Quantum states in an AdS-invariant theory

Felix M. Lev; Valery E. Lyubovitskij

REVIEW

Quantum states in an AdS-invariant theory

Felix M. Lev, Valery E. Lyubovitskij

High Energy Physics - Theory · Submitted 29 Sep 2026 · 18 references

Pith's verdict: The specific counterexample is miscalculated, but the underlying non-separability observation survives; the load-bearing gap is the never-defined operator class.

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arXiv ID2609.37401 (version 1)

Pith IDEDLUJTCV, Pith's permanent record of this paper and its review

CitationFelix M. Lev, Valery E. Lyubovitskij. "Quantum states in an AdS-invariant theory." arXiv:2609.37401 (2026). https://pith.science/paper/EDLUJTCV

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Editor's note

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What should you know about this one. The headline claim — that the standard Conjecture (distinct states distinguishable by a self-adjoint operator) fails in AdS theory — is not established. But the reason is not the one the stress-test gives. The stress test is right that the concrete example is wrong: Sec. V claims e(2,0,0) and e(0,1,1) share h1=h2=q0+1, yet the paper's own spectrum (Sec. VI, h_j = q0 + n/2 + 2n_j) gives e(2,0,0) = (q0+4, q0) and e(0,1,1) = (q0+1/2, q0+5/2). With e(n1,n2,n) ordered as in Eq. (26), those do not match. The example as printed is simply arithmetic junk. But the stress test then overreaches. It claims the map (n,n1,n2) -> (h1,h2) is injective, "hence" no two basis states share Cartan eigenvalues. Wrong. Take e(1,1,0) = a''1 a''2 e0 and e(0,0,4) = (A++)^4 e0. Both give (h1,h2) = (q0+2, q0+2), and both exist — norms are positive for q0>2 by Eqs. (6) and (25). So the paper's underlying observation is real: the Cartan subalgebra does not uniquely label the basis, and n is invisible to it. The example is botched; the phenomenon survives with different states. The actual load-bearing problem is the one the reader flags. The Conjecture-failure step requires ruling out separating self-adjoint operators, and the paper never defines the allowed class. On the unrestricted reading it is trivially false: for any two orthogonal states, |1><1| - |2><2| distinguishes them. On a restricted reading (operators built from the algebra generators), no impossibility is proved, and elements like M34 = b' + b'' are not even diagonal in this basis, so nothing about separation follows. "Rank two, therefore no additional independent operator" (b142) is asserted, not shown. The step from Cartan non-separability to Conjecture failure is a genuine gap and arguably fatal on the broad reading. Credit where earned: the UIR basis construction and norm computations in Sec. IV are handled competently; the partition-function arithmetic in Sec. VI checks out, including the low-T expansions; the Cartan non-separability observation is real and not in the cited literature. But the thermodynamics is bookkeeping — U_mod ~ 2kT vs ~ 3kT follows from the S1∪S2 postulate by direct summation, not from any independent argument. Verdict: not publishable as is. The example needs correcting (easy) and the operator-class question needs a real answer (hard). I would send it to a referee who can pin that question immediately — the observation is genuine and the foundational issue is worth engaging — but I'd expect heavy revision and a downgraded, probably conditional, claim. For you: maybe one reading-group session to settle the operator class; I wouldn't cite it in its current form.

Referee report

Significance

If established, a genuine failure of operator distinguishability inside an exact AdS symmetry would be a significant foundational result with sharp phenomenological consequences, including the stiffer equation of state (Eq. 41) and modified hadronic sum rules. Credit is due for a largely self-contained UIR construction (Sec. IV) with an explicit positivity computation for the norms a(n) (Eq. 25), and the thermodynamic arithmetic in Eqs. (28)\u2013(44) is internally consistent once the partition functions are accepted. However, the central claim is not established: the explicit counterexample is numerically wrong under the paper's own spectrum formula, the Conjecture as literally stated in Sec. I is trivially satisfied by projection operators for orthogonal states, and the rank-2 no-go step is unproven. The thermodynamic results are therefore bookkeeping of an unsupported postulate rather than an independent derivation.

Major objections (4)

[Sec. V (b104\u2013b105) vs. Sec. VI (text before Eq. 28)] The stated counterexample is internally inconsistent with the paper's own spectrum formula. Sec. VI states that on the basis e(n1,n2,n) the Cartan eigenvalues are h_j = q0 + n/2 + 2 n_j. For e(2,0,0) this gives (h1,h2) = (q0+1, q0+1), but for e(0,1,1) it gives (h1,h2) = (q0+2, q0+2), since n=0 while n1=n2=1 each contribute +2. These eigenvalues are not identical, contradicting the assertion in Sec. V that both states share the eigenvalues (q0+1, q0+1). Because this pair of states is the load-bearing premise for the restriction in Eq. (27), the central argument collapses on its own terms.
[Sec. I (Conjecture) and Sec. V (b104)] As stated in Sec. I, the Conjecture is trivially satisfied for any two distinct orthogonal states: the projection operator P = |\u03a81\u27e9\u27e8\u03a81| is self-adjoint, with eigenvalue 1 on \u03a81 and 0 on \u03a82. The Sec. V states are asserted to be mutually orthogonal (b104), so the claimed failure contradicts the Conjecture exactly as written. If the intended claim concerns only operators constructed from the algebra generators, the Conjecture must first be restated for that restricted operator class, and the paper supplies no no-go proof for that class. The assertion in Sec. I that no theorem proving the Conjecture has ever been established is therefore misleading as it stands.
[Sec. V (b101, b142)] The inference from the rank-2 Cartan subalgebra to the conclusion that no additional operator can separate the two states is not established. The rank of the Cartan subalgebra bounds only the size of a commuting family of operators diagonal in a fixed weight basis; the enveloping algebra contains non-diagonal self-adjoint elements, for example M34 = b' + b'' (Eq. 15), whose matrix elements on the basis in Eq. (26) are not fixed by the Cartan labels. No impossibility argument for any explicit operator class is provided, so the conclusion that a physically consistent formulation requires restricting to S1 \u222a S2 does not follow from the premises given.
[Sec. V\u2013VI (Eq. 27; Eqs. 34\u201341)] Even taking the paper's spectrum formula at face value, genuine degeneracies of Cartan eigenvalues do occur \u2014 for example e(4m,0,0) and e(0,m,m) both carry (h1,h2) = (q0+2m, q0+2m) for m \u2265 1 \u2014 but this is a different pair from the one claimed in Sec. V, and per the preceding comment such degeneracy does not violate the Conjecture as stated, since projection operators separate the states. Consequently the restriction in Eq. (27) is unmotivated, and the thermodynamic consequences in Eqs. (34)\u2013(41), including U_mod \u2248 2k_BT, are exact consequences of that ad hoc postulate rather than an independent derivation. The paper should present these results explicitly as conditional on the restriction.

Minor objections (5)

[Eq. (17)] The second-order Casimir expansion contains the asymmetric term \u22124h2, which is not what one would expect from a symmetric trace contraction over the ten generators; please verify this expression and fix any transcription error.
[Sec. VI (b130) and Sec. V (b101)] The parameter n is called 'unphysical' in Sec. V (b101) and then 'topological' in Sec. VI (b130) without any definition of the latter term; the physical status of n and the terminology used for it should be pinned down consistently.
[Sec. IV (Eq. 18)] The half-integer factors (h_j \u2212 1/2) in the shift operators are asserted to follow from the 'i-convention' normalization; a short derivation, or at least an explicit statement of the convention, would allow the reader to verify the stated action of A\u00b1\u00b1 on minimal vectors.
[Sec. VI (b121\u2013b122)] The identification of the T^3 scaling of Z_std with a '(3+1)-dimensional conformal bulk field theory' (citing Refs. [4,5]) is asserted rather than derived; a sentence connecting the discrete sums over (n,n1,n2) to the cited continuum results would clarify the comparison.
[Sec. I (b13\u2013b16)] The historical examples used to motivate the Conjecture (momentum, energy, angular momentum) all concern operators from the symmetry algebra, whereas the Conjecture as stated ranges over all self-adjoint operators; aligning the statement with the intended operator class would remove the ambiguity discussed in Major Comment 2.

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The paper

The paper claims

This paper claims that inside anti-de Sitter (AdS) quantum theory the usual assumption that distinct physical states can always be separated by a self-adjoint operator fails, because the rank-2 Cartan subalgebra leaves two orthogonal…

The reading

This paper claims that inside anti-de Sitter (AdS) quantum theory the standard quantum-mechanical Conjecture, that any two distinct physical states can be distinguished by some self-adjoint operator, fails. Because the AdS algebra has a rank-2 Cartan subalgebra, basis states such as $e(2,0,0)$ and $e(0,1,1)$ share identical eigenvalues of both commuting generators $h_1$ and $h_2$, and the paper argues that no additional operator constructed from the algebra can separate them. To restore one-to-one correspondence between states and operator eigenvalues, the paper restricts the physical Hilbert space to the subsets $S_1$ and $S_2$, freezing the unphysical parameter $n$ to zero. The consequence is a measurable change in thermodynamics: the high-temperature internal energy of an AdS quantum gas becomes $U_{\mathrm{mod}}\approx 2k_B T$ instead of the standard $U_{\mathrm{std}}\approx 3k_B T$, and similar sum-rule modifications are anticipated in AdS/QCD hadronic form factors.

What carries the argument

The central object is the rank-2 Cartan subalgebra of the AdS algebra, spanned by the two commuting generators $h_1$ and $h_2$ (whose combinations give the energy operator $M_{04} = \tfrac12(h_1+h_2)$ and the angular momentum $L_3 = h_1 - h_2$), together with the triplet index $(n,n_1,n_2)$ labelling basis vectors $e(n_1,n_2,n) = (a''_1)^{n_1}(a''_2)^{n_2}(A_{++})^n e_0$. The parameter $n$ is 'topological': it is not an eigenvalue of any operator in the algebra, and the two states $e(2,0,0)$ and $e(0,1,1)$ share the same Cartan eigenvalues. The paper uses this degeneracy to justify restricting physical states to $S_1 \cup S_2$, which freezes $n=0$ and removes one effective degree of freedom from the spectrum.

Extended reading notes

Core claim

On the paper's own terms, the central discovery is that the rank-2 Cartan subalgebra of $\mathrm{so}(3,2)$ makes the standard quantum-mechanical Conjecture fail for AdS elementary particles. In the massive spinless UIR, states are labelled by the triplet $(n,n_1,n_2)$, where $(n_1,n_2)$ are eigenvalues of the two Cartan generators $h_1,h_2$ and $n$ counts applications of the shift operator $A_{++}$; the parameter $n$ is not the eigenvalue of any algebra operator. The states $e(2,0,0)$ and $e(0,1,1)$ are mutually orthogonal, have non-zero norms, and carry identical eigenvalues $(q_0+1)$ for both $h_1$ and $h_2$. Because the algebra rank is strictly two, the paper claims, no independent self-adjoint operator can be constructed from the generators to separate them, so the Conjecture fails and the full UIR space contains states with identical quantum numbers and no algebraic means of differentiation. The physical resolution proposed is to restrict the state space to $S_1 = e(0,n_1,n_2)$ and $S_2 = b''e(0,n_1,n_2)$, freezing $n=0$; the thermodynamic consequence is a single-particle partition function that scales as $T^2$ rather than $T^3$ at high temperature, giving $U_{\mathrm{mod}}\approx 2k_B T$ instead of $U_{\mathrm{std}}\approx 3k_B T$.

Load-bearing premise

The load-bearing premise is the claim that because the AdS algebra has rank 2, no self-adjoint operator built from the algebra generators can separate the degenerate states $e(2,0,0)$ and $e(0,1,1)$; the paper does not prove this impossibility for operators that are not simultaneously diagonal in the Cartan basis.

Editorial extensions

If this is right

The single-particle AdS partition function changes from $Z_{\mathrm{std}} = e^{-q_0\beta}/((1-e^{-\beta/2})(1-e^{-\beta})^2)$, scaling as $T^3$, to $Z_{\mathrm{mod}} = e^{-q_0\beta}(1+e^{-\beta})/(1-e^{-\beta})^2$, scaling as $T^2$ at high temperature.
At high temperature the internal energy of an AdS quantum gas becomes $U_{\mathrm{mod}}\approx 2k_B T$ instead of $U_{\mathrm{std}}\approx 3k_B T$, lowering the heat capacity and altering the early-Universe cooling rate.
At low temperature the restricted gas shows a first excitation gap of $\Delta E = 1$ rather than a spurious $\Delta E = 1/2$ step, so it is protected from low-energy state mixtures the standard UIR admits.
Restricting the Hilbert space to $S_1 \cup S_2$ changes the completeness relations and sum rules in AdS/QCD, modifying meson and nucleon electromagnetic form factors at intermediate momentum transfer.
Because the Poincar\'e algebra is recovered from AdS in the $R \to \infty$ contraction, all these effects vanish in the flat limit and appear only where the finite length scale $R$ matters.

Reading between the lines

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

The claimed counterexample to the Conjecture is not established by the paper as written: the rank of the Cartan subalgebra limits only simultaneously diagonalizable commuting families, whereas non-commuting self-adjoint elements of the enveloping algebra (for example $M_{34} = b' + b''$) need not be diagonal in the chosen basis and could in principle separate the two states.
For any two orthogonal states the difference of their projection operators is itself a self-adjoint operator that separates them, so the claimed failure of the Conjecture only holds under an implicit restriction on which operators count as 'physical'; a reader should treat the state-space restriction as conditional on that stricter definition.
If the restriction to $S_1 \cup S_2$ is instead imposed as a postulate, the $T^2$ versus $T^3$ scaling of the partition function is a clean, testable discriminator between the restricted AdS gas and ordinary conformal field theory in a cosmological setting.

Original abstract

We note that the description of elementary particles in anti-de Sitter (AdS) quantum theory differs radically from standard approaches. Since the Cartan subalgebra of the AdS algebra has rank 2, it is necessary to consider only those elements that explicitly depend on the eigenvalues of operators in the irreducible representations (IRs) of the algebra. In the literature, AdS symmetry is widely invoked in various quantum applications, such as AdS/QCD. However, such frameworks typically do not take into account the unconventional properties of the AdS algebra IRs investigated in the present paper.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-30: 1 request, 3,600 input tokens.

What the abstract itself states, as probabilities: claims first 0.10 · states limitation 0.10 · human participants 0.01 · controlled comparison 0.06 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.76 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; show every role.

We note that the description of elementary particles in anti-de Sitter (AdS) quantum theory differs radically from standard approaches. Since the Cartan subalgebra of the AdS algebra has rank 2, it is necessary to consider only those elements that explicitly depend on the eigenvalues of operators in the irreducible representations (IRs) of the algebra. In the literature, AdS symmetry is widely invoked in various quantum applications, such as AdS/QCD. However, such frameworks typically do not take into account the unconventional properties of the AdS algebra IRs investigated in the present paper.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We note that the description of elementary particles in anti-de Sitter (AdS) quantum theory differs radically from standard approaches.	background 0.91	0.27	0.19	asserted 1.00
s1	Since the Cartan subalgebra of the AdS algebra has rank 2, it is necessary to consider only those elements that explicitly depend on the eigenvalues of operators in the irreducible representations (IRs) of the algebra.	method 0.35	0.25	0.14	asserted 1.00
s2	In the literature, AdS symmetry is widely invoked in various quantum applications, such as AdS/QCD.	background 1.00	0.03	0.02	asserted 1.00
s3	However, such frameworks typically do not take into account the unconventional properties of the AdS algebra IRs investigated in the present paper.	gap 1.00	0.10	0.11	asserted 0.98

What kind of paper the classifier reports this is: theoretical result 0.84 · evidence from argument 0.56.

What was examined, and what was not

sources read

arXiv listing abstract v1

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

References

Works cited (18)

[1]

leave the eigenvalues ofh 2 invariant, and (a′ 2,a′′

View on Pith
[2]

factors, leading to the following precise definition of the shift operators: A++ =b ′′ h1− 1 2 h2− 1 2 −a′′ 1L− h2− 1 2 −a′′ 2L+ h1− 1 2 +a′′ 1a′′ 2b′, A+− =L + h1− 1 2 −a′′ 1b′, A −+ =L− h2− 1 2 −a′′ 2b′, A−− =b ′. (18) In standard mathematical approaches, one considers the action of these operators exclusively on the subspace of minimalsp(2)×sp(2) vecto...

View on Pith
[3]

do not alter those ofh 1. For illustration, we restrict our attention to the massive, positive-energy case whereq 1≥q 2 >2. Under this setup, e0 represents the state of minimum energyµ=q 0, which defines the AdS rest mass, ands=q 1−q 2 corresponds to the particle spin. We further simplify to the spinless case (q 1 =q 2 =q 0,s= 0). The states: en = (A++)ne...

View on Pith
[4]

F. Lev,Finite mathematics as the foundation of classical mathematics and quantum theory. With application to gravity and particle theory. ISBN 978-3-030-61101-9. Springer, Cham, Switzerland (2020)

View on Pith 2020
[5]

F. G. Dyson, Missed opportunities, Bull. Amer. Math. Soc.78, 635 (1972)

View on Pith 1972
[6]

N. T. Evans, Discrete series for the universal covering group of the 3+2 de Sitter Group, J. Math. Phys.8, 170 (1967)

View on Pith 1967
[7]

S. W. Hawking and D. N. Page, Thermodynamics of black holes in anti-de Sitter space, Commun. Math. Phys.87, 577 (1983)

View on Pith 1983
[8]

W. S. Elias, C. Molina, and M. C. Baldiotti, Thermodynamics of bosonic systems in anti-de Sitter spacetime, Phys. Rev. D99, no.8, 084028 (2019) [arXiv:1803.05921 [hep-th]]

View on Pith Pith review arXiv 2019
[9]

J. Ehrlich, E. Katz, D. T. Son, and M. A. Stephanov, QCD and a holographic model of hadrons, Phys. Rev. Lett.95, 261602 (2005) [arXiv:hep-ph/0501128 [hep-ph]]

View on Pith Pith review arXiv 2005
[10]

A. Karch, E. Katz, D. T. Son, and M. A. Stephanov, Linear confinement and AdS/QCD. Phys. Rev. D74, 015005 (2006) [arXiv:hep-ph/0602229 [hep-ph]]

View on Pith Pith review arXiv 2006
[11]

S. J. Brodsky, G. F. de Teramond, H. G. Dosch and J. Erlich, Light-front holographic QCD and emerging confinement. Phys. Rept.584, 1-105 (2015) [arXiv:1407.8131 [hep-ph]]

View on Pith Pith review arXiv 2015
[12]

S. J. Brodsky and G. F. de Teramond, Light-front dynamics and AdS/QCD correspondence: The Pion Form Factor in the Space- and Time-Like Regions, Phys. Rev. D77, 056007 (2008) [arXiv:0707.3859 [hep-ph]]

View on Pith Pith review arXiv 2008
[13]

H. R. Grigoryan and A. V. Radyushkin, Form factors and wave functions of vector mesons in holographic QCD, Phys. Lett. B650, 421 (2007) [arXiv:hep-ph/0703069 [hep-ph]]

View on Pith Pith review arXiv 2007
[14]

H. R. Grigoryan and A. V. Radyushkin, Structure of vector mesons in holographic model with linear confinement, Phys. Rev. D76, 095007 (2007) [arXiv:0706.1543 [hep-ph]]

View on Pith Pith review arXiv 2007
[15]

G. F. de Teramond and S. J. Brodsky, Hadronic spectrum of a holographic dual of QCD, Phys. Rev. Lett.94, 201601 (2005) [arXiv:hep-th/0501022 [hep-th]]

View on Pith Pith review arXiv 2005
[16]

T. Gutsche, V. E. Lyubovitskij, I. Schmidt, and A. Vega, Dilaton in a soft-wall holographic approach to mesons and baryons, Phys. Rev. D85, 076003 (2012) [arXiv:1108.0346 [hep-ph]]; Nucleon structure in a light-front quark model consistent with quark counting rules and data, Phys. Rev. D91, 054028 (2015) [arXiv:1411.1710 [hep-ph]]

View on Pith Pith review arXiv 2012
[17]

T. Gutsche, V. E. Lyubovitskij, and I. Schmidt, Deuteron electromagnetic structure functions and polarization properties in soft-wall AdS/QCD, Phys. Rev. D94, no.11, 116006 (2016) [arXiv:1607.04124 [hep-ph]]; Nucleon parton distributions in a light-front quark model, Eur. Phys. J. C77, no.2, 86 (2017) [arXiv:1610.03526 [hep-ph]]; Electromagnetic propertie...

View on Pith Pith review arXiv 2016
[18]

V. E. Lyubovitskij and I. Schmidt, Bulk-to-boundary propagators with arbitrary total angular momentumJin soft-wall AdS/QCD, Phys. Rev. D108, no.5, 054030 (2023) [arXiv:2307.05450 [hep-ph]]

View on Pith Pith review arXiv 2023

Discussion

Disagree with the review, or know something it missed? Leave a comment, highlight any passage above to comment on it, or challenge this review formally.

[1] [1]

leave the eigenvalues ofh 2 invariant, and (a′ 2,a′′

View on Pith

[2] [2]

factors, leading to the following precise definition of the shift operators: A++ =b ′′ h1− 1 2 h2− 1 2 −a′′ 1L− h2− 1 2 −a′′ 2L+ h1− 1 2 +a′′ 1a′′ 2b′, A+− =L + h1− 1 2 −a′′ 1b′, A −+ =L− h2− 1 2 −a′′ 2b′, A−− =b ′. (18) In standard mathematical approaches, one considers the action of these operators exclusively on the subspace of minimalsp(2)×sp(2) vecto...

View on Pith

[3] [3]

do not alter those ofh 1. For illustration, we restrict our attention to the massive, positive-energy case whereq 1≥q 2 >2. Under this setup, e0 represents the state of minimum energyµ=q 0, which defines the AdS rest mass, ands=q 1−q 2 corresponds to the particle spin. We further simplify to the spinless case (q 1 =q 2 =q 0,s= 0). The states: en = (A++)ne...

View on Pith

[4] [4]

F. Lev,Finite mathematics as the foundation of classical mathematics and quantum theory. With application to gravity and particle theory. ISBN 978-3-030-61101-9. Springer, Cham, Switzerland (2020)

View on Pith 2020

[5] [5]

F. G. Dyson, Missed opportunities, Bull. Amer. Math. Soc.78, 635 (1972)

View on Pith 1972

[6] [6]

N. T. Evans, Discrete series for the universal covering group of the 3+2 de Sitter Group, J. Math. Phys.8, 170 (1967)

View on Pith 1967

[7] [7]

S. W. Hawking and D. N. Page, Thermodynamics of black holes in anti-de Sitter space, Commun. Math. Phys.87, 577 (1983)

View on Pith 1983

[8] [8]

W. S. Elias, C. Molina, and M. C. Baldiotti, Thermodynamics of bosonic systems in anti-de Sitter spacetime, Phys. Rev. D99, no.8, 084028 (2019) [arXiv:1803.05921 [hep-th]]

View on Pith Pith review arXiv 2019

[9] [9]

J. Ehrlich, E. Katz, D. T. Son, and M. A. Stephanov, QCD and a holographic model of hadrons, Phys. Rev. Lett.95, 261602 (2005) [arXiv:hep-ph/0501128 [hep-ph]]

View on Pith Pith review arXiv 2005

[10] [10]

A. Karch, E. Katz, D. T. Son, and M. A. Stephanov, Linear confinement and AdS/QCD. Phys. Rev. D74, 015005 (2006) [arXiv:hep-ph/0602229 [hep-ph]]

View on Pith Pith review arXiv 2006

[11] [11]

S. J. Brodsky, G. F. de Teramond, H. G. Dosch and J. Erlich, Light-front holographic QCD and emerging confinement. Phys. Rept.584, 1-105 (2015) [arXiv:1407.8131 [hep-ph]]

View on Pith Pith review arXiv 2015

[12] [12]

S. J. Brodsky and G. F. de Teramond, Light-front dynamics and AdS/QCD correspondence: The Pion Form Factor in the Space- and Time-Like Regions, Phys. Rev. D77, 056007 (2008) [arXiv:0707.3859 [hep-ph]]

View on Pith Pith review arXiv 2008

[13] [13]

H. R. Grigoryan and A. V. Radyushkin, Form factors and wave functions of vector mesons in holographic QCD, Phys. Lett. B650, 421 (2007) [arXiv:hep-ph/0703069 [hep-ph]]

View on Pith Pith review arXiv 2007

[14] [14]

H. R. Grigoryan and A. V. Radyushkin, Structure of vector mesons in holographic model with linear confinement, Phys. Rev. D76, 095007 (2007) [arXiv:0706.1543 [hep-ph]]

View on Pith Pith review arXiv 2007

[15] [15]

G. F. de Teramond and S. J. Brodsky, Hadronic spectrum of a holographic dual of QCD, Phys. Rev. Lett.94, 201601 (2005) [arXiv:hep-th/0501022 [hep-th]]

View on Pith Pith review arXiv 2005

[16] [16]

T. Gutsche, V. E. Lyubovitskij, I. Schmidt, and A. Vega, Dilaton in a soft-wall holographic approach to mesons and baryons, Phys. Rev. D85, 076003 (2012) [arXiv:1108.0346 [hep-ph]]; Nucleon structure in a light-front quark model consistent with quark counting rules and data, Phys. Rev. D91, 054028 (2015) [arXiv:1411.1710 [hep-ph]]

View on Pith Pith review arXiv 2012

[17] [17]

T. Gutsche, V. E. Lyubovitskij, and I. Schmidt, Deuteron electromagnetic structure functions and polarization properties in soft-wall AdS/QCD, Phys. Rev. D94, no.11, 116006 (2016) [arXiv:1607.04124 [hep-ph]]; Nucleon parton distributions in a light-front quark model, Eur. Phys. J. C77, no.2, 86 (2017) [arXiv:1610.03526 [hep-ph]]; Electromagnetic propertie...

View on Pith Pith review arXiv 2016

[18] [18]

V. E. Lyubovitskij and I. Schmidt, Bulk-to-boundary propagators with arbitrary total angular momentumJin soft-wall AdS/QCD, Phys. Rev. D108, no.5, 054030 (2023) [arXiv:2307.05450 [hep-ph]]

View on Pith Pith review arXiv 2023