Double-Trace Deformations, Mixed Boundary Conditions and Functional Determinants in AdS/CFT

Leonardo Rastelli; Thomas Hartman

REVIEW

Double-Trace Deformations, Mixed Boundary Conditions and Functional Determinants in AdS/CFT

Thomas Hartman, Leonardo Rastelli

High Energy Physics - Theory · Submitted 10 Feb 2006 · 37 references

Pith's verdict: A clean, honest clarifying note: the bulk and boundary determinant ratios are shown to be the same object, with one bounded rigor gap in extending the determinant-ratio formula to the non-Sturm-Liouville radial operator.

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CitationLeonardo Rastelli, Thomas Hartman. "Double-Trace Deformations, Mixed Boundary Conditions and Functional Determinants in AdS/CFT." arXiv:hep-th/0602106 (2006). https://pith.science/paper/XV3GNNJ2

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Editor's note

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This is a clarifying note, and it does what it sets out to do. The known agreement between bulk and boundary computations of c_UV - c_IR (Gubser-Mitra, Gubser-Klebanov) gets a step-by-step explanation: the ratio of bulk functional determinants with two mixed boundary conditions equals the boundary CFT determinant ratio, term by term in a sum over boundary modes. That identity, Eq. (4.4), is the real content, and it is not in the cited prior work. The paper also gives a clean diagrammatic argument in section 5 that using Delta_- propagators is equivalent to the Klebanov-Witten Legendre transform, and the appendix re-derives the Gubser-Mitra effective potential with a different regulator, confirming the BF-bound assumption. Those are genuine, reusable contributions, and the writing is direct about scope: this is a kinematic explanation of a known result, not a new prediction. No free parameters, no invented entities, no circularity that I can see. The bulk determinant and the boundary mode sum are independently defined; showing they coincide is a computation, not a tautology. On the stress-test concern: it lands, but it is smaller than it looks. The determinant-ratio formula (4.13) is proved by the zeta-function contour argument of Kirsten-McKane, and the only assumption is the falloff (4.16). The authors acknowledge the radial operator is not Sturm-Liouville (footnote 6) and check (4.16) explicitly in Poincare coordinates, Eq. (4.26). In hyperbolic coordinates they verify the final ratio numerically to six or seven digits at d=4, l=3, m^2=-3.5. The stress-test is right that nu -> 0 and large l are not covered by that numerical point. But the appendix's independent derivation of V+ - V- covers all nu, including nu -> 0, and confirms V+(m_BF) = V-(m_BF); so the BF-bound corner is indirectly closed by a separate route. What remains is a rigor gap in the general proof, not evidence that (4.4) is wrong. Worth flagging to the authors, not a reason to hold up the paper. Who should read it: anyone working on double-trace deformations, mixed boundary conditions, or holographic RG, and anyone who wants a worked example of comparing functional determinants across the correspondence. It is a useful reference, not a landmark. I would send it to referees; the central identity is sound and the checks are real.

Referee report

Significance

The paper supplies a structural, 'kinematic' reason for a universal agreement that had previously been established only by two superficially unrelated calculations. The identity is exact, holds for arbitrary d and arbitrary Delta_-, and is independent of supersymmetry, so it is a genuine organizing statement rather than a case-by-case check. The diagrammatic proof in Section 5 that Delta_- propagators implement the Legendre transform is a useful clarification of the Klebanov-Witten prescription, and the appendix's independent regulator calculation of the one-loop potential, which confirms the Breitenlohner-Freedman-bound assumption of Gubser-Mitra rather than assuming it, is a real (if modest) added check. The methods are stated to extend to black-hole backgrounds and to designer gravity, which gives the result reach beyond the immediate computation. The paper is self-contained and the key steps are verifiable by the reader.

Major objections (1)

[§4.3, Eq. (4.26) and the sentence preceding it] The general proof of the determinant-ratio formula (4.13) for the radial operator rests on the asymptotic condition (4.16), and the paper correctly notes that the radial operator is not of Sturm-Liouville type. The verification in (4.26), however, is presented through the large-order Bessel limit K_{nu+1}(x)/K_nu(x) -> 2 nu/x as nu -> infinity, while (4.16) is a statement about lambda -> infinity, i.e. about large argument k epsilon of the Bessel functions at fixed nu. These are different limits, and the text introducing (4.26) refers to 'large Re nu', which does not obviously match the contour deformation in (4.15). Please state explicitly which limit is being taken and, if the intended check is the large-argument expansion k epsilon -> infinity, display that expansion and the resulting lambda^{-3/2} falloff. I note that this concern is substantially mitigated by §4.4, where the ratio (4.35) is checked analytically against the CFT answer (4.36) using the explicit hypergeometric solution (4.31), independently of the contour argument, and by the numerical results in Table 1 and Figure 2; the request is therefore about making the scope of the general proof explicit, not about the correctness of the identity (4.4).

Minor objections (8)

[Abstract, first sentence] The phrase 'the UV ad IR fixed points' should read 'the UV and IR fixed points'.
[§4.1, paragraph following Eq. (4.11)] 'for deﬁnitene ss' should read 'for definiteness'; similarly, in §5 the phrase 'the same functional for m in x0' should read 'the same functional form in x0'.
[§5, Eqs. (5.1)-(5.2)] Please re-check the normalization displayed in (5.1) and (5.2). As printed, the epsilon -> 0 limit of (5.1) appears to be independent of x0, whereas the bulk-to-boundary propagator should scale as (x0/epsilon)^{Delta_-} at fixed k. The ratio (5.3), which is what the subsequent argument uses, is unaffected, but the intermediate expressions should be corrected or the convention stated.
[Appendix, Eq. (A.12)] The derivation states that the t -> 0 limit, the infinite sum over n, and the integral over nu-tilde are interchanged, and that 'everything but the final limit is finite'. A sentence justifying this interchange (or a citation to the DeWitt-Schwinger treatment of [34], Section 6.1, which is invoked earlier) would make the regularization prescription reproducible.
[Appendix, final paragraph] The compatibility with the zeta-function calculation of [37] is stated conditionally ('if one assumes that we can obtain V_- by simply replacing Delta_+ -> Delta_-'). Please say whether this is offered as an independent check or only as a consistency remark, since the conditional phrasing weakens what would otherwise be a second confirmation of the results.
[Table 1 and Figure 2] The numerical check is performed at a single parameter point (d = 4, l = 3, m^2 = -3.5, i.e. nu approximately 0.71). Since the delicate regimes for the asymptotics are nu -> 0, where the two roots coalesce, and large l, where the hypergeometric parameters in (4.31) grow, adding one point near the Breitenlohner-Freedman bound and one at larger l would materially strengthen the numerical evidence.
[§4.4, Eq. (4.32)] The boundary condition at rho = 2 is described as an 'inessential modification' of (4.9). A brief justification that the determinant ratio is insensitive to this choice, or a pointer to where the insensitivity is used, would help the reader.
[§4.2, following Eq. (4.19)] The paper never displays the resulting expression for c_UV - c_IR itself. A one-line statement connecting (4.19) to the known results of [2,3] would let the reader see the 'kinematic' explanation concretely rather than having to reconstruct it from the determinant identity.

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The paper

The paper claims

The paper reduces the matching central-charge change in a holographic double-trace flow to a single functional-determinant identity.

The reading

The paper asks why two very different calculations—a boundary large-$N$ mode sum and a bulk one-loop effective potential—give exactly the same change in the central charge when a conformal field theory is deformed by a double-trace operator $fO^2$. It answers by rewriting both calculations as the same ratio of functional determinants: the bulk ratio of radial determinants with two mixed boundary conditions equals the boundary ratio $(1+f_1G)/(1+f_2G)$. Because the equality holds mode by mode, the agreement is a bookkeeping identity rather than a coincidence of two separate computations. The paper also shows that using the alternative $��_-$ boundary conditions in bulk Feynman diagrams is exactly the Legendre transform of the standard $��_+$ prescription.

What carries the argument

The machinery is the ratio formula for functional determinants of the same operator with different mixed Neumann/Dirichlet boundary conditions, Eq. (4.13): $$ ��rac{��det_{��_1}P}{��det_{��_2}P} = ��rac{��gamma_1 p(a)+p'(a)}{��gamma_2 p(a)+p'(a)}, $$ where $p$ solves the radial equation with a Dirichlet condition in the AdS interior and $��gamma$ is the mixed-boundary parameter. The paper proves this from the zeta function by a contour integral, then uses the boundary expansion of $p$ to show $p(��epsilon)/(��gamma p(��epsilon)+��epsilon p'(��epsilon))=Q_f$. That turns the bulk determinant ratio into the CFT kernel ratio. The second piece is the diagrammatic identity $G_{��Delta_+}-G_{��Delta_-}��propto P_{��Delta_+}P_{��Delta_+}$, which makes the Legendre transform of $��Delta_+$ correlators equal to the correlators built with $��Delta_-$ propagators.

Extended reading notes

Core claim

The central result is Eq. (4.4): $$ ��rac{��det_{��_1}(-��Box+$m^{2}$)}{��det_{��_2}(-��Box+$m^{2}$)} = ��rac{1+f_1 G}{1+f_2 G} = ��rac{Q_{f_2}}{Q_{f_1}}. $$ The left side is the change in the bulk one-loop partition function when the boundary condition on the dual scalar is changed from $��_1$ to $��_2$; the right side is the change in the boundary CFT partition function produced by the corresponding double-trace couplings $f_1,f_2$. The proof reduces the bulk determinant ratio to a boundary-value expression involving the solution of the radial wave equation that is regular in the interior, then identifies that expression with the CFT kernel $Q_f=G/(1+fG)$. Thus the $c_{UV}-c_{IR}$ agreement found in earlier work is not an accident of two calculations but follows from one determinant identity applied to each boundary mode.

Load-bearing premise

The load-bearing premise is that the ratio of radial functional determinants with different mixed boundary conditions is given by the boundary values of the Dirichlet solution through Eq. (4.13), which requires the falloff condition (4.16) that the authors verify explicitly in Poincaré coordinates and numerically in hyperbolic coordinates rather than proving for all backgrounds.

Editorial extensions

If this is right

The change in central charge between the UV and IR fixed points is equal in the bulk and boundary theories for any dimension $d$ and any allowed $��Delta_-$, because the equality is term by term in the boundary mode sum.
The same determinant-ratio method should apply to other backgrounds, such as AdS black holes, where the bulk partition function is the thermal partition function of the boundary theory.
The $��Delta_-$ prescription for AdS/CFT correlators is not an extra rule: it follows from using mixed-boundary propagators in ordinary bulk Feynman diagrams, and equals the Legendre transform of the $��Delta_+$ correlators.
The appendix confirms the earlier bulk calculation's assumption that the one-loop effective potential difference vanishes at the Breitenlohner-Freedman bound, by computing $V_+-V_-$ with a different regulator.

Reading between the lines

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

If the determinant identity is independent of the detailed radial geometry, it should extend to higher-spin fields and to one-loop corrections in interacting bulk theories, giving a general statement that one-loop holographic RG flows commute with the Legendre transform.
The ratio formula could be used as a practical shortcut for finite-temperature central-charge or entanglement-entropy corrections, since it replaces a bulk eigenvalue problem with a boundary mode sum.
The diagrammatic equivalence suggests that changing quantization in AdS/CFT is a general operation on Feynman rules—replace $��Delta_+$ propagators by $��Delta_-$ propagators—rather than a special trick for scalar two-point functions.

Original abstract

According to the AdS/CFT dictionary, perturbing the large N boundary theory by a relevant double-trace deformation of the form f O^2 corresponds in the bulk to imposing ``mixed'' boundary conditions for the field dual to O. In this note we address various aspects of this correspondence. The change c_{UV} - c_{IR} of the central charge between the UV ad IR fixed points is known from explicit calculations (hep-th/0210093, hep-th/0212138) to be exactly the same in the bulk and in the boundary theories. By comparing the appropriate bulk and boundary functional determinants, we give a simple ``kinematic'' explanation for this universal agreement. We also clarify the prescription for computing AdS/CFT correlators with Delta_- boundary conditions.

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-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,326 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.08 · human participants 0.01 · controlled comparison 0.05 · randomized assignment 0.01 · states quantitative result 0.11 · compares with prior results 0.81 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; show every role.

According to the AdS/CFT dictionary, perturbing the large N boundary theory by a relevant double-trace deformation of the form f O^2 corresponds in the bulk to imposing ``mixed'' boundary conditions for the field dual to O. In this note we address various aspects of this correspondence. The change c_{UV} - c_{IR} of the central charge between the UV ad IR fixed points is known from explicit calculations (hep-th/0210093, hep-th/0212138) to be exactly the same in the bulk and in the boundary theories. By comparing the appropriate bulk and boundary functional determinants, we give a simple ``kinematic'' explanation for this universal agreement. We also clarify the prescription for computing AdS/CFT correlators with Delta_- boundary conditions.

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	According to the AdS/CFT dictionary, perturbing the large N boundary theory by a relevant double-trace deformation of the form f O^2 corresponds in the bulk to imposing ``mixed'' boundary conditions for the field dual to O.	background 1.00	0.05	0.09	asserted 1.00
s1	In this note we address various aspects of this correspondence.	contribution 0.70	0.37	0.03	unclear 0.81
s2	The change c_{UV} - c_{IR} of the central charge between the UV ad IR fixed points is known from explicit calculations (hep-th/0210093, hep-th/0212138) to be exactly the same in the bulk and in the boundary theories.	background 0.96	0.07	0.26	asserted 1.00
s3	By comparing the appropriate bulk and boundary functional determinants, we give a simple ``kinematic'' explanation for this universal agreement.	contribution 0.73	0.94	0.58	asserted 1.00
s4	We also clarify the prescription for computing AdS/CFT correlators with Delta_- boundary conditions.	contribution 0.99	0.87	0.08	asserted 0.98

What kind of paper the classifier reports this is: theoretical result 0.98 · evidence from proof or derivation 0.93.

What was examined, and what was not

sources read

arXiv listing abstract v2

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

Figures

**Figure 1.** The contour and branch cut in Eq. (4.15) [31]. taken r = a = ǫ, while the right extremum is taken to correspond to the “deep interior” of AdS – for example x0 = ∞ in Poincar´e coordinates and ρ = 2 in hyperbolic coordinates. We immediately have detγ1 (− + m2 ) detγ2 (− + m2) = γ1p(ǫ) + ǫp′ (ǫ) γ2p(ǫ) + ǫp′(ǫ) , (4.17) where p is the solution of the radial wave equation obeying Dirichlet boundary conditions in the interior of AdS. For example in Poincar´e coordinates, p(k, x0) = ψ(k, x0) as defined in (3.14). Using the identity p(ǫ) γp(ǫ) + ǫp′ (ǫ) = Qf , (4.18) 14

**Figure 2.** Numerical value of R in eq. (4.37) versus the number of roots included in the computation. The curve converges nicely to the horizontal line (the analytical answer). 18

Figures reproduced from arXiv:hep-th/0602106 by the authors.

References

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hep-th 2011-09 conditional novelty 7.0 of 10

The singlet-sector O(N) vector model in 2+1 dimensions undergoes a Gross-Witten thermal transition at temperature of order sqrt(N), the bulk Planck energy, implying no stable large AdS black hole at the AdS scale.
AdS/CFT beyond the unitarity bound
hep-th 2011-05 conditional novelty 7.0 of 10

Conformally invariant (Neumann) boundary conditions for scalars above the Breitenlohner-Freedman window are ghost-free in Poincare AdS, evading unitarity bounds via pure gauge modes and an IR divergence, but ghosts re...
On the AdS Higher Spin / O(N) Vector Model Correspondence: degeneracy of the holographic image
hep-th 2006-03 conditional novelty 7.0 of 10

The free O(N) vector model four-point function closes on the minimal-twist higher-spin sector with analytically derived fusion coefficients, and the same structure extends to the IR fixed point via Legendre transform ...
A Holographic Open Quantum System
hep-th 2026-09 conditional novelty 6.0 of 10

A closed-form analytic treatment of quasinormal-mode dissipation in double-trace-coupled AdS and BTZ systems, benchmarked against prior numerics for non-rotating cases, extended to rotating BTZ, and capped by a high-f...
Self-dual holography: four-point AdS/CFT correlators in higher-spin gravity
hep-th 2026-05 unverdicted novelty 6.0 of 10

Develops holographic dictionary for self-dual higher-spin theories and computes four-point AdS/CFT correlators in a higher-spin extension of self-dual Yang-Mills.
Higher-form (quasi)hydrodynamics from holography: deformations and dualities
hep-th 2025-09 conditional novelty 6.0 of 10

Massless and massive higher-form gauge fields in anti-de Sitter space yield a full low-energy map of diffusive, relaxing, and emergent-photon modes governed by double-trace deformations.
Black hole perturbation theory and multiple polylogarithms
hep-th 2023-07 conditional novelty 6.0 of 10

A recursive expansion in multiple polylogarithms yields analytic series for black hole quasinormal frequencies in Schwarzschild (anti) de Sitter space, reproducing published numerical values and extending the hydrodyn...
A Derivation of AdS/CFT for Vector Models
hep-th 2020-11 conditional novelty 6.0 of 10

An explicit linear map turns the free or critical vector model path integral into a path integral over higher-spin fields on fixed anti-de Sitter space, yielding a non-local bulk action usable for loop computations.
"Old" Conformal Bootstrap on AdS: $O(N)$ symmetric scalar model
hep-th 2019-08 conditional novelty 6.0 of 10

The paper derives simplified 'old bootstrap' equations on AdS and solves them for O(N) conformal dimensions, e.g. Δψ = 2 - sqrt(3/2) for N=1 in d=4.
A Mellin Space Approach to Cosmological Correlators
hep-th 2019-06 accept novelty 6.0 of 10

A Mellin-Barnes representation reduces late-time de Sitter correlators to contour integrals whose poles give general-dimension, general-mass results for contact and exchange diagrams, matching known d=3 cases.
Light-Front Bootstrap for Chern-Simons Matter Theories
hep-th 2018-11 conditional novelty 6.0 of 10

Requiring the conformal algebra to close at cubic order in light-cone gauge fixes all three-point functions of higher-spin currents in Chern-Simons matter theories up to two parameters, and produces the cubic higher-s...
Non-supersymmetric Wilson loop in N=4 SYM and defect 1d CFT
hep-th 2017-12 conditional novelty 6.0 of 10

The two-loop circular Wilson loop in N=4 SYM depends on the scalar-coupling parameter zeta only through (1-zeta^2)^2, and the standard loop has a larger log-expectation value than the supersymmetric one, consistent wi...
Spinning AdS Loop Diagrams: Two Point Functions
hep-th 2017-08 accept novelty 6.0 of 10

A spectral decomposition of spinning propagators reduces AdS one-loop two-point Witten diagrams to Mellin-Barnes spectral integrals times boundary conformal integrals, and shows that bubble diagrams alone miss the ano...
Higher spins in AdS_5 at one loop: vacuum energy, boundary conformal anomalies and AdS/CFT
hep-th 2014-10 conditional novelty 6.0 of 10

General formulas for one-loop vacuum energy and conformal anomaly coefficients of arbitrary higher-spin AdS5 fields are derived, and applied to show that each Kaluza-Klein level p of type IIB supergravity on S5 contri...
Duality in N=2 minimal model holography
hep-th 2012-07 conditional novelty 6.0 of 10

The quantum W-algebra of N=2 higher spin AdS3 gravity depends on one coupling beyond the central charge, and four distinct values of the shs[mu] parameter give the same algebra, proving the bulk and boundary symmetrie...
The Wave Function of Vasiliev's Universe - A Few Slices Thereof
hep-th 2012-07 conditional novelty 6.0 of 10

The free Sp(N) model dual to Vasiliev higher-spin de Sitter gravity has a partition function that diverges at large negative scalar mass, which the authors interpret as an instability of the de Sitter vacuum.
Higher Spin Gravity with Matter in AdS_3 and Its CFT Dual
hep-th 2011-06 conditional novelty 6.0 of 10

Tree-level three-point functions in Vasiliev higher-spin gravity in AdS3 match the spin-3 current correlator of a subsector of the W_N minimal model at 't Hooft coupling 1/2.
Logarithmic Corrections to Extremal Black Hole Entropy from Quantum Entropy Function
hep-th 2010-05 accept novelty 6.0 of 10

The one-loop contribution of all matter multiplet fields to the logarithmic correction of quarter BPS black hole entropy cancels to zero, making the correction independent of the number of matter multiplets.
Black hole determinants and quasinormal modes
hep-th 2009-08 conditional novelty 6.0 of 10

Functional determinants in thermal spacetimes equal a product over quasinormal modes times a local polynomial, checked against known thermal AdS3, BTZ, and sphere results.
Multi-Trace Deformations in AdS/CFT: Exploring the Vacuum Structure of the Deformed CFT
hep-th 2007-03 conditional novelty 6.0 of 10

Multi-trace deformations of a holographic CFT correspond to mixed boundary conditions in the bulk, and the resulting effective action can be computed in a derivative expansion via Hamilton-Jacobi theory, yielding new ...
Remarks on Resonant Scalars in the AdS/CFT Correspondence
hep-th 2006-04 conditional novelty 6.0 of 10

Resonant scalars in AdS/CFT induce a type B trace anomaly and a marginal multi-trace deformation, with the bulk logarithmic branch reproducing both.
Approximate higher-form symmetries and dualities of massive p-forms in the holographic bulk
hep-th 2026-05 unverdicted novelty 5.0 of 10

Develops a holographic realization of approximate higher-form symmetries via massive antisymmetric tensor fields and derives dualities between boundary theories from bulk Hodge dualities, including constraints on curr...
From dS to AdS and back
hep-th 2021-09 conditional novelty 5.0 of 10

Perturbative dS boundary correlators with Bunch-Davies initial conditions can be decomposed into EAdS Witten diagrams with sinusoidal coefficients fixed by on-shell factorisation.
Comments on $T \bar T$ double trace deformations and boundary conditions
hep-th 2018-01 conditional novelty 5.0 of 10

Extending the Fourier-transform treatment of double-trace deformations from scalars and vectors to the metric, the authors argue the T Tbar deformation's holographic cutoff surface should carry a Neumann, not Dirichle...
Notes on Spinning Operators in Fermionic CFT
hep-th 2017-01 conditional novelty 5.0 of 10

The anomalous dimensions of double-trace spinning operators in the Gross-Neveu CFT, computed directly in the 1/N expansion, are exactly reproduced by an analytic bootstrap sum over weakly broken higher-spin currents o...
On higher spin partition functions
hep-th 2015-03 conditional novelty 5.0 of 10

The regularized product of one-loop partition functions over all free massless higher spins equals one, a cancellation attributed to the theory's large gauge symmetry.
On partition function and Weyl anomaly of conformal higher spin fields
hep-th 2013-09 accept novelty 5.0 of 10

The 4D conformal higher-spin partition function factorizes into partially-massless determinants, yielding spin-s Weyl anomaly coefficients whose bosonic a_s matches an independent AdS/CFT result and whose regularized ...
The Higher Spin/Vector Model Duality
hep-th 2012-08 conditional novelty 5.0 of 10

Parity violating Vasiliev theory yields a parity odd s-s'-0 three point structure proportional to sin theta0, matching the form expected from slightly broken higher spin symmetry.
On Higher Spin Gauge Theory and the Critical O(N) Model
hep-th 2011-05 conditional novelty 5.0 of 10

The critical O(N) vector model's correlators are shown to follow from the free theory's by flipping the boundary condition on the bulk scalar in Vasiliev's higher-spin gravity, giving a perturbative derivation of the ...
Boundary Conditions and Dualities: Vector Fields in AdS/CFT
hep-th 2006-06 accept novelty 4.5 of 10

For vector fields in AdS, the authors classify allowed boundary conditions and argue that the conjugate choice in AdS4 makes the dual of the bulk photon a dynamical gauge field, with a tensor-field analogue suggesting...
Dirichlet, Neumann, Mixed and self-dual holography: (self-dual) Yang--Mills theory II
hep-th 2026-06 unverdicted novelty 4.0 of 10

Derives bulk and boundary propagators and computes 3- and 4-point correlators for YM, CS and SDYM in AdS/CFT with multiple boundary conditions to relate their observables.

How later papers used it

82 later papers cite it

Evidence: some. 82 of the citing papers share no author with it, and 20 of those carry a confident label from Pith's citation classifier.

Pith read 8 of the 150 citing sentences, choosing only those whose citation markers point at this paper alone, and wrote the paraphrases from them. The summary, the counts, the evidence level, the links and the quotes come from code; the summary counts the papers listed below. A later paper is listed under a label when Pith's citation classifier gives one of its sentences that label at probability 0.8 or more (0.95 for support), Pith's reading finds that the citing paper itself did it, and a second check confirms the paraphrase against the sentence. This section lists uses only. It does not list criticism or disagreement, so their absence here says nothing about how the paper has been received. Papers that share an author with this one are listed apart, under "By the same authors". A quote is the citing authors' own sentence, shown when their paper's licence is CC BY, CC BY-SA or CC0. JSON

1 later paper by other authors is listed below: 1 built on it.

Builds on it 1 of 2 papers with this label

Described its work as an extension of the analysis presented in this paper to a pair of real massive scalars and to different boundary conditions.

Supersymmetric Mixed Boundary Conditions in AdS$_2$ and DCFT$_1$ Marginal Deformations (2019) · 1.00 · paraphrased: the licence does not allow quoting

How the literature uses it

74 arXiv papers cite this in 139 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 88 sentences without a confident label

Contests it 1 paper

And compatibility condition ([ref]) is evidently not fulfilled for $V^(5)_vac(GM)$ ([ref]) considered in [ref] , [ref] , [ref] .

Sakharov's induced gravity on the AdS background: SM scale as inverse mass parameter of the Schwinger-DeWitt expansion · Strange discrepancy in calculations of induced vacuum energy density · contest 0.82

Builds on it 2 papers

One can also show explicitly that the two CFTs are connected by an RG flow generated by double-trace deformations [ref] , generalizing the AdS results in Ref. [ref] via an appropriate analytic continuation.

Wavefunctions in dS/CFT revisited: principal series and double-trace deformations · Relation between the two CFTs · 0.86
Our work can be understood as an extension of the analysis presented in [ref] to a pair of real massive scalars and to the different boundary conditions we have described in previous sections.

Supersymmetric Mixed Boundary Conditions in AdS$_2$ and DCFT$_1$ Marginal Deformations · Correlators · 1.00

Uses its method or tool 6 papers

To compute this correction we may use the general result for the difference of effective actions with standard (D or +) and alternate (N or -) boundary conditions for a scalar with mass $m$ in AdS$_d+1$ [ref] [equation] where $ν$ is defined by 2.6 m^2 = Δ(Δ-d) , Δ_± = d/2±ν, ν≡√(d^2/4+m^2) .

Non-supersymmetric Wilson loop in N=4 SYM and defect 1d CFT · Standard Wilson loop · 0.99
In the COFI scenario, the scalar potential on the UV brane, dual to the deformations to the CFT in 4D, fixes the boundary conditions to [equation] We must then consider its modification to the scaling behavior by computing the two-point function $⟨⟩$ from the on-shell 5D action in the presence of a boundary source $Φ_b(x)$ [ref] , using the AdS/CFT dictionary, [equation] in the limit where the IR brane $zIR →∞$.

Conformal Freeze-in Dark Matter: 5D Dual and Phase Transition · Two Boundary Theories · 0.92
Hubbard-Stratonovich method We can approximate this result in another way, called Hubbard-Stratonovich method [ref] .

Mixed boundary conditions and Double-trace like deformations in Celestial holography and Wedge-like holography · two-point function from the Celestial CFT · 1.00

Compares with it 8 papers

Rastelli for pointing this out to us.] Upon completion of this paper, we were informed that the results of section 4 and the key observation of the factorization of the difference between $Δ=1$ and $Δ=2$ bulk scalar propagators in momentum space have already appeared in [ref] .

On Higher Spin Gauge Theory and the Critical O(N) Model · Introduction · 0.87
For $s = 0$ this result coincides with one of [ref] - [ref] , but drastically differs from the results (also coinciding) of [ref] and [ref] obtained in different ways (Saharian [ref] obtained expression for LHS of ([ref]) by the direct calculation of the energy-momentum tensor with use of Green functions ([ref])).

Scalar field on AdS: quantum one loop "in one line" · Doubtfulness of expressions for $a$-anomaly obtained for zero spin by Mitra & Gubser (2002) CITEMARK10Z (and also by Dia · 0.86
This result is consistent with the previous one in [ref] , which was written with the momentum basis.

The masses of higher spin fields on AdS_4 and conformal perturbation theory · Anomalous dimensions at the IR fixed point · 0.99

Cites it as support 3 papers

Furthermore, we demonstrate that $W$-freedom, which modifies the bulk boundary conditions, corresponds to a multi-trace deformation in the boundary theory [ref] (and for a systematic treatment of multi-trace deformations see also [ref] and also [ref] ).

Freelance Holography, Part I: Setting Boundary Conditions Free in Gauge/Gravity Correspondence · Introduction · 0.97
Starting from the $Δ_-$ CFT, this is a relevant deformation, which will produce an renormalization-group flow which is expected to end at the $Δ_+$ CFT in the IR; evidence for this picture has been obtained in [ref] .

Reversing Renormalization-Group Flows with AdS/CFT · Introduction · 0.96
As supporting evidence, Hartman and Rastelli [ref] gave a “kinematical” explanation.

Polyakov formulas for GJMS operators from AdS/CFT · The functional determinants · 1.00

Cites it as background 26 papers

Gubser and Mitra showed in [ref] (see also [ref] , [ref] ) that difference of bulk Green functions satisfying asymptotic b.c.

Simple way to calculate UV-finite one-loop quantum energy in Randall-Sundrum model · Introduction · 0.86
In the case of a $d$-dimensional CFT with a large $N$ expansion, a well-known example of RG flow is obtained by turning on a relevant double-trace deformation [ref] [equation] where $O$ is a single-trace operator in the original CFT with scaling dimension $Δ< d/2$.

RG Interfaces from Double-Trace Deformations · Introduction and Summary · 0.93
Double-trace deformations have been the predominant focus in the context of AdS/CFT [ref] .

The AdS/CFT partition function, AdS as a lift of a CFT, and holographic RG flow from conformal deformations · Introduction · 0.97

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.

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