs. (3.2)-(3.3)] The identification of the most divergent part of the HSC with the holographic fidelity susceptibility is assumed from Ref. [8] rather than derived. Consequently, the paper's conclusion that 'the HFS is shown to provide an effective measure of the degree of noncommutativity' is largely a restatement of the geometric relation ΔG_a ∝ l - l_C, which follows from the deformed metric alone. An independent field-theoretic computation of fidelity susceptibility, or at least a critical discussion of the conjecture's validity for NCYM, would be needed to support this claim.
minor comments (5)
  1. [References] Reference [36] contains the editorial note '(Check if published by 2026)' inside the citation. This should be resolved before submission: either cite the published version or remove the note.
  2. [Fig. 13 caption] The caption of Fig. 13 is corrupted: it contains the unrelated phrase 'It (2) is also straightforward to verify that, in the limit uKK→ 0...' from the main text. Please replace it with a proper caption.
  3. [Consistency of notation] The dimensionless HFS uses different prefactors in different sections (e.g., 12π^2 u_*/(u_Λ^3 N^2 L^2) in Eqs. (3.3)-(3.4) and 12π^2 u_*^2/(u_Λ^3 N^2 L) in Fig. 13). While the figures state their normalizations, this is a source of confusion; a unified definition would improve readability.
  4. [Sec. 6, Eq. (6.6)] The two displayed forms of V_γKK^(div2) are joined by 'equals' with two expressions, but the brace formatting is unclear. Please clarify whether these are two equivalent expressions of the same quantity or two distinct options, as done around Eqs. (2.24b) and (2.26b).
  5. [General] The paper uses 'we find that' statements without error bars or convergence checks for the numerical integrals. A brief description of the numerical method and accuracy would strengthen the reproducibility of the figures.

Circularity Check

1 steps flagged

No significant circularity: the HSC geometry is self-contained; only the HFS identification is self-definitional and openly conjectural.

specific steps
  1. self definitional [Sec. 3, Eqs. (3.3) and (3.4)]
    "From the perspective of the holographic subregion complexity, its most divergent part is presumed to correspond to the holographic fidelity susceptibility ... By interpreting C^(div1)_A = V^(div1)_γ/(8πG^(10)_N R) as the holographic fidelity susceptibility G_a ... we obtain: G_a = N^2/(12π^2) u_Λ^3 L^2 l ... where ∆l ≡ l − l_C."

    The quantity called HFS is defined, via the adopted conjecture, as the divergent part of the HSC itself. Since that divergent part is proportional to the geometric length l (Eq. (2.21)), the later 'findings' that G_a and ΔG_a increase monotonically with the noncommutativity parameter a (Figs. 3 and 4) are direct restatements of the a-dependence already contained in the extremal-surface length l(a u_*). Thus the claimed 'measure of noncommutativity' is built into the identification rather than obtained from an independent field-theoretic fidelity computation. The paper itself labels this as a presumption/conjecture, so this is a definitional input, not a hidden fitting step.

full rationale

The core HSC derivation is a self-contained geometric calculation: starting from the NCYM metric (2.1)–(2.2), the RT profile (2.7) determines l(u_*), and the enclosed volume (2.11) is integrated to yield the universal terms (2.15), (2.18)–(2.20). No parameter is fitted to the target results, and no load-bearing claim is justified solely by the author's own previous papers. The only definitional identification is the HFS/HSC-divergent-part correspondence in Sec. 3, which the paper explicitly treats as a conjecture; because it is an assumed input rather than a derived prediction, it introduces a mild self-definitional element but does not infect the geometric HSC, SSA, finite-temperature, or soliton computations. The unresolved branch selection for the double-valued l(u_*) noted after Eq. (2.7) is a correctness/ambiguity concern rather than a circularity. Overall, the paper's central geometric results are independent of the conjectural HFS identification, so the circularity score is low.

Axiom & Free-Parameter Ledger

0 free parameters · 5 axioms · 0 invented entities

No free parameters are fitted to data; a, u_*, u_T, u_KK are theory parameters or integration settings. The central claims rely on the standard holographic conjectures listed above, especially the CV and HFS identifications.

axioms (5)
  • domain assumption The background (2.1)-(2.2) with NS-NS B-field is the holographic dual of NCYM at large N and strong coupling.
    Invoked in Sec. 2 from Refs. [38-41]; all subsequent computations are inside this background.
  • domain assumption The entanglement entropy/RT area functional includes the string-frame dilaton factor e^{-2φ} and integrates over eight dimensions.
    Eq. (2.4) generalizes [9,43] to nonconformal holography; used for all surfaces.
  • domain assumption Holographic subregion complexity equals the regulated codimension-one volume enclosed by the RT surface, Vγ/(8πG_N R).
    Eqs. (2.8)-(2.10), adopted from [8,11].
  • domain assumption The most divergent part of HSC is the holographic fidelity susceptibility.
    Sec. 3, Eqs. (3.2)-(3.3), following [8,15,37]; the interpretation of ΔG_a as measuring θ depends on this.
  • domain assumption The infinite-strip geometry with width l and large L captures the qualitative behavior claimed.
    The paper restricts to a rectangular subregion (Sec. 2, Eq. (2.5)); generalization to other shapes is left to future work (Sec. 7).

pith-pipeline@v1.3.0-alltime-deepseek · 17310 in / 23366 out tokens · 213657 ms · 2026-08-02T23:11:43.673495+00:00 · methodology

0 comments
read the original abstract

We analyze the behavior of holographic subregion complexity (HSC) and holographic fidelity susceptibility (HFS) in noncommutative Yang--Mills theory. The emergence of a minimum length scale, dictated by the degree of noncommutativity, induces a behavioral transition in the HSC and establishes a lower bound. In the large noncommutativity regime, the qualitative features of the complexity deviate significantly from the commutative case. The HFS is shown to provide an effective measure of the degree of noncommutativity. Although the HSC generally satisfies strong subadditivity, this property fails abruptly when the subregion size approaches the minimum length scale. At finite temperature, the long-range behavior of the HSC is modified, and its lower bound scales positively with temperature. Furthermore, temperature enhances the sensitivity of the fidelity susceptibility to the degree of noncommutativity. Within the AdS soliton background, a competition between connected and disconnected configurations arises in the HSC, signaling a phase-transition-like behavior. Finally, the compactification scale is found to diminish the sensitivity of the HFS to the degree of noncommutativity.

Figures

Figures reproduced from arXiv: 2602.14448 by Tadahito Nakajima.

Figure 1
Figure 1. Figure 1: The variation of the dimensionless quantity CA ≡ 6π 2a 2 N2L2 C (univ) A with respect to the dimensionless length l/a, in units where a = 1. The solid and dotted lines corre￾spond to the noncommutative case and the commutative limit (a → 0), respectively. and the commutative limit. However, this distinction becomes more pronounced as l approaches lmin. Furthermore, at short range scales, the behavior of C … view at source ↗
Figure 2
Figure 2. Figure 2: The variation of the dimensionless quantity CA ≡ 6π 2a 2 N2L2 C (univ) A with respect to the dimensionless length l/a, in units where a = 1. The solid and dashed lines correspond to the noncommutative case and the noncommutative limit, respectively. The quantity Gρ is also called the (quantum) information metric or Bures metric. It measures the distance between two infinitesimally different quantum states … view at source ↗
Figure 3
Figure 3. Figure 3: The variation of the dimensionless quantity Ga ≡ 12π 2 au3 ΛN2L2 Ga as a function of the parameter au∗, in units where a = 1. The solid and dotted lines correspond to the noncommutative case and the commutative limit, respectively. where the characteristic length is given by l = 2X(u→∞). The numerical evaluation of the dependence of Ga on the parameter u∗ is shown in Fig.3. Interpreting u∗ as an inverse sc… view at source ↗
Figure 4
Figure 4. Figure 4: The variation of the dimensionless quantity ∆Ga ≡ 12π 2u∗ u 3 ΛN2L2 ∆Ga as a function of the dimensionless parameter au∗, in units where u∗ = 1. Fig.4. As shown in Fig.4, the regularized holographic fidelity susceptibility, ∆Ga, of the noncommutative Yang–Mills theory increases monotonically as a function of the noncommutativity parameter a. 4 Strong subadditivity There are several important properties tha… view at source ↗
Figure 5
Figure 5. Figure 5: (Left) Two overlapping infinite boundary strips A and B, with their respective volumes VA and VB enclosed by the Ryu–Takayanagi surface. (Right) Two overlapping infinite boundary strips A∪B and A∩B, with their respective volumes VA∪B and VA∩B enclosed by the Ryu–Takayanagi surface. is an inverse square function of lC, where lC denotes the characteristic length of the subregion. It is straightforward to ver… view at source ↗
Figure 6
Figure 6. Figure 6: The behavior of the dimensionless quantity DA|B ≡ 6π 2a 2 N2L2 DA|B as a function of the width ax, in units where a = 1. The range of the width x is lmin ≤ x ≤ 15 lmin. The solid line corresponds to the noncommutative case (a = 1), while the dotted line corresponds to the commutative limit (a → 0). as the width x approaches lmin. While the quantity DA|B remains positive for most of the range, ensuring the … view at source ↗
Figure 7
Figure 7. Figure 7: Plot of the dimensionless quantity CAT ≡ 6π 2a 2 N2L2 C (univ) AT as a function of the dimensionless length lT , evaluated at auT = 0.47245 in units where a = 1. The solid line corresponds to the noncommutative theory, whereas the dotted line indicates the commutative limit (a → 0). The label lT min indicates the minimum value of lT in the noncommutative theory. zero at auT ≈ 0.47245, denoted as auT0. As d… view at source ↗
Figure 8
Figure 8. Figure 8: Plot of the dimensionless quantity CAT ≡ 6π 2 N2L2 C (univ) AT as a function of the dimensionless length lT , for auT = 0.47245 in units where a = 1. The solid line corresponds to the noncommutative theory, whereas the dotted line indicates the com￾mutative limit (a → 0). V (div1) γT /(8πG(10) N R), as GaT = N2 12π 2 u 3 ΛL 2 lT . (5.10) The numerical evaluation of the dependence of GaT on the parameter uT… view at source ↗
Figure 9
Figure 9. Figure 9: Plot of the dimensionless quantity GaT ≡ 12π 2u∗ u 3 ΛN2L2 GaT as a function of the dimensionless parameter uT /u∗, in units where u∗ = 1. The noncommutativity parame￾ter is held fixed at a = 1. The solid and dotted lines correspond to the noncommutative case, and the commutative limit, respectively. the noncommutativity parameter a, regardless of the magnitude of the parameter uT . Notably, the rate of th… view at source ↗
Figure 10
Figure 10. Figure 10: Plot of the dimensionless quantity ∆GaT ≡ 12π 2u∗ u 3 ΛN2L2 ∆GaT as a function of the dimensionless parameter au∗, in units where u∗ = 1. The solid, dotted, and dashed lines correspond to a low-temperature case ((uT /u∗) 4 = 0.1), an intermediate￾temperature case ((uT /u∗) 4 = 0.65), and a high-temperature case ((uT /u∗) 4 = 0.9), respectively. of the gauge/gravity correspondence [49, 50, 51]. This backgr… view at source ↗
Figure 11
Figure 11. Figure 11: The dimensionless quantity CAKK ≡ 6π 2a 2 N2LuKK C (univ) AKK versus the dimension￾less length lKK/a, evaluated at auKK = 0.07 in units where a = 1. The solid line corresponds to the noncommutative theory, whereas the dotted line indicates the com￾mutative limit (a → 0). The label lKKmin indicates the minimum value of lKK in the noncommutative theory. a transition between the connected and disconnected co… view at source ↗
Figure 12
Figure 12. Figure 12: The dimensionless quantity CAKK ≡ 6π 2a 2 N2LuKK C (univ) AKK versus the dimension￾less length lKK/a, evaluated at auKK = 0.07 in units where a = 1. The solid line corresponds to the noncommutative theory, whereas the dotted line indicates the com￾mutative limit (a → 0). sensitive to variations in the parameter uKK and shows the same qualitative depen￾dence in both the noncommutative case and its commutat… view at source ↗
Figure 13
Figure 13. Figure 13: Plot of the dimensionless quantity GaKK ≡ 12π 2u 2 ∗ u 3 ΛN2L GaKK as a function of the dimensionless parameter uKK/u∗, in units where u∗ = 1. The noncommutativity parameter is held fixed at a = 1. The solid and dotted lines correspond to the non￾commutative case and the commutative limit, respectively. susceptibility. 7 Conclusions In this paper, we compute the holographic subregion complexity (HSC) of a… view at source ↗
Figure 14
Figure 14. Figure 14: Plot of the dimensionless quantity ∆GaKK ≡ 12π 2u 2 ∗ u 3 ΛN2L ∆GaKK as a function of the dimensionless parameter au∗, in units where u∗ = 1. The solid, dotted, and dashed lines correspond to a large compactification radius case ((uKK/u∗) 4 = 0.1), an inter￾mediate compactification radius case ((uKK/u∗) 4 = 0.5), and a small compactification radius case ((uKK/u∗) 4 = 0.9), respectively. HSC exhibits a sha… view at source ↗

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Combinatorial aspects of holographic quantum secret sharing

    hep-th 2026-07 conditional novelty 6.0

    Bulk regions in AdS3/CFT2 get a holographic secret-sharing distance d and thresholds (r,s), with r = n - d + 1; pure states satisfy s = d - 1 while mixed states can satisfy s >= d.

  2. A Timelike Quantum Focusing Conjecture

    hep-th 2026-04 unverdicted novelty 5.0

    A timelike quantum focusing conjecture implies a complexity-based quantum strong energy condition and a complexity bound analogous to the covariant entropy bound for suitable codimension-0 field theory complexity measures.

Reference graph

Works this paper leans on

55 extracted references · 54 linked inside Pith · cited by 2 Pith papers

  1. [1]

    Susskind,Three Lectures on Complexity and Black Holes

    L. Susskind,Three Lectures on Complexity and Black Holes. Springer, 2020. arXiv:1810.11563 [hep-th]

    Pith/arXiv arXiv 2020

  2. [2]

    A geometric approach to quantum circuit lower bounds,

    M. A. Nielsen, “A geometric approach to quantum circuit lower bounds,” Quantum Info. Comput.6(2006) 213,arXiv:quant-ph/0502070

    Pith/arXiv arXiv 2006

  3. [3]

    Second law of quantum complexity,

    A. R. Brown and L. Susskind, “Second law of quantum complexity,”Phys. Rev. D97(2018) 086015,arXiv:1701.01107 [hep-th]

    Pith/arXiv arXiv 2018

  4. [4]

    Computational Complexity and Black Hole Horizons,

    L. Susskind, “Computational Complexity and Black Hole Horizons,”Fortsch. Phys.64(2016) 24–43,arXiv:1403.5695 [hep-th]. [Addendum: Fortsch. Phys. 64, 44 (2016)]

    Pith/arXiv arXiv 2016

  5. [5]

    Complexity and Shock Wave Geometries,

    D. Stanford and L. Susskind, “Complexity and Shock Wave Geometries,”Phys. Rev. D90(2014) 126007,arXiv:1406.2678 [hep-th]

    Pith/arXiv arXiv 2014

  6. [6]

    Holographic Complexity Equals Bulk Action?,

    A. R. Brown, D. A. Roberts, L. Susskind, B. Swingle, and Y. Zhao, “Holographic Complexity Equals Bulk Action?,”Phys. Rev. Lett.116(2016) 191301,arXiv:1509.07876 [hep-th]

    Pith/arXiv arXiv 2016

  7. [7]

    Complexity, action, and black holes,

    A. R. Brown, D. A. Roberts, L. Susskind, B. Swingle, and Y. Zhao, “Complexity, action, and black holes,”Phys. Rev. D93(2016) 086006,arXiv:1512.04993 [hep-th]

    Pith/arXiv arXiv 2016

  8. [8]

    Holographic Complexity,

    M. Alishahiha, “Holographic Complexity,”Phys. Rev. D92(2015) 126009, arXiv:1509.06614 [hep-th]

    Pith/arXiv arXiv 2015

  9. [9]

    Holographic derivation of entanglement entropy from AdS/CFT,

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

    Pith/arXiv arXiv 2006

  10. [10]

    Aspects of Holographic Entanglement Entropy,

    S. Ryu and T. Takayanagi, “Aspects of Holographic Entanglement Entropy,” JHEP08(2006) 045,arXiv:hep-th/0605073

    Pith/arXiv arXiv 2006

  11. [11]

    On Volumes of Subregions in Holography and Complexity,

    O. Ben-Ami and D. Carmi, “On Volumes of Subregions in Holography and Complexity,”JHEP11(2016) 129,arXiv:1609.02514 [hep-th]. 29

    Pith/arXiv arXiv 2016

  12. [12]

    Note on subregion holographic complexity and renormalization group flows,

    P. Roy and T. Sarkar, “Note on subregion holographic complexity and renormalization group flows,”Phys. Rev. D97(2018) 086018, arXiv:1708.05313 [hep-th]

    Pith/arXiv arXiv 2018

  13. [13]

    HEE and HSC for flavors: perturbative structure in open string geometries,

    A. Banerjee, A. Bhattacharya, and S. Maulik, “HEE and HSC for flavors: perturbative structure in open string geometries,”JHEP04(2021) 212, arXiv:2008.02705 [hep-th]

    Pith/arXiv arXiv 2021

  14. [14]

    Subsystem Complexity and Measurements in Holography,

    S.-K. Jian and Y. Zhang, “Subsystem Complexity and Measurements in Holography,”JHEP05(2024) 241,arXiv:2312.04437 [hep-th]

    Pith/arXiv arXiv 2024

  15. [15]

    Distance between Quantum States and Holographic Information Metric,

    M. Miyaji, T. Numasawa, N. Shiba, T. Takayanagi, and K. Watanabe, “Distance between Quantum States and Holographic Information Metric,”Phys. Rev. Lett. 115(2015) 261602,arXiv:1507.07555 [hep-th]

    Pith/arXiv arXiv 2015

  16. [16]

    Noncommutative geometry and Matrix theory: Compactification on tori,

    A. Connes, M. R. Douglas, and A. Schwarz, “Noncommutative geometry and Matrix theory: Compactification on tori,”JHEP02(1998) 003, arXiv:hep-th/9711162

    Pith/arXiv arXiv 1998

  17. [17]

    D-branes and the noncommutative torus,

    M. R. Douglas and C. M. Hull, “D-branes and the noncommutative torus,” JHEP02(1998) 008,arXiv:hep-th/9711165

    Pith/arXiv arXiv 1998

  18. [18]

    Noncommutative geometry from strings and branes,

    F. Ardalan, H. Arfaei, and M. M. Sheikh-Jabbari, “Noncommutative geometry from strings and branes,”JHEP02(1999) 016,arXiv:hep-th/9810072

    Pith/arXiv arXiv 1999

  19. [19]

    String theory and noncommutative geometry,

    N. Seiberg and E. Witten, “String theory and noncommutative geometry,” JHEP09(1999) 032,arXiv:hep-th/9908142

    Pith/arXiv arXiv 1999

  20. [20]

    Noncommutative perturbative dynamics,

    S. Minwalla, M. V. Raamsdonk, and N. Seiberg, “Noncommutative perturbative dynamics,”JHEP02(2000) 020,arXiv:hep-th/9912072

    Pith/arXiv arXiv 2000

  21. [21]

    Comments on perturbative dynamics of noncommutative Yang-Mills theory,

    A. Armoni, “Comments on perturbative dynamics of noncommutative Yang-Mills theory,”Nucl. Phys. B593(2001) 229–242,arXiv:hep-th/0005208

    Pith/arXiv arXiv 2001

  22. [22]

    D1 / D5 system and Wilson loops in (non)commutative gauge theories,

    H. Takahashi, T. Nakajima, and K. Suzuki, “D1 / D5 system and Wilson loops in (non)commutative gauge theories,”Phys. Lett. B546(2002) 273–281, arXiv:hep-th/0206081. 30

    Pith/arXiv arXiv 2002

  23. [23]

    Glueball mass spectra for supergravity duals of noncommutative gauge theories,

    T. Nakajima, K. Suzuki, and H. Takahashi, “Glueball mass spectra for supergravity duals of noncommutative gauge theories,”JHEP01(2006) 016, arXiv:hep-th/0508054

    Pith/arXiv arXiv 2006

  24. [24]

    The spectrum of low spin mesons at finite temperature in holographic noncommutative QCD,

    T. Nakajima, Y. Ohtake, and K. Suzuki, “The spectrum of low spin mesons at finite temperature in holographic noncommutative QCD,”Int. J. Mod. Phys. A 28(2013) 1350171,arXiv:1310.0393 [hep-th]

    Pith/arXiv arXiv 2013

  25. [25]

    Chiral Symmetry Restoration in Holographic Noncommutative QCD,

    T. Nakajima, Y. Ohtake, and K. Suzuki, “Chiral Symmetry Restoration in Holographic Noncommutative QCD,”JHEP09(2011) 054,arXiv:1011.2906 [hep-th]

    Pith/arXiv arXiv 2011

  26. [26]

    Baryon number current in holographic noncommutative QCD,

    T. Nakajima, Y. Ohtake, and K. Suzuki, “Baryon number current in holographic noncommutative QCD,”Phys. Rev. D96(2017) 046018,arXiv:1702.06989 [hep-th]

    Pith/arXiv arXiv 2017

  27. [27]

    Universal terms for holographic entanglement entropy in noncommutative Yang-Mills theory,

    T. Nakajima, “Universal terms for holographic entanglement entropy in noncommutative Yang-Mills theory,”Phys. Rev. D103(2021) 086005, arXiv:2006.14165 [hep-th]

    Pith/arXiv arXiv 2021

  28. [28]

    Volume Law for the Entanglement Entropy in Non-local QFTs,

    N. Shiba and T. Takayanagi, “Volume Law for the Entanglement Entropy in Non-local QFTs,”JHEP02(2014) 033,arXiv:1311.1643 [hep-th]

    Pith/arXiv arXiv 2014

  29. [29]

    Holographic entanglement entropy in nonlocal theories,

    J. L. Karczmarek and C. Rabideau, “Holographic entanglement entropy in nonlocal theories,”JHEP10(2013) 078,arXiv:1307.3517 [hep-th]

    Pith/arXiv arXiv 2013

  30. [30]

    Confinement, Phase Transitions and non-Locality in the Entanglement Entropy,

    U. Kol, C. Nunez, D. Schofield, J. Sonnenschein, and M. Warschawski, “Confinement, Phase Transitions and non-Locality in the Entanglement Entropy,”JHEP06(2014) 005,arXiv:1403.2721 [hep-th]

    Pith/arXiv arXiv 2014

  31. [31]

    On holographic entanglement entropy of non-local field theories,

    D.-W. Pang, “On holographic entanglement entropy of non-local field theories,” Phys. Rev. D89(2014) 126005,arXiv:1404.5419 [hep-th]

    Pith/arXiv arXiv 2014

  32. [32]

    Holographic entanglement entropy probes (non)locality,

    J. L. F. Barbon and C. A. Fuertes, “Holographic entanglement entropy probes (non)locality,”JHEP04(2008) 096,arXiv:0803.1928 [hep-th]

    Pith/arXiv arXiv 2008

  33. [33]

    Holographic Entanglement in a Noncommutative Gauge Theory,

    W. Fischler, A. Kundu, and S. Kundu, “Holographic Entanglement in a Noncommutative Gauge Theory,”JHEP01(2014) 137,arXiv:1307.2932 [hep-th]. 31

    Pith/arXiv arXiv 2014

  34. [34]

    Noncommutativity and Holographic Entanglement Entropy,

    T. Jia and Z. Xu, “Noncommutativity and Holographic Entanglement Entropy,” Phys. Rev. D95(2017) 066002,arXiv:1612.04857 [hep-th]

    Pith/arXiv arXiv 2017

  35. [35]

    Holographic complexity and noncommutative gauge theory,

    J. Couch, S. Eccles, W. Fischler, and M.-L. Xiao, “Holographic complexity and noncommutative gauge theory,”JHEP03(2018) 108,arXiv:1710.07833 [hep-th]

    Pith/arXiv arXiv 2018

  36. [36]

    Quantum Complexity of Nonlocal Field Theories,

    G. Katoch, M. S. Balusu, S. Parihar, and S. R. Roy, “Quantum Complexity of Nonlocal Field Theories,”arXiv preprint arXiv:2511.00649(2024) . (Check if published by 2026)

    arXiv 2024

  37. [37]

    Holographic Fidelity Susceptibility,

    M. Alishahiha and A. F. Astaneh, “Holographic Fidelity Susceptibility,”Phys. Rev. D96(2017) 086004,arXiv:1705.01834 [hep-th]

    Pith/arXiv arXiv 2017

  38. [38]

    Noncommutative Yang-Mills and the AdS / CFT correspondence,

    A. Hashimoto and N. Itzhaki, “Noncommutative Yang-Mills and the AdS / CFT correspondence,”Phys. Lett. B465(1999) 142–147,arXiv:hep-th/9907166

    Pith/arXiv arXiv 1999

  39. [39]

    Large N limit of noncommutative gauge theories,

    J. M. Maldacena and J. G. Russo, “Large N limit of noncommutative gauge theories,”JHEP09(1999) 025,arXiv:hep-th/9908134

    Pith/arXiv arXiv 1999

  40. [40]

    Supergravity and large N noncommutative field theories,

    M. Alishahiha, Y. Oz, and M. M. Sheikh-Jabbari, “Supergravity and large N noncommutative field theories,”JHEP11(1999) 007,arXiv:hep-th/9909215

    Pith/arXiv arXiv 1999

  41. [41]

    Holography and noncommutative Yang-Mills theory,

    M. Li and Y.-S. Wu, “Holography and noncommutative Yang-Mills theory,” Phys. Rev. Lett.84(2000) 2084–2087,arXiv:hep-th/9909085

    Pith/arXiv arXiv 2000

  42. [42]

    Generalized gravitational entropy,

    A. Lewkowycz and J. Maldacena, “Generalized gravitational entropy,”JHEP08 (2013) 090,arXiv:1304.4926 [hep-th]

    Pith/arXiv arXiv 2013

  43. [43]

    AdS Bubbles, Entropy and Closed String Tachyons,

    T. Nishioka and T. Takayanagi, “AdS Bubbles, Entropy and Closed String Tachyons,”JHEP01(2007) 090,arXiv:hep-th/0611035

    Pith/arXiv arXiv 2007

  44. [44]

    Fidelity approach to quantum phase transitions,

    S.-J. Gu, “Fidelity approach to quantum phase transitions,”Int. J. Mod. Phys. B24(2010) 4371,arXiv:0811.3127 [quant-ph]

    Pith/arXiv arXiv 2010

  45. [45]

    Holographic Entanglement Entropy, Complexity, Fidelity Susceptibility and Hierarchical UV/IR Mixing Problem in AdS2/open strings,

    K. Bamba, D. Momeni, and M. A. Ajmi, “Holographic Entanglement Entropy, Complexity, Fidelity Susceptibility and Hierarchical UV/IR Mixing Problem in AdS2/open strings,”Int. J. Mod. Phys. A33(2018) 1850100, arXiv:1806.02209 [hep-th]. 32

    Pith/arXiv arXiv 2018

  46. [46]

    A Holographic proof of the strong subadditivity of entanglement entropy,

    M. Headrick and T. Takayanagi, “A Holographic proof of the strong subadditivity of entanglement entropy,”Phys. Rev. D76(2007) 106013, arXiv:0704.3719 [hep-th]

    Pith/arXiv arXiv 2007

  47. [47]

    Holographic Entanglement Entropy: An Overview,

    T. Nishioka, S. Ryu, and T. Takayanagi, “Holographic Entanglement Entropy: An Overview,”J. Phys. A42(2009) 504008,arXiv:0905.0932 [hep-th]

    Pith/arXiv arXiv 2009

  48. [48]

    The AdS / CFT correspondence and a new positive energy conjecture for general relativity,

    G. T. Horowitz and R. C. Myers, “The AdS / CFT correspondence and a new positive energy conjecture for general relativity,”Phys. Rev. D59(1998) 026005,arXiv:hep-th/9808079

    Pith/arXiv arXiv 1998

  49. [49]

    Entanglement as a Probe of Confinement,

    I. R. Klebanov, D. Kutasov, and A. Murugan, “Entanglement as a Probe of Confinement,”Nucl. Phys. B796(2008) 274–293,arXiv:0709.2140 [hep-th]

    Pith/arXiv arXiv 2008

  50. [50]

    Low energy properties of hadrons from holographic QCD,

    T. Sakai and S. Sugimoto, “Low energy properties of hadrons from holographic QCD,”Prog. Theor. Phys.113(2005) 1083–1118,arXiv:hep-th/0412141

    Pith/arXiv arXiv 2005

  51. [51]

    More on holographic QCD,

    T. Sakai and S. Sugimoto, “More on holographic QCD,”Prog. Theor. Phys.114 (2005) 1083–1118,arXiv:hep-th/0507073

    Pith/arXiv arXiv 2005

  52. [52]

    Complexity, scaling, and a phase transition,

    J. Yang and A. R. Frey, “Complexity, scaling, and a phase transition,”JHEP09 (2023) 029,arXiv:2307.08229 [hep-th]

    Pith/arXiv arXiv 2023

  53. [53]

    Krylov complexity as an order parameter for deconfinement phase transitions at large N,

    T. Anegawa, N. Iizuka, and M. Nishida, “Krylov complexity as an order parameter for deconfinement phase transitions at large N,”JHEP04(2024) 119, arXiv:2401.01501 [hep-th]

    Pith/arXiv arXiv 2024

  54. [54]

    Yang-Baxterσ-models, conformal twists, and noncommutative Yang-Mills theory,

    T. Araujo, I. Bakhmatov, E. ´O. Colg´ ain, J. i. Sakamoto, M. M. Sheikh-Jabbari, and K. Yoshida, “Yang-Baxterσ-models, conformal twists, and noncommutative Yang-Mills theory,”Phys. Rev. D95(2017) 105006,arXiv:1702.02861 [hep-th]

    Pith/arXiv arXiv 2017

  55. [55]

    Conformal Twists, Yang-Baxterσ-models & Holographic Noncommutativity,

    T. Araujo, I. Bakhmatov, E. ´O. Colg´ ain, J. i. Sakamoto, M. M. Sheikh-Jabbari, and K. Yoshida, “Conformal Twists, Yang-Baxterσ-models & Holographic Noncommutativity,”J. Phys. A51(2018) 235401,arXiv:1705.02063 [hep-th]. 33

    Pith/arXiv arXiv 2018