Pith. sign in

REVIEW 2 major objections 4 minor 55 references

This paper derives the CFT state dual to quarter-BPS AdS bubble geometries through quadratic order, including a subleading 1/N correction that produces a non-protected three-point function.

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

2026-08-04 06:38 UTC pith:4IVUBOBW

load-bearing objection Solid bulk work and a genuinely new CFT-side ansatz, but the headline claim of reconstruction “from supergravity alone” is not earned: one 1/N coefficient is fixed by an imported finite-N assumption. the 2 major comments →

arxiv 2512.07767 v2 pith:4IVUBOBW submitted 2025-12-08 hep-th

Holography of quarter-BPS AdS bubbles

Bogdan Ganchev , Anthony Houppe This is my paper
classification hep-th
keywords AdS/CFTquarter-BPSbubbling geometriesN=4 super Yang-Millsholographic dictionarychiral primariesthree-point functions1/N corrections
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 aims to extend the holographic dictionary beyond the well-understood half-BPS sector by identifying the CFT state that describes a family of quarter-BPS 'bubble' geometries in AdS5. Working perturbatively to quadratic order in the deformation, it derives the state as a specific combination of half-BPS double-trace operators and the unique [2,0,2] quarter-BPS operator, with the quarter-BPS coefficient fixed by matching protected three-point functions to supergravity. This provides the first bulk-to-boundary matching for 1/4-BPS geometries beyond linearized order, including a subleading 1/N correction. The payoff is an explicit example of a correlator involving quarter-BPS operators that differs from its free-field value, showing it is not protected. If correct, it establishes that classical supergravity data can reconstruct protected quarter-BPS operators with their 1/N corrections.

Core claim

The central claim is that the state dual to the 1/4-BPS AdS bubble geometries, to quadratic order in the deformation parameter epsilon, is |psi> = N [1 - 1/2 epsilon (beta1 TrX^2 + beta2 TrY^2) + 1/8 epsilon^2 (beta1 TrX^2 + beta2 TrY^2)^2 - 1/(3N) epsilon^2 beta1 beta2 (TrXXYY - TrXYXY) + O(epsilon^3)] |0>. Equivalently, the quadratic piece splits into a half-BPS double-trace part and the unique [2,0,2] quarter-BPS operator O_1/4 with coefficient beta1 beta2 / 6. The paper argues this is the first 1/4-BPS geometry/state matching beyond linearized order, and that the 1/N coefficient of the quarter-BPS operator - previously fixed at weak coupling by diagonalizing the one-loop dilatation opera

What carries the argument

The argument runs through a decoupled form of the BPS equations for the five-dimensional consistent truncation, written in terms of fields sigma_+ and sigma_- satisfying xi d_xi (xi d_xi sigma_±) - 4 C xi^2 sinh sigma_± = 0, which organize the perturbative expansion. The matching uses the holographic dictionary: asymptotic expansions of the supergravity fields give expectation values of dimension-2 chiral primaries and R-charges, and a non-renormalization theorem protects the corresponding three-point functions. The central identity is the operator O_1/4 = TrX^2 TrY^2 - (TrXY)^2 - (2/N)(TrXXYY - TrXYXY), whose unique [2,0,2] representation enters the quadratic state; imposing that the matchi

Load-bearing premise

The load-bearing premise is that the holographic matching equations, verified at large N, continue to hold at finite N (at least to first 1/N^2 order); this unproven extrapolation fixes the coefficient and sign of the quarter-BPS operator in the quadratic state.

What would settle it

Compute the quadratic coefficient of O_1/4 in the heavy state by an independent method, for example a direct evaluation of the relevant three-point function in N=4 super Yang-Mills at small but finite N, and check whether the coefficient is -beta1 beta2 / (3N); a different value would overturn the finite-N identification. Alternatively, solve the wave equation in the bubble background and check whether the predicted unprotected three-point function actually differs from its free-theory value.

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

If this is right

  • The state (4.32)/(4.33) is a concrete prediction for the CFT dual of a 1/4-BPS bubble, testable at quadratic order.
  • The 1/N coefficient in the quarter-BPS piece is determined by supergravity and agrees with the weak-coupling one-loop diagonalization, so the protected dimension survives at strong coupling.
  • The correlator involving two quarter-BPS and one half-BPS operators computed in the supergravity regime differs from the free-theory result, giving an explicit unprotected quarter-BPS observable.
  • The paper states that Heavy-Heavy-Light-Light and Light-Light-Light-Light correlators with quarter-BPS operators become computable by solving wave equations in these backgrounds, which would be a direct next application.

Where Pith is reading between the lines

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

  • If the finite-N extrapolation is valid, the same method could fix higher-order terms in the heavy state and determine whether the quarter-BPS component remains the only non-half-BPS contribution beyond quadratic order.
  • The decoupled BPS form and the matching strategy may carry over to spinning 1/4-BPS solutions and to 1/8- or 1/16-BPS geometries within the truncation, potentially producing microstate data relevant to black holes.
  • A direct independent check would be to compute the O(epsilon^2) state from the coherent-state integral over unitary matrices in a suitable limit and compare coefficients; the present paper leaves that matrix-integral route unresolved.
  • The unprotected three-point function provides a sharp target for a future stringy or bootstrap computation outside the supergravity regime.

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

2 major / 4 minor

Summary. The manuscript studies a class of static 1/4-BPS AdS bubble solutions in a five-dimensional consistent truncation of type IIB supergravity, with the goal of identifying their dual heavy states in N=4 SYM beyond linear order. The authors introduce a new ansatz that decouples the BPS equations (Sec. 3.4), construct the geometries perturbatively to 12th order and numerically (Secs. 3.6, 5), and use KK holography to extract the expectation values of dimension-2 chiral primaries and R-charges (Sec. 4.1). In the CFT, they propose a perturbative ansatz for the heavy state and match free-field Wick-contraction results to the holographic data. This yields the claimed quadratic-order state (4.32)-(4.33), expressed in terms of half-BPS double-traces and the lightest quarter-BPS operator O1/4 with an explicit subleading 1/N coefficient, together with an associated non-protected three-point function. The central claim is that protected quarter-BPS operators, including subleading 1/N corrections, can be fully reconstructed from supergravity alone.

Significance. If established, this would be the first explicit matching of 1/4-BPS geometries to N=4 SYM states beyond the linearized approximation, including subleading 1/N structure, and would provide a useful template for heavy-state holography in AdS5. The paper has concrete strengths: the decoupling of the BPS equations (Sec. 3.4), the clean derivation of the holographic vevs (4.19)-(4.21), the high-order perturbative expansion, and the numerical checks with residuals of order 10^-50 and consistency E=J1+J2. The advertised non-protected three-point function is a valuable byproduct. However, as detailed below, the central identification is conditional on an external input for the 1/N coefficient; the paper's abstract overstates what has been derived from supergravity alone.

major comments (2)
  1. [Sec. 4.3, Eqs. (4.31)-(4.33)] The quadratic-order state is not fully determined by the supergravity data. The leading-order matching fixes all coefficients except gamma_tilde_7 and the sign delta. These are subsequently fixed either by imposing that O(2) be expressible as a sum of the 1/4-BPS operator O1/4 and half-BPS double-traces, or by assuming that the matching equations (4.30) hold at finite N to first 1/N^2 order. Both are extra inputs rather than consequences of the holographic computation: the first imposes the 1/4-BPS structure by fiat, and the second is an extrapolation from the 1/2-BPS analysis of [36]. Thus the coefficient -1/(3N) epsilon^2 beta1 beta2 (TrXXYY - TrXYXY) in Eq. (4.32) is conditional on an unproven assumption. The abstract's statement that protected quarter-BPS operators 'can be fully reconstructed from supergravity alone' is therefore not supported by the manuscript as written. The consis
  2. [Sec. 4.3, finite-N assumption after Eq. (4.31)] The finite-N matching assumption is load-bearing: it is used to fix the subleading 1/N mixing of O1/4, which is precisely the novel part of the claimed result. No derivation or independent check of this extension to 1/4-BPS heavy states is provided; the paper explicitly notes that a dimension-4 expectation value could fix the coefficient but does not compute it. As written, the claimed 1/N correction remains a conjecture supported by an input external to the supergravity data. I recommend either computing the dimension-4 vev within the paper's framework or reformulating the result as explicitly conditional, with the abstract and conclusions adjusted accordingly.
minor comments (4)
  1. [Sec. 2] Typo: 'kay role' should be 'key role'.
  2. [Sec. 4.1] Typo: 'expectation vales' should be 'expectation values'.
  3. [Sec. 4.3] The explicit linear system from the Wick contractions that determines the coefficients other than gamma_tilde_7 is not displayed. Providing this system (or an ancillary file) would substantially improve the verifiability of the matching.
  4. [Abstract and Introduction] There are several formatting issues: 'subleading1/Ncorrections' appears without proper spacing; the claim 'fully reconstructed from supergravity alone' should be softened if the finite-N assumption is retained as an input.

Circularity Check

1 steps flagged

Leading-order state matching is genuinely overdetermined, but the advertised subleading 1/N mixing of the quarter-BPS operator is fixed by an imported ansatz/dictionary assumption rather than by the holographic data.

specific steps
  1. self definitional [Sec. 4.3, eqs. (2.5), (4.30)-(4.33)]
    "This missing coefficient is not a failure of the holographic dictionary, but an artifact of the incomplete matching: it could be fixed by considering the expectation values of chiral primaries of dimension 4 or higher. There are however, two indirect, simpler ways to determine it. The first approach is to refine the ansatz, to incorporate the fact that the heavy state must be 1/4-BPS. Under this assumption, O(2) should be expressible as a sum of the operator O1/4 defined in (2.5), and of a 1/2-BPS component."

    The subleading 1/N term in the final state, -(1/3N)ε^2 β1β2(TrXXYY−TrXYXY), is presented as reconstructed from supergravity. But the input that fixes it is the assumption that O(2) decomposes into half-BPS double traces plus the operator O1/4 defined in (2.5). That defining expression already contains -2/N(TrXXYY−TrXYXY); imposing the decomposition forces γ̃7 and δ to the values making the non-half-BPS part proportional to O1/4. The alternative route, assuming the matching equations (4.30) hold at finite N (first 1/N^2 order), is likewise an unproven extrapolation, not a consequence of the computed leading-order vevs. Thus the 1/N mixing is effectively an input relabeled as a supergravity-derived prediction. The leading-order coefficients are independently overdetermined, so the circularit

full rationale

Most of the paper is a genuine holographic computation. The bulk asymptotic data (Sec. 3.6, App. B) are fed through the KK holographic dictionary [13,14] to produce the dimension-2 vevs (4.19), R-charges (4.20), and energy (4.21); these are matched, via the non-renormalization theorem [52], to free-field Wick contractions in an 8-parameter symmetric ansatz (4.29). The matching equations (4.30) at leading N overdetermine the double-trace coefficients and fix all but one combination (γ̃7 and the sign δ). That part is not circular. The circularity/conditionality enters at the final step: the remaining subleading 1/N coefficient is not fixed by the leading-order holographic data; it is obtained either by imposing the 1/4-BPS decomposition of O(2) in terms of O1/4 defined in (2.5), or by assuming the matching equations hold at order 1/N^2 (an extrapolation from the 1/2-BPS result [36]). In both routes the 1/N mixing is an input rather than a computed supergravity prediction, so the abstract's claim that quarter-BPS operators 'including their subleading 1/N corrections, can be fully reconstructed from supergravity alone' is too strong for that coefficient. The paper itself flags the incompleteness ('This missing coefficient is not a failure of the holographic dictionary, but an artifact of the incomplete matching'). Self-citations ([9], [54]) are technical or programmatic and not load-bearing for the central CFT-state claim. Overall: partial circularity in the subleading 1/N claim; the leading-order matching is independent and nontrivial.

Axiom & Free-Parameter Ledger

1 free parameters · 5 axioms · 0 invented entities

The paper introduces no new particles, forces, or dimensions. Its central claim rests on the consistency of the 5D truncation, the non-renormalization theorem for protected three-point functions, and an explicitly assumed finite-N extension of the holographic matching—the last being the main additional input beyond standard large-N AdS/CFT. The deformation parameters β1, β2 are physical labels of the solution family rather than fit parameters.

free parameters (1)
  • β1, β2
    Amplitudes of the two leading scalar deformations (3.37); they label the family of 1/4-BPS bubbles and appear as expansion parameters in the CFT state. They are solution parameters chosen by hand, not fitted to data.
axioms (5)
  • domain assumption The 5D SO(6)-gauged supergravity truncation of Type IIB on S^5 is consistent, and the diagonal U(1)^3 subsector retains the 1/4-BPS solutions of interest.
    Invoked in Sec. 3.1 to reduce the problem to fields (3.7)–(3.8); relies on the consistent reduction of [51].
  • domain assumption Three-point functions of the form (4.1) are protected (non-renormalized) when the inequalities (4.2) hold.
    Invoked in Sec. 4 to equate free-theory Wick contractions with strong-coupling supergravity results; cited to [52] and reviewed in [43].
  • ad hoc to paper The matching equations (4.30) hold at finite N, at least to first 1/N² order, not only at leading large N.
    Sec. 4.3: used to fix γ̃7 and δ (the 1/N mixing in O1/4). Explicitly labeled as an assumption, extrapolated from the 1/2-BPS case [36]; no derivation is given here.
  • domain assumption ⟨Op⟩ = 0 for all single-particle chiral primaries of dimension p > 2 in these geometries.
    Sec. 4.1 (eq. 4.22): argued from the consistent truncation projecting out higher KK modes; verified for one dimension-4 example (4.24), but not exhaustively.
  • domain assumption The operator O1/4 in (2.5) is the unique [2,0,2] quarter-BPS operator with protected dimension Δ = 4.
    Sec. 2: one-loop protected dimension from [45]; conjectured to receive no higher-loop corrections [50]. Used to identify the quarter-BPS component in the reconstructed state.

pith-pipeline@v1.3.0-alltime-deepseek · 23962 in / 20158 out tokens · 536144 ms · 2026-08-04T06:38:28.496214+00:00 · methodology

0 comments
read the original abstract

We consider the quarter-BPS sector of the AdS$_5$/CFT$_4$ duality, and provide a precise matching between specific CFT states and supergravity geometries beyond the linearized approximation. In the bulk, we focus on AdS bubbles geometries that fit within a consistent truncation to five-dimensional gauged supergravity. We show that the BPS equations can be decoupled, and study the resulting geometries both perturbatively and numerically. Applying the holographic dictionary, we compute the expectation values of light chiral primaries in these backgrounds. This data allows us to determine the dual CFT state up to quadratic order in the fluctuations, and to provide non-trivial consistency checks of the result. The resulting state is expressed as a linear combination of half-BPS double-trace operators, and of the unique $[2,0,2]$ quarter-BPS operator of the theory. As an application, we compute three-point functions involving two quarter-BPS operators and a half-BPS operator in the supergravity regime, finding an explicit example of a correlator that differs from its free theory value and that is therefore not protected.

discussion (0)

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

Reference graph

Works this paper leans on

55 extracted references · 53 linked inside Pith

  1. [1]

    J. M. Maldacena,The LargeNlimit of superconformal field theories and supergravity,Adv. Theor. Math. Phys.2(1998) 231–252, [hep-th/9711200]

    Pith/arXiv arXiv 1998

  2. [2]

    Strominger and C

    A. Strominger and C. Vafa,Microscopic origin of the Bekenstein-Hawking entropy,Phys. Lett. B379(1996) 99–104, [hep-th/9601029]

    Pith/arXiv arXiv 1996

  3. [3]

    Lunin and S

    O. Lunin and S. D. Mathur,AdS / CFT duality and the black hole information paradox,Nucl. Phys. B623(2002) 342–394, [hep-th/0109154]

    Pith/arXiv arXiv 2002

  4. [4]

    I. Bena, S. Giusto, R. Russo, M. Shigemori, and N. P. Warner,Habemus Superstratum! A constructive proof of the existence of superstrata,JHEP05(2015) 110, [arXiv:1503.01463]

    Pith/arXiv arXiv 2015

  5. [5]

    I. Bena, S. Giusto, E. J. Martinec, R. Russo, M. Shigemori, D. Turton, and N. P. Warner, Smooth horizonless geometries deep inside the black-hole regime,Phys. Rev. Lett.117(2016), no. 20 201601, [arXiv:1607.03908]

    Pith/arXiv arXiv 2016

  6. [6]

    I. Bena, S. Giusto, E. J. Martinec, R. Russo, M. Shigemori, D. Turton, and N. P. Warner, Asymptotically-flat supergravity solutions deep inside the black-hole regime,JHEP02(2018) 014, [arXiv:1711.10474]

    Pith/arXiv arXiv 2018

  7. [7]

    Čeplak, R

    N. Čeplak, R. Russo, and M. Shigemori,Supercharging Superstrata,JHEP03(2019) 095, [arXiv:1812.08761]

    Pith/arXiv arXiv 2019

  8. [8]

    Heidmann, D

    P. Heidmann, D. R. Mayerson, R. Walker, and N. P. Warner,Holomorphic Waves of Black Hole Microstructure,JHEP02(2020) 192, [arXiv:1910.10714]

    Pith/arXiv arXiv 2020

  9. [9]

    Ganchev, S

    B. Ganchev, S. Giusto, A. Houppe, R. Russo, and N. P. Warner,Microstrata,JHEP10(2023) 163, [arXiv:2307.13021]

    Pith/arXiv arXiv 2023

  10. [10]

    Čeplak and S

    N. Čeplak and S. D. Hampton,Vector superstrata. Part II,JHEP10(2024) 011, [arXiv:2405.05341]

    Pith/arXiv arXiv 2024

  11. [11]

    I. Bena, E. J. Martinec, S. D. Mathur, and N. P. Warner,Fuzzballs and Microstate Geometries: Black-Hole Structure in String Theory,arXiv:2204.13113

    Pith/arXiv arXiv

  12. [12]

    Bena and N

    I. Bena and N. P. Warner,Microstate Geometries,arXiv:2503.17310

    Pith/arXiv arXiv

  13. [13]

    Skenderis and M

    K. Skenderis and M. Taylor,Kaluza-Klein holography,JHEP05(2006) 057, [hep-th/0603016]

    Pith/arXiv arXiv 2006

  14. [14]

    Skenderis and M

    K. Skenderis and M. Taylor,Anatomy of bubbling solutions,JHEP09(2007) 019, [arXiv:0706.0216]

    Pith/arXiv arXiv 2007

  15. [15]

    Kanitscheider, K

    I. Kanitscheider, K. Skenderis, and M. Taylor,Holographic anatomy of fuzzballs,JHEP04 (2007) 023, [hep-th/0611171]

    Pith/arXiv arXiv 2007

  16. [16]

    Giusto, E

    S. Giusto, E. Moscato, and R. Russo,AdS3 holography for 1/4 and 1/8 BPS geometries,JHEP 11(2015) 004, [arXiv:1507.00945]

    Pith/arXiv arXiv 2015

  17. [17]

    Giusto, S

    S. Giusto, S. Rawash, and D. Turton,Ads3 holography at dimension two,JHEP07(2019) 171, [arXiv:1904.12880]

    Pith/arXiv arXiv 2019

  18. [18]

    Rawash and D

    S. Rawash and D. Turton,Supercharged AdS3 Holography,JHEP07(2021) 178, [arXiv:2105.13046]

    Pith/arXiv arXiv 2021

  19. [19]

    Turton and A

    D. Turton and A. Tyukov,Precision holography of AdS5 bubbling geometries,JHEP07(2025) 027, [arXiv:2503.19760]. – 28 –

    Pith/arXiv arXiv 2025

  20. [20]

    Galliani, S

    A. Galliani, S. Giusto, and R. Russo,Holographic 4-point correlators with heavy states,JHEP 10(2017) 040, [arXiv:1705.09250]

    Pith/arXiv arXiv 2017

  21. [21]

    Bombini, A

    A. Bombini, A. Galliani, S. Giusto, E. Moscato, and R. Russo,Unitary 4-point correlators from classical geometries,Eur. Phys. J. C78(2018), no. 1 8, [arXiv:1710.06820]

    Pith/arXiv arXiv 2018

  22. [22]

    Giusto, R

    S. Giusto, R. Russo, and C. Wen,Holographic correlators in AdS3,JHEP03(2019) 096, [arXiv:1812.06479]

    Pith/arXiv arXiv 2019

  23. [23]

    Bombini and A

    A. Bombini and A. Galliani,AdS3 four-point functions from 1 8 -BPS states,JHEP06(2019) 044, [arXiv:1904.02656]

    Pith/arXiv arXiv 2019

  24. [24]

    Ceplak, S

    N. Ceplak, S. Giusto, M. R. R. Hughes, and R. Russo,Holographic correlators with multi-particle states,JHEP09(2021) 204, [arXiv:2105.04670]

    Pith/arXiv arXiv 2021

  25. [25]

    Turton and A

    D. Turton and A. Tyukov,Four-point correlators inN= 4 SYM from AdS5 bubbling geometries,JHEP10(2024) 244, [arXiv:2408.16834]

    Pith/arXiv arXiv 2024

  26. [26]

    Sen,Black Hole Entropy Function, Attractors and Precision Counting of Microstates,Gen

    A. Sen,Black Hole Entropy Function, Attractors and Precision Counting of Microstates,Gen. Rel. Grav.40(2008) 2249–2431, [arXiv:0708.1270]

    Pith/arXiv arXiv 2008

  27. [27]

    Benini, K

    F. Benini, K. Hristov, and A. Zaffaroni,Black hole microstates in AdS4 from supersymmetric localization,JHEP05(2016) 054, [arXiv:1511.04085]

    Pith/arXiv arXiv 2016

  28. [28]

    Azzurli, N

    F. Azzurli, N. Bobev, P. M. Crichigno, V. S. Min, and A. Zaffaroni,A universal counting of black hole microstates in AdS4,JHEP02(2018) 054, [arXiv:1707.04257]

    Pith/arXiv arXiv 2018

  29. [29]

    Cabo-Bizet, D

    A. Cabo-Bizet, D. Cassani, D. Martelli, and S. Murthy,Microscopic origin of the Bekenstein-Hawking entropy of supersymmetric AdS5 black holes,JHEP10(2019) 062, [arXiv:1810.11442]

    Pith/arXiv arXiv 2019

  30. [30]

    H. Lin, O. Lunin, and J. M. Maldacena,Bubbling AdS space and 1/2 BPS geometries,JHEP10 (2004) 025, [hep-th/0409174]

    Pith/arXiv arXiv 2004

  31. [31]

    Berenstein,A Toy model for the AdS / CFT correspondence,JHEP07(2004) 018, [hep-th/0403110]

    D. Berenstein,A Toy model for the AdS / CFT correspondence,JHEP07(2004) 018, [hep-th/0403110]

    Pith/arXiv arXiv 2004

  32. [32]

    Berenstein and S

    D. Berenstein and S. Wang,BPS coherent states and localization,JHEP08(2022) 164, [arXiv:2203.15820]

    Pith/arXiv arXiv 2022

  33. [33]

    Anempodistov, A

    P. Anempodistov, A. Holguin, V. Kazakov, and H. Murali,(Un)solvable Matrix Models for BPS Correlators,arXiv:2508.20094

    Pith/arXiv arXiv

  34. [34]

    Giusto and A

    S. Giusto and A. Rosso,The geometry of large charge multi-traces inN= 4 SYM,JHEP10 (2024) 200, [arXiv:2401.01254]

    Pith/arXiv arXiv 2024

  35. [35]

    Aprile, S

    F. Aprile, S. Giusto, and R. Russo,Holographic correlators with BPS bound states inN= 4 SYM,Phys. Rev. Lett.134(2025), no. 9 091602, [arXiv:2409.12911]

    Pith/arXiv arXiv 2025

  36. [36]

    Aprile, S

    F. Aprile, S. Giusto, and R. Russo,Four-point correlators with BPS bound states in AdS3 and AdS5,JHEP08(2025) 193, [arXiv:2503.02855]

    Pith/arXiv arXiv 2025

  37. [37]

    Donos,A Description of 1/4 BPS configurations in minimal type IIB SUGRA,Phys

    A. Donos,A Description of 1/4 BPS configurations in minimal type IIB SUGRA,Phys. Rev. D 75(2007) 025010, [hep-th/0606199]

    Pith/arXiv arXiv 2007

  38. [38]

    B. Chen, S. Cremonini, A. Donos, F.-L. Lin, H. Lin, J. T. Liu, D. Vaman, and W.-Y. Wen, – 29 – Bubbling AdS and droplet descriptions of BPS geometries in IIB supergravity,JHEP10(2007) 003, [arXiv:0704.2233]

    Pith/arXiv arXiv 2007

  39. [39]

    Lunin,Brane webs and 1/4-BPS geometries,JHEP09(2008) 028, [arXiv:0802.0735]

    O. Lunin,Brane webs and 1/4-BPS geometries,JHEP09(2008) 028, [arXiv:0802.0735]

    Pith/arXiv arXiv 2008

  40. [40]

    Kimura and H

    Y. Kimura and H. Lin,Young diagrams, Brauer algebras, and bubbling geometries,JHEP01 (2012) 121, [arXiv:1109.2585]

    Pith/arXiv arXiv 2012

  41. [41]

    Z. W. Chong, H. Lu, and C. N. Pope,BPS geometries and AdS bubbles,Phys. Lett. B614 (2005) 96–103, [hep-th/0412221]

    Pith/arXiv arXiv 2005

  42. [42]

    J. T. Liu, H. Lu, C. N. Pope, and J. F. Vazquez-Poritz,New supersymmetric solutions of N=2, D=5 gauged supergravity with hyperscalars,JHEP10(2007) 093, [arXiv:0705.2234]

    Pith/arXiv arXiv 2007

  43. [43]

    Bissi, G

    A. Bissi, G. Fardelli, and A. Manenti,Rebooting quarter-BPS operators inN= 4 super Yang-Mills,JHEP04(2022) 016, [arXiv:2111.06857]

    Pith/arXiv arXiv 2022

  44. [44]

    D’Hoker, P

    E. D’Hoker, P. Heslop, P. Howe, and A. V. Ryzhov,Systematics of quarter BPS operators in N=4 SYM,JHEP04(2003) 038, [hep-th/0301104]

    Pith/arXiv arXiv 2003

  45. [45]

    A. V. Ryzhov,Quarter BPS operators in N=4 SYM,JHEP11(2001) 046, [hep-th/0109064]

    Pith/arXiv arXiv 2001

  46. [46]

    H. J. Kim, L. J. Romans, and P. van Nieuwenhuizen,Mass spectrum of chiral ten-dimensional n=2 supergravity onS5,Phys. Rev. D32(Jul, 1985) 389–399

    1985

  47. [47]

    Aprile, J

    F. Aprile, J. Drummond, P. Heslop, and H. Paul,Double-trace spectrum ofN= 4 supersymmetric Yang-Mills theory at strong coupling,Phys. Rev. D98(2018), no. 12 126008, [arXiv:1802.06889]

    Pith/arXiv arXiv 2018

  48. [48]

    Aprile, J

    F. Aprile, J. M. Drummond, P. Heslop, H. Paul, F. Sanfilippo, M. Santagata, and A. Stewart, Single particle operators and their correlators in freeN= 4 SYM,JHEP11(2020) 072, [arXiv:2007.09395]

    Pith/arXiv arXiv 2020

  49. [49]

    Lewis-Brown and S

    C. Lewis-Brown and S. Ramgoolam,Quarter-BPS states, multi-symmetric functions and set partitions,JHEP03(2021) 153, [arXiv:2007.01734]

    Pith/arXiv arXiv 2021

  50. [50]

    Pasukonis and S

    J. Pasukonis and S. Ramgoolam,From counting to construction of BPS states in N=4 SYM, JHEP02(2011) 078, [arXiv:1010.1683]

    Pith/arXiv arXiv 2011

  51. [51]

    Cvetic, H

    M. Cvetic, H. Lu, C. N. Pope, A. Sadrzadeh, and T. A. Tran,Consistent SO(6) reduction of type IIB supergravity on S**5,Nucl. Phys. B586(2000) 275–286, [hep-th/0003103]

    Pith/arXiv arXiv 2000

  52. [52]

    D’Hoker and A

    E. D’Hoker and A. V. Ryzhov,Three point functions of quarter BPS operators in N=4 SYM, JHEP02(2002) 047, [hep-th/0109065]

    Pith/arXiv arXiv 2002

  53. [53]

    Ó. J. C. Dias, J. E. Santos, and B. Way,Numerical Methods for Finding Stationary Gravitational Solutions,Class. Quant. Grav.33(2016), no. 13 133001, [arXiv:1510.02804]

    Pith/arXiv arXiv 2016

  54. [54]

    Aprile, B

    F. Aprile, B. Ganchev, S. Giusto, A. Houppe, R. Russo, and J. Vilas Boas Work in progress, 2026

    2026

  55. [55]

    F. A. Dolan and H. Osborn,On short and semi-short representations for four-dimensional superconformal symmetry,Annals Phys.307(2003) 41–89, [hep-th/0209056]. – 30 –

    Pith/arXiv arXiv 2003