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arxiv: 2406.19441 · v2 · submitted 2024-06-27 · ✦ hep-th

Moduli Spaces in CFT: Large Charge Operators

Gabriel Cuomo , Leonardo Rastelli , Adar Sharon This is my paper

Pith reviewed 2026-05-23 23:55 UTC · model grok-4.3

classification ✦ hep-th
keywords CFTmoduli spacelarge charge expansionconformal symmetry breakingcharged operatorsscaling dimensionsBPS boundthree-dimensional CFT
0
0 comments X

The pith

A CFT that breaks conformal symmetry while also breaking a continuous global symmetry on its moduli space must have a tower of charged operators whose dimensions grow linearly with charge.

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

The paper uses the large-charge expansion to derive a necessary condition on the operator spectrum of any CFT that breaks conformal invariance. Under the assumption that a continuous global symmetry is likewise broken on the moduli space, such a theory is required to contain an infinite tower of charged local operators whose scaling dimensions become linear in the charge at large values. The same linear growth is automatic in supersymmetric models with an R-symmetry and holomorphic moduli space because of the BPS bound. The argument is checked in explicit three-dimensional N=1 examples, where the leading linear term receives calculable corrections, and a scaling limit is used to map the large-charge spectrum on the cylinder onto the spectrum of massive particles propagating on the moduli space.

Core claim

Using the large-charge expansion, we prove a necessary condition for a CFT to exhibit conformal symmetry breaking, under the assumption that a continuous global symmetry is also broken on the moduli space: there must be a tower of charged local operators whose scaling dimensions are asymptotically linear in the charge. In supersymmetric theories with a continuous R-symmetry and a holomorphic moduli space, the existence of such a tower of operators follows trivially from a BPS condition: their scaling dimensions are then exactly linear in the R-charge. We illustrate the more general statement in several examples of three-dimensional N=1 CFTs, where the leading linear behavior receives nontriv

What carries the argument

Large-charge expansion on the moduli space, which isolates the required tower of charged operators and relates their dimensions to the geometry of the broken-symmetry vacuum.

If this is right

  • In supersymmetric theories the tower exists automatically and the linearity is exact by the BPS bound.
  • In non-supersymmetric three-dimensional N=1 models the linear term is still present but receives nontrivial corrections that can be computed.
  • A scaling limit maps the large-charge spectrum of local operators on the cylinder to the spectrum of massive particles on the moduli space.
  • The condition supplies a diagnostic for the presence of a moduli space in any CFT that breaks both conformal and global symmetries.

Where Pith is reading between the lines

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

  • The linear tower offers a spectral signature that could be searched for in lattice or bootstrap studies of candidate CFTs with broken symmetries.
  • The cylinder-to-moduli-space map suggests that low-energy effective actions on the moduli space can be constrained directly by CFT data at large charge.
  • Corrections to linearity in non-supersymmetric cases encode dynamical information about the metric and potential on the moduli space.

Load-bearing premise

A continuous global symmetry is also broken on the moduli space.

What would settle it

A concrete CFT that breaks conformal symmetry and breaks a continuous global symmetry on its moduli space, yet whose charged operators fail to show asymptotically linear scaling dimensions with charge.

read the original abstract

Using the large-charge expansion, we prove a necessary condition for a CFT to exhibit conformal symmetry breaking, under the assumption that a continuous global symmetry is ${\it also}$ broken on the moduli space: there must be a tower of charged local operators whose scaling dimensions are asymptotically linear in the charge. In supersymmetric theories with a continuous R-symmetry and a holomorphic moduli space, the existence of such a tower of operators follows trivially from a BPS condition: their scaling dimensions are then exactly linear in the R-charge. We illustrate the more general statement in several examples of three-dimensional ${\cal N}=1$ CFTs, where the leading linear behavior receives nontrivial corrections. By considering a suitable scaling limit, we also relate the spectrum of states with large charge on the cylinder (isomorphic to local operators) to the spectrum of massive particles on the moduli space.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

0 major / 3 minor

Summary. The manuscript uses the large-charge expansion to prove a necessary condition for a CFT to exhibit conformal symmetry breaking on its moduli space, under the explicit assumption that a continuous global symmetry is also broken there: there must exist a tower of charged local operators whose scaling dimensions are asymptotically linear in the charge. In supersymmetric theories with a continuous R-symmetry and holomorphic moduli space the tower follows from the BPS condition. The claim is illustrated with examples of three-dimensional N=1 CFTs (where the leading linear term receives nontrivial corrections) and a scaling limit is used to relate the large-charge spectrum on the cylinder to the spectrum of massive particles on the moduli space.

Significance. If the central claim holds, the result supplies a concrete, testable link between the geometry of the moduli space and the asymptotic operator spectrum in CFTs. The explicit separation of the SUSY (BPS) case from the non-SUSY illustrations, together with the cylinder-to-moduli-space relation obtained via a controlled scaling limit, are concrete strengths that could be used to constrain possible patterns of symmetry breaking or to organize large-charge data in both supersymmetric and non-supersymmetric models.

minor comments (3)
  1. [Abstract] The abstract states that the non-SUSY examples receive 'nontrivial corrections' to the linear behavior; a brief indication of the functional form of the first correction (e.g., logarithmic or 1/Q) would help the reader assess how generic the leading linearity remains.
  2. The relation between cylinder states and moduli-space particles is obtained by 'a suitable scaling limit'; the precise limit (which charges or radii are sent to infinity, and in what ratio) should be stated explicitly in the main text so that the isomorphism can be reproduced.
  3. Notation for the global symmetry charge Q versus the R-charge in the SUSY section should be kept distinct throughout to avoid any momentary confusion when the two cases are compared.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive assessment of the manuscript, including the summary and significance statements, and for recommending minor revision. No specific major comments were provided in the report.

Circularity Check

0 steps flagged

No significant circularity; derivation self-contained under stated assumption

full rationale

The central claim is a conditional necessary condition derived via the large-charge expansion under an explicitly flagged assumption (continuous global symmetry broken on moduli space). No equations or steps in the provided abstract reduce by construction to fitted parameters, self-definitions, or load-bearing self-citations; the SUSY case is noted as following from BPS (external to the non-SUSY illustrations), and the cylinder-moduli relation is presented as a separate scaling limit. The derivation chain therefore remains independent of its inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the validity of the large-charge expansion (a domain assumption from prior literature) and the explicit assumption that a continuous global symmetry is broken on the moduli space. No free parameters or invented entities are indicated in the abstract.

axioms (1)
  • domain assumption The large-charge expansion applies to the CFTs under consideration and yields the stated asymptotic behavior.
    The proof is performed using this expansion as stated in the abstract.

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Reference graph

Works this paper leans on

99 extracted references · 99 canonical work pages · 45 internal anchors

  1. [1]

    Cuomo, L

    G. Cuomo, L. Rastelli and A. Sharon, Moduli Spaces in CFT: Bootstrap Equation in a Perturbative Example, 2406.02679

    work page arXiv

  2. [2]

    G. K. Karananas and M. Shaposhnikov, CFT data and spontaneously broken conformal invariance, Phys. Rev. D 97 (2018) 045009 [ 1708.02220]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  3. [3]

    Ivanovskiy, S

    V. Ivanovskiy, S. Komatsu, V. Mishnyakov, N. Terziev, N. Zaigraev and K. Zarembo, Vacuum Condensates on the Coulomb Branch , 2405.19043

    work page arXiv

  4. [4]

    On the CFT Operator Spectrum at Large Global Charge,

    S. Hellerman, D. Orlando, S. Reffert and M. Watanabe, On the CFT Operator Spectrum at Large Global Charge, JHEP 12 (2015) 071 [ 1505.01537]

    work page arXiv 2015

  5. [5]

    L. A. Gaum´ e, D. Orlando and S. Reffert,Selected topics in the large quantum number expansion , Phys. Rept. 933 (2021) 1 [ 2008.03308]

    work page arXiv 2021

  6. [6]

    Operator Dimensions from Moduli

    S. Hellerman, S. Maeda and M. Watanabe, Operator Dimensions from Moduli, JHEP 10 (2017) 089 [1706.05743]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  7. [7]

    M. A. Luty and W. Taylor, Varieties of vacua in classical supersymmetric gauge theories , Phys. Rev. D 53 (1996) 3399 [ hep-th/9506098]

    work page internal anchor Pith review Pith/arXiv arXiv 1996

  8. [8]

    Curious Aspects of Three-Dimensional ${\cal N}=1$ SCFTs

    D. Gaiotto, Z. Komargodski and J. Wu, Curious Aspects of Three-Dimensional N = 1 SCFTs, JHEP 08 (2018) 004 [ 1804.02018]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  9. [9]

    L. Fei, S. Giombi, I. R. Klebanov and G. Tarnopolsky, Yukawa CFTs and Emergent Supersymmetry, PTEP 2016 (2016) 12C105 [ 1607.05316]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  10. [10]

    Thomas, Emergent Supersymmetry,

    S. Thomas, Emergent Supersymmetry,

    work page

  11. [11]

    Badel, G

    G. Badel, G. Cuomo, A. Monin and R. Rattazzi, The Epsilon Expansion Meets Semiclassics , JHEP 11 (2019) 110 [ 1909.01269]

    work page arXiv 2019

  12. [12]

    Convexity of charged operators in CFTs and the weak gravity conjecture,

    O. Aharony and E. Palti, Convexity of charged operators in CFTs and the weak gravity conjecture, Phys. Rev. D 104 (2021) 126005 [ 2108.04594]

    work page arXiv 2021

  13. [13]

    Sharon and M

    A. Sharon and M. Watanabe, A counterexample to the CFT convexity conjecture , JHEP 05 (2023) 202 [ 2301.08262]

    work page arXiv 2023

  14. [14]

    Conformal Bootstrap At Large Charge

    D. Jafferis, B. Mukhametzhanov and A. Zhiboedov, Conformal Bootstrap At Large Charge, JHEP 05 (2018) 043 [ 1710.11161]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  15. [15]

    Salam and J

    A. Salam and J. A. Strathdee, Nonlinear realizations. 2. Conformal symmetry , Phys. Rev. 184 (1969) 1760

    work page 1969

  16. [16]

    C. J. Isham, A. Salam and J. A. Strathdee, Spontaneous breakdown of conformal symmetry , Phys. Lett. B 31 (1970) 300

    work page 1970

  17. [17]

    J. R. Ellis, Phenomenological actions for spontaneously-broken conformal symmetry , Nucl. Phys. B 26 (1971) 536

    work page 1971

  18. [18]

    M. A. Luty, J. Polchinski and R. Rattazzi, The a-theorem and the Asymptotics of 4D Quantum Field Theory, JHEP 01 (2013) 152 [ 1204.5221]

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  19. [19]

    Generalized Dimensional Analysis

    H. Georgi, Generalized dimensional analysis, Phys. Lett. B 298 (1993) 187 [ hep-ph/9207278]. – 50 –

    work page internal anchor Pith review Pith/arXiv arXiv 1993

  20. [20]

    Spontaneous Breaking of Conformal Invariance and Trace Anomaly Matching

    A. Schwimmer and S. Theisen, Spontaneous Breaking of Conformal Invariance and Trace Anomaly Matching, Nucl. Phys. B 847 (2011) 590 [ 1011.0696]

    work page internal anchor Pith review Pith/arXiv arXiv 2011

  21. [21]

    On Renormalization Group Flows in Four Dimensions

    Z. Komargodski and A. Schwimmer, On Renormalization Group Flows in Four Dimensions , JHEP 12 (2011) 099 [ 1107.3987]

    work page internal anchor Pith review Pith/arXiv arXiv 2011

  22. [22]

    The dilaton Wess-Zumino action in higher dimensions

    F. Baume and B. Keren-Zur, The dilaton Wess-Zumino action in higher dimensions , JHEP 11 (2013) 102 [ 1307.0484]

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  23. [23]

    A naturally light dilaton

    F. Coradeschi, P. Lodone, D. Pappadopulo, R. Rattazzi and L. Vitale, A naturally light dilaton , JHEP 11 (2013) 057 [ 1306.4601]

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  24. [24]

    A Naturally Light Dilaton and a Small Cosmological Constant

    B. Bellazzini, C. Csaki, J. Hubisz, J. Serra and J. Terning, A Naturally Light Dilaton and a Small Cosmological Constant, Eur. Phys. J. C 74 (2014) 2790 [ 1305.3919]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  25. [25]

    Cuomo, OPE meets semiclassics , Phys

    G. Cuomo, OPE meets semiclassics , Phys. Rev. D 103 (2021) 085005 [ 2103.01331]

    work page arXiv 2021

  26. [26]

    Semiclassics, Goldstone Bosons and CFT data

    A. Monin, D. Pirtskhalava, R. Rattazzi and F. K. Seibold, Semiclassics, Goldstone Bosons and CFT data, JHEP 06 (2017) 011 [ 1611.02912]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  27. [27]

    D. T. Son, Low-energy quantum effective action for relativistic superfluids , hep-ph/0204199

    work page internal anchor Pith review Pith/arXiv arXiv

  28. [28]

    Zoology of condensed matter: Framids, ordinary stuff, extra-ordinary stuff

    A. Nicolis, R. Penco, F. Piazza and R. Rattazzi, Zoology of condensed matter: Framids, ordinary stuff, extra-ordinary stuff, JHEP 06 (2015) 155 [ 1501.03845]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  29. [29]

    On the eigenfunctions of the Dirac operator on spheres and real hyperbolic spaces

    R. Camporesi and A. Higuchi, On the Eigenfunctions of the Dirac operator on spheres and real hyperbolic spaces, J. Geom. Phys. 20 (1996) 1 [ gr-qc/9505009]

    work page internal anchor Pith review Pith/arXiv arXiv 1996

  30. [30]

    Conformal QED$_d$, $F$-Theorem and the $\epsilon$ Expansion

    S. Giombi, I. R. Klebanov and G. Tarnopolsky, Conformal QED d, F -Theorem and the ϵ Expansion, J. Phys. A 49 (2016) 135403 [ 1508.06354]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  31. [31]

    Cuomo, A note on the large charge expansion in 4d CFT , Phys

    G. Cuomo, A note on the large charge expansion in 4d CFT , Phys. Lett. B 812 (2021) 136014 [2010.00407]

    work page arXiv 2021

  32. [32]

    Dilaton: Saving Conformal Symmetry

    F. Gretsch and A. Monin, Perturbative conformal symmetry and dilaton , Phys. Rev. D 92 (2015) 045036 [1308.3863]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  33. [33]

    The Constraints of Conformal Symmetry on RG Flows

    Z. Komargodski, The Constraints of Conformal Symmetry on RG Flows , JHEP 07 (2012) 069 [1112.4538]

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  34. [34]

    Grassi, Z

    A. Grassi, Z. Komargodski and L. Tizzano, Extremal correlators and random matrix theory , JHEP 04 (2021) 214 [ 1908.10306]

    work page arXiv 2021

  35. [35]

    Beccaria, F

    M. Beccaria, F. Galvagno and A. Hasan, N = 2 conformal gauge theories at large R-charge: the SU (N) case, JHEP 03 (2020) 160 [ 2001.06645]

    work page arXiv 2020

  36. [36]

    C. Beem, M. Lemos, P. Liendo, W. Peelaers, L. Rastelli and B. C. van Rees, Infinite Chiral Symmetry in Four Dimensions , Commun. Math. Phys. 336 (2015) 1359 [ 1312.5344]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  37. [37]

    Lemos, Lectures on chiral algebras of N ⩾ 2 superconformal field theories, 2006.13892

    M. Lemos, Lectures on chiral algebras of N ⩾ 2 superconformal field theories, 2006.13892

    work page arXiv 2006

  38. [38]

    On the Large $R$-charge Expansion in ${\mathcal N} = 2$ Superconformal Field Theories

    S. Hellerman and S. Maeda, On the Large R-charge Expansion in N = 2 Superconformal Field Theories, JHEP 12 (2017) 135 [ 1710.07336]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  39. [39]

    Hellerman, S

    S. Hellerman, S. Maeda, D. Orlando, S. Reffert and M. Watanabe, Universal correlation functions in rank 1 SCFTs , JHEP 12 (2019) 047 [ 1804.01535]

    work page arXiv 2019

  40. [40]

    Hellerman, S

    S. Hellerman, S. Maeda, D. Orlando, S. Reffert and M. Watanabe, S-duality and correlation functions at large R-charge , JHEP 04 (2021) 287 [ 2005.03021]. – 51 –

    work page arXiv 2021

  41. [41]

    Hellerman, On the exponentially small corrections to N = 2 superconformal correlators at large R-charge, 2103.09312

    S. Hellerman, On the exponentially small corrections to N = 2 superconformal correlators at large R-charge, 2103.09312

    work page arXiv

  42. [42]

    Hellerman and D

    S. Hellerman and D. Orlando, Large R-charge EFT correlators in N=2 SQCD , 2103.05642

    work page arXiv

  43. [43]

    Watanabe, Accessing large global charge via the ϵ-expansion, JHEP 04 (2021) 264 [1909.01337]

    M. Watanabe, Accessing large global charge via the ϵ-expansion, JHEP 04 (2021) 264 [1909.01337]

    work page arXiv 2021

  44. [44]

    Benini and S

    F. Benini and S. Benvenuti, N = 1 QED in 2 + 1 dimensions: dualities and enhanced symmetries, JHEP 05 (2021) 176 [ 1804.05707]

    work page arXiv 2021

  45. [45]

    Sharon and M

    A. Sharon and M. Watanabe, Transition of Large R-Charge Operators on a Conformal Manifold , JHEP 01 (2021) 068 [ 2008.01106]

    work page arXiv 2021

  46. [46]

    Cuomo, M

    G. Cuomo, M. Mezei and A. Raviv-Moshe, Boundary conformal field theory at large charge , JHEP 10 (2021) 143 [ 2108.06579]

    work page arXiv 2021

  47. [47]

    Rabinovici, B

    E. Rabinovici, B. Saering and W. A. Bardeen, Critical Surfaces and Flat Directions in a Finite Theory, Phys. Rev. D 36 (1987) 562

    work page 1987

  48. [48]

    W. A. Bardeen, M. Moshe and M. Bander, Spontaneous breaking of scale invariance and the ultraviolet fixed point in O(n)-symmetric ( φ6

    work page

  49. [49]

    theory, Phys. Rev. Lett. 52 (1984) 1188

    work page 1984

  50. [50]

    N. Chai, S. Chaudhuri, C. Choi, Z. Komargodski, E. Rabinovici and M. Smolkin, Thermal Order in Conformal Theories , Phys. Rev. D 102 (2020) 065014 [ 2005.03676]

    work page arXiv 2020

  51. [51]

    N. Chai, S. Chaudhuri, C. Choi, Z. Komargodski, E. Rabinovici and M. Smolkin, Symmetry Breaking at All Temperatures, Phys. Rev. Lett. 125 (2020) 131603

    work page 2020

  52. [52]

    Antipin, J

    O. Antipin, J. Bersini, F. Sannino, Z.-W. Wang and C. Zhang, Charging the O(N) model, Phys. Rev. D 102 (2020) 045011 [ 2003.13121]

    work page arXiv 2020

  53. [53]

    Alvarez-Gaume, D

    L. Alvarez-Gaume, D. Orlando and S. Reffert, Large charge at large N , JHEP 12 (2019) 142 [1909.02571]

    work page arXiv 2019

  54. [54]

    Giombi and J

    S. Giombi and J. Hyman, On the large charge sector in the critical O(N) model at large N , JHEP 09 (2021) 184 [ 2011.11622]

    work page arXiv 2021

  55. [55]

    New integrable non-gauge 4D QFTs from strongly deformed planar N=4 SYM

    O. G¨ urdo˘ gan and V. Kazakov,New Integrable 4D Quantum Field Theories from Strongly Deformed Planar N = 4 Supersymmetric Yang-Mills Theory , Phys. Rev. Lett. 117 (2016) 201602 [1512.06704]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  56. [56]

    G. K. Karananas, V. Kazakov and M. Shaposhnikov, Spontaneous Conformal Symmetry Breaking in Fishnet CFT , Phys. Lett. B 811 (2020) 135922 [ 1908.04302]

    work page arXiv 2020

  57. [57]

    Continuum limit of fishnet graphs and AdS sigma model

    B. Basso and D.-l. Zhong, Continuum limit of fishnet graphs and AdS sigma model , JHEP 01 (2019) 002 [ 1806.04105]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  58. [58]

    Caetano, S

    J. Caetano, S. Komatsu and Y. Wang, Large charge ’t Hooft limit of N = 4 super-Yang-Mills, JHEP 02 (2024) 047 [ 2306.00929]

    work page arXiv 2024

  59. [59]

    J. R. Ellis, Aspects of conformal symmetry and chirality , Nucl. Phys. B 22 (1970) 478

    work page 1970

  60. [60]

    A Light Dilaton in Walking Gauge Theories

    T. Appelquist and Y. Bai, A Light Dilaton in Walking Gauge Theories , Phys. Rev. D 82 (2010) 071701 [1006.4375]

    work page internal anchor Pith review Pith/arXiv arXiv 2010

  61. [61]

    Walking, Weak first-order transitions, and Complex CFTs

    V. Gorbenko, S. Rychkov and B. Zan, Walking, Weak first-order transitions, and Complex CFTs , JHEP 10 (2018) 108 [ 1807.11512]. – 52 –

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  62. [62]

    Zan, Studies in strongly coupled quantum field theories and renormalization group flows , Ph.D

    B. Zan, Studies in strongly coupled quantum field theories and renormalization group flows , Ph.D. thesis, Ecole Polytechnique, Lausanne, 2019. 10.5075/epfl-thesis-9660

    work page doi:10.5075/epfl-thesis-9660 2019

  63. [63]

    Benini, C

    F. Benini, C. Iossa and M. Serone, Conformality Loss, Walking, and 4D Complex Conformal Field Theories at Weak Coupling , Phys. Rev. Lett. 124 (2020) 051602 [ 1908.04325]

    work page arXiv 2020

  64. [64]

    Aharony and Y.-N

    O. Aharony and Y.-N. Breitstein, Tests of the Charge Convexity Conjecture in Caswell-Banks-Zaks theory, JHEP 08 (2023) 044 [ 2305.08947]

    work page arXiv 2023

  65. [65]

    Antipin, J

    O. Antipin, J. Bersini, F. Sannino, Z.-W. Wang and C. Zhang, More on the weak gravity conjecture via convexity of charged operators, JHEP 12 (2021) 204 [ 2109.04946]

    work page arXiv 2021

  66. [66]

    Ishii and Y

    T. Ishii and Y. Nakayama, Convexity restoration from hairy black hole in Einstein-Maxwell-charged scalar system in AdS , JHEP 05 (2024) 197 [ 2402.04552]

    work page arXiv 2024

  67. [67]

    Palti and A

    E. Palti and A. Sharon, Convexity of charged operators in CFTs with multiple Abelian symmetries, JHEP 09 (2022) 078 [ 2206.06703]

    work page arXiv 2022

  68. [68]

    Orlando and E

    D. Orlando and E. Palti, Goldstone bosons and convexity , Phys. Rev. D 108 (2023) 085002 [2303.02178]

    work page arXiv 2023

  69. [69]

    Eigenstate Thermalization Hypothesis in Conformal Field Theory

    N. Lashkari, A. Dymarsky and H. Liu, Eigenstate Thermalization Hypothesis in Conformal Field Theory, J. Stat. Mech. 1803 (2018) 033101 [ 1610.00302]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  70. [70]

    Komargodski, M

    Z. Komargodski, M. Mezei, S. Pal and A. Raviv-Moshe, Spontaneously broken boosts in CFTs , JHEP 09 (2021) 064 [ 2102.12583]

    work page arXiv 2021

  71. [71]

    Eberhardt, Superconformal symmetry and representations, J

    L. Eberhardt, Superconformal symmetry and representations, J. Phys. A 54 (2021) 063002 [2006.13280]

    work page arXiv 2021

  72. [72]

    F. A. Dolan and H. Osborn, Conformal four point functions and the operator product expansion , Nucl. Phys. B 599 (2001) 459 [ hep-th/0011040]

    work page internal anchor Pith review Pith/arXiv arXiv 2001

  73. [73]

    F. A. Dolan and H. Osborn, Conformal partial waves and the operator product expansion , Nucl. Phys. B 678 (2004) 491 [ hep-th/0309180]

    work page internal anchor Pith review Pith/arXiv arXiv 2004

  74. [74]

    I. R. Klebanov and E. Witten, AdS / CFT correspondence and symmetry breaking , Nucl. Phys. B 556 (1999) 89 [ hep-th/9905104]

    work page internal anchor Pith review Pith/arXiv arXiv 1999

  75. [75]

    Large branes in AdS and their field theory dual

    A. Hashimoto, S. Hirano and N. Itzhaki, Large branes in AdS and their field theory dual , JHEP 08 (2000) 051 [ hep-th/0008016]

    work page internal anchor Pith review Pith/arXiv arXiv 2000

  76. [76]

    Invasion of the Giant Gravitons from Anti-de Sitter Space

    J. McGreevy, L. Susskind and N. Toumbas, Invasion of the giant gravitons from Anti-de Sitter space, JHEP 06 (2000) 008 [ hep-th/0003075]

    work page internal anchor Pith review Pith/arXiv arXiv 2000

  77. [77]

    Giant Gravitons in Conformal Field Theory

    V. Balasubramanian, M. Berkooz, A. Naqvi and M. J. Strassler, Giant gravitons in conformal field theory, JHEP 04 (2002) 034 [ hep-th/0107119]

    work page internal anchor Pith review Pith/arXiv arXiv 2002

  78. [78]

    Exact Correlators of Giant Gravitons from dual N=4 SYM

    S. Corley, A. Jevicki and S. Ramgoolam, Exact correlators of giant gravitons from dual N=4 SYM theory, Adv. Theor. Math. Phys. 5 (2002) 809 [ hep-th/0111222]

    work page internal anchor Pith review Pith/arXiv arXiv 2002

  79. [79]

    H. Lin, O. Lunin and J. M. Maldacena, Bubbling AdS space and 1/2 BPS geometries , JHEP 10 (2004) 025 [ hep-th/0409174]

    work page internal anchor Pith review Pith/arXiv arXiv 2004

  80. [80]

    The supersymmetric index in four dimensions

    L. Rastelli and S. S. Razamat, The supersymmetric index in four dimensions , J. Phys. A 50 (2017) 443013 [ 1608.02965]. – 53 –

    work page internal anchor Pith review Pith/arXiv arXiv 2017

Showing first 80 references.