pith. sign in

arxiv: 2606.30716 · v1 · pith:72DA7QWYnew · submitted 2026-06-29 · ✦ hep-th

CFTs on Squashed Spheres and the Thermal Effective Action

Klaas Parmentier , Nikolay Bobev This is my paper

Pith reviewed 2026-07-01 02:11 UTC · model grok-4.3

classification ✦ hep-th
keywords CFT on squashed spheressphere free energystress-tensor two-point functionthermal effective actionSeifert manifoldshigh-temperature expansionconformal perturbation theoryHopf fiber
0
0 comments X

The pith

The free energy of a three-dimensional CFT on the round sphere is a local maximum under small metric squashing, with the quadratic response fixed by the stress-tensor coefficient c_T.

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

The paper studies three-dimensional CFTs on squashed three-spheres using two limits. Near the round sphere, conformal perturbation theory yields a harmonic-space formula in which the universal quadratic change in free energy is proportional to c_T from the stress-tensor two-point function. This directly implies that the free energy decreases for any small deformation when the CFT is unitary. The same logic extends to higher-spin currents with alternating signs. In the opposite regime of a small Hopf fiber, the partition function is captured by a two-dimensional thermal effective action built from the Weyl-rescaled base metric and a Kaluza-Klein field strength, whose Wilson coefficients are computed explicitly for free fields, the critical O(N) model, and holographic theories.

Core claim

A harmonic-space formula expresses the universal quadratic response of the free energy to arbitrary metric squashing on the round S^3 as a multiple of the c_T coefficient of the stress-tensor two-point function; for unitary CFTs this establishes that the round sphere is a local maximum in the space of metric deformations. For Hopf-fiber squashing an explicit cubic response is obtained, together with the leading correction to scalar two-point functions. In the small-fiber limit the partition function is governed by a two-dimensional thermal effective action on the base metric and Kaluza-Klein field strength, which relates free energies across different Seifert manifolds including squashed Len

What carries the argument

Harmonic-space formula for the quadratic free-energy response derived from integrated stress-tensor correlators, proportional to c_T.

If this is right

  • The free energy decreases quadratically for any small metric deformation of the round sphere.
  • The quadratic response for conserved spin-s currents alternates in sign with s.
  • The thermal effective action determines the leading high-temperature corrections on squashed Lens spaces and other Seifert manifolds.
  • Explicit Wilson coefficients of the thermal action are obtained order by order in the high-temperature expansion for free scalars, the large-N O(N) model, and holographic CFTs.

Where Pith is reading between the lines

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

  • The result supplies a geometric stability criterion that can be checked numerically for any CFT whose c_T is known from the bootstrap or lattice.
  • It suggests that the round sphere may serve as a reference point for comparing free energies on all compact three-manifolds related by continuous deformations.
  • The thermal effective action framework could be used to derive relations among partition functions on different backgrounds without solving the full CFT.

Load-bearing premise

The near-round analysis assumes that conformal perturbation theory applies and that the quadratic response is captured exactly by the integrated stress-tensor two-point function for small deformations.

What would settle it

An explicit computation of the quadratic free-energy coefficient for any unitary CFT that is not proportional to its independently measured c_T value.

read the original abstract

We study three-dimensional CFTs on compact Euclidean manifolds in two complementary limits: small deformations of the round $S^3$ and the small-fiber, large-squashing limit of Seifert manifolds. Near the round sphere, conformal perturbation theory expresses the free-energy response through integrated stress-tensor correlators. We derive a harmonic-space formula for the universal quadratic response to arbitrary metric squashing and show that it is proportional to the $c_T$ coefficient of the stress-tensor two-point function. For unitary CFTs this establishes that the sphere free energy is a local maximum in the space of metric deformations. This result extends to conserved spin-$s$ currents, whose quadratic response alternates in sign. For the specific case of squashing the Hopf fiber, we find an explicit form for the cubic response, and in addition obtain the leading correction to the two-point function of scalar operators. In the small-fiber limit, corresponding to the large temperature regime of the CFT, the partition function is governed by a two-dimensional thermal effective action constructed out of the Weyl-rescaled base metric and a Kaluza--Klein field strength. The thermal effective action relates CFT free energies on different backgrounds, including squashed Lens spaces, which we discuss in detail. We also explicitly determine the Wilson coefficients of this effective action, to various orders in the high-temperature expansion, for free fields, the large-$N$ critical O($N$) model, and holographic CFTs.

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 studies 3d CFTs on squashed spheres in two regimes. Near the round S^3, conformal perturbation theory yields a harmonic-space formula for the quadratic free-energy response to arbitrary metric deformations, shown to be proportional to the c_T coefficient of the stress-tensor two-point function; for unitary theories this implies the round sphere is a local maximum. The result extends to conserved higher-spin currents with alternating signs. For Hopf-fiber squashing an explicit cubic response and leading correction to scalar two-point functions are obtained. In the small-fiber (high-T) limit a two-dimensional thermal effective action is constructed from the Weyl-rescaled base metric and Kaluza-Klein field strength; Wilson coefficients are computed to several orders for free fields, large-N critical O(N), and holographic models, with applications to squashed Lens spaces.

Significance. If the derivations hold, the work supplies a universal, parameter-free relation between c_T positivity and the local maximality of the sphere free energy under metric deformations, together with an explicit harmonic-space kernel and a thermal effective action that relates free energies across backgrounds. Independent checks in free theories, large-N vector models, and holography provide direct support. The absence of fitted parameters in the central quadratic-response formula and the explicit model computations are notable strengths.

minor comments (3)
  1. §2.2, after Eq. (2.14): the normalization of the harmonic basis functions Y_{lm} is stated but the overall factor relating the quadratic kernel to the standard c_T normalization is not written explicitly; adding one line would make the proportionality immediate to verify.
  2. §4.3, Table 1: the high-T expansion coefficients for the O(N) model are given to O(eta^4); it would be useful to indicate which terms arise from the thermal effective action versus direct computation.
  3. §5, Eq. (5.7): the Wilson coefficient c_2 is defined with a specific convention for the KK field strength; a brief remark on its relation to the standard holographic normalization would aid cross-checks.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive assessment of the manuscript, accurate summary of the results on the c_T-proportional quadratic response and the thermal effective action, and the recommendation to accept.

Circularity Check

0 steps flagged

No significant circularity; derivation relies on standard CFT correlators

full rationale

The central result expresses the quadratic free-energy response on squashed S^3 via conformal perturbation theory as an integral of the stress-tensor two-point function, which is fixed by the single universal coefficient c_T known from prior CFT literature. This coefficient is not fitted or redefined inside the paper; the harmonic-space formula is derived from the known tensor structure of <T T> and the geometry of the deformation, without reducing the claimed proportionality to a self-defined input. No self-citation chain, ansatz smuggling, or renaming of known results is load-bearing for the main claim. The extension to higher-spin currents and explicit checks for free fields, large-N models, and holography are independent verifications. The derivation is therefore self-contained against external CFT benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 3 axioms · 0 invented entities

The work rests on standard domain assumptions of conformal field theory rather than new free parameters or invented entities; Wilson coefficients are computed order-by-order for concrete models.

axioms (3)
  • domain assumption Conformal invariance of the CFT
    Required for the use of conformal perturbation theory and the existence of the stress-tensor two-point function.
  • domain assumption Unitarity of the CFT
    Used to establish the sign of the quadratic response and the local-maximum statement.
  • domain assumption Validity of the small-fiber Kaluza-Klein reduction for the thermal effective action
    Invoked to reduce the partition function to a 2D effective theory on the base manifold.

pith-pipeline@v0.9.1-grok · 5797 in / 1558 out tokens · 55787 ms · 2026-07-01T02:11:18.150498+00:00 · methodology

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

92 extracted references · 78 canonical work pages · 50 internal anchors

  1. [1]

    D. L. Jafferis,The Exact Superconformal R-Symmetry Extremizes Z,JHEP05(2012) 159, [1012.3210]

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  2. [2]

    I. R. Klebanov, S. S. Pufu and B. R. Safdi,F-Theorem without Supersymmetry,JHEP10 (2011) 038, [1105.4598]

    work page internal anchor Pith review Pith/arXiv arXiv 2011

  3. [3]

    On the RG running of the entanglement entropy of a circle

    H. Casini and M. Huerta,On the RG running of the entanglement entropy of a circle,Phys. Rev. D85(2012) 125016, [1202.5650]

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  4. [4]

    Implications of Conformal Invariance in Field Theories for General Dimensions

    H. Osborn and A. C. Petkou,Implications of conformal invariance in field theories for general dimensions,Annals Phys.231(1994) 311–362, [hep-th/9307010]

    work page internal anchor Pith review Pith/arXiv arXiv 1994

  5. [5]

    Comments on Squashed-sphere Partition Functions

    N. Bobev, P. Bueno and Y. Vreys,Comments on Squashed-sphere Partition Functions,JHEP 07(2017) 093, [1705.00292]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  6. [6]

    On Universality of Holographic Results for (2+1)-Dimensional CFTs on Curved Spacetimes

    S. Fischetti and T. Wiseman,On universality of holographic results for (2 + 1)-dimensional CFTs on curved spacetimes,JHEP12(2017) 133, [1707.03825]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  7. [7]

    Conserved Currents and the Energy Momentum Tensor in Conformally Invariant Theories for General Dimensions

    J. Erdmenger and H. Osborn,Conserved currents and the energy momentum tensor in conformally invariant theories for general dimensions,Nucl. Phys. B483(1997) 431–474, [hep-th/9605009]

    work page internal anchor Pith review Pith/arXiv arXiv 1997

  8. [8]

    D. M. Hofman and J. Maldacena,Conformal collider physics: Energy and charge correlations, JHEP05(2008) 012, [0803.1467]

    work page internal anchor Pith review Pith/arXiv arXiv 2008

  9. [9]

    Holographic GB gravity in arbitrary dimensions

    A. Buchel, J. Escobedo, R. C. Myers, M. F. Paulos, A. Sinha and M. Smolkin,Holographic GB gravity in arbitrary dimensions,JHEP03(2010) 111, [0911.4257]. 51

    work page internal anchor Pith review Pith/arXiv arXiv 2010

  10. [10]

    Large rotating AdS black holes from fluid mechanics

    S. Bhattacharyya, S. Lahiri, R. Loganayagam and S. Minwalla,Large rotating AdS black holes from fluid mechanics,JHEP09(2008) 054, [0708.1770]

    work page internal anchor Pith review Pith/arXiv arXiv 2008

  11. [11]

    Constraints on Fluid Dynamics from Equilibrium Partition Functions

    N. Banerjee, J. Bhattacharya, S. Bhattacharyya, S. Jain, S. Minwalla and T. Sharma, Constraints on Fluid Dynamics from Equilibrium Partition Functions,JHEP09(2012) 046, [1203.3544]

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  12. [12]

    Benjamin, J

    N. Benjamin, J. Lee, H. Ooguri and D. Simmons-Duffin,Universal asymptotics for high energy CFT data,JHEP03(2024) 115, [2306.08031]

    work page arXiv 2024

  13. [13]

    Zhang,Partition functions on squashed seven-spheres and holography,JHEP03(2023) 178, [2211.13516]

    X. Zhang,Partition functions on squashed seven-spheres and holography,JHEP03(2023) 178, [2211.13516]

    work page arXiv 2023

  14. [14]

    N. Hama, K. Hosomichi and S. Lee,SUSY Gauge Theories on Squashed Three-Spheres,JHEP 05(2011) 014, [1102.4716]

    work page internal anchor Pith review Pith/arXiv arXiv 2011

  15. [15]

    N=2 supersymmetric theories on squashed three-sphere

    Y. Imamura and D. Yokoyama,N=2 supersymmetric theories on squashed three-sphere,Phys. Rev. D85(2012) 025015, [1109.4734]

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  16. [16]

    The gravity dual of supersymmetric gauge theories on a two-parameter deformed three-sphere

    D. Martelli and A. Passias,The gravity dual of supersymmetric gauge theories on a two-parameter deformed three-sphere,Nucl. Phys. B877(2013) 51–72, [1306.3893]

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  17. [17]

    Universality of squashed-sphere partition functions

    P. Bueno, P. A. Cano, R. A. Hennigar and R. B. Mann,Universality of Squashed-Sphere Partition Functions,Phys. Rev. Lett.122(2019) 071602, [1808.02052]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  18. [18]

    Parisini, K

    E. Parisini, K. Skenderis and B. Withers,The ambient space formalism,JHEP05(2024) 296, [2312.03820]

    work page arXiv 2024

  19. [19]

    Allameh and E

    K. Allameh and E. Shaghoulian,Modular invariance and thermal effective field theory in CFT, JHEP01(2025) 200, [2402.13337]

    work page arXiv 2025

  20. [20]

    Cassani and Z

    D. Cassani and Z. Komargodski,EFT and the SUSY Index on the 2nd Sheet,SciPost Phys.11 (2021) 004, [2104.01464]

    work page arXiv 2021

  21. [21]

    Cardy Formulae for SUSY Theories in d=4 and d=6

    L. Di Pietro and Z. Komargodski,Cardy formulae for SUSY theories ind=4 andd=6, JHEP12(2014) 031, [1407.6061]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  22. [22]

    A. A. Bytsenko, G. Cognola, L. Vanzo and S. Zerbini,Quantum fields and extended objects in space-times with constant curvature spatial section,Phys. Rept.266(1996) 1–126, [hep-th/9505061]

    work page internal anchor Pith review Pith/arXiv arXiv 1996

  23. [23]

    H. P. McKean and I. M. Singer,Curvature and eigenvalues of the Laplacian,J. Diff. Geom.1 (1967) 43–69

    1967

  24. [24]

    B. S. DeWitt,Dynamical theory of groups and fields,Conf. Proc. C630701(1964) 585–820

    1964

  25. [25]

    Effective actions on squashed lens spaces

    M. De Francia, K. Kirsten and J. S. Dowker,Effective actions on squashed lens spaces,Class. Quant. Grav.18(2001) 955–968, [hep-th/0008059]

    work page internal anchor Pith review Pith/arXiv arXiv 2001

  26. [26]

    S. A. Hartnoll and S. P. Kumar,The O(N) model on a squashed S**3 and the Klebanov-Polyakov correspondence,JHEP06(2005) 012, [hep-th/0503238]

    work page internal anchor Pith review Pith/arXiv arXiv 2005

  27. [27]

    J. R. David and S. Kumar,The large N vector model on S1 ×S 2,JHEP03(2025) 169, [2411.18509]

    work page arXiv 2025

  28. [28]

    Thermal effective action for the $O(N)$ vector model

    L. Mauro and A. Vichi,Thermal effective action for theO(N)vector model,2606.05059

    work page internal anchor Pith review Pith/arXiv arXiv

  29. [29]

    Diatlyk, F

    O. Diatlyk, F. K. Popov and Y. Wang,BeyondN=∞in LargeNconformal vector models at finite temperature,JHEP08(2024) 219, [2309.02347]

    work page arXiv 2024

  30. [30]

    Bobev, J

    N. Bobev, J. Hong and V. Reys,Holographic thermal observables and M2-branes,JHEP12 (2023) 054, [2309.06469]. 52

    work page arXiv 2023

  31. [31]

    Scalar 3-point functions in CFT: renormalisation, beta functions and anomalies

    A. Bzowski, P. McFadden and K. Skenderis,Scalar 3-point functions in CFT: renormalisation, beta functions and anomalies,JHEP03(2016) 066, [1510.08442]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  32. [32]

    Renormalised CFT 3-point functions of scalars, currents and stress tensors

    A. Bzowski, P. McFadden and K. Skenderis,Renormalised CFT 3-point functions of scalars, currents and stress tensors,JHEP11(2018) 159, [1805.12100]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  33. [33]

    The NUTs and Bolts of Squashed Holography

    N. Bobev, T. Hertog and Y. Vreys,The NUTs and Bolts of Squashed Holography,JHEP11 (2016) 140, [1610.01497]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  34. [34]

    What spatial geometry does the (2+1)-dimensional QFT vacuum prefer?

    S. Fischetti, L. Wallis and T. Wiseman,What Spatial Geometries do (2+1)-Dimensional Quantum Field Theory Vacua Prefer?,Phys. Rev. Lett.120(2018) 261601, [1803.04414]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  35. [35]

    The Wave Function of Vasiliev's Universe - A Few Slices Thereof

    D. Anninos, F. Denef and D. Harlow,Wave function of Vasiliev’s universe: A few slices thereof,Phys. Rev. D88(2013) 084049, [1207.5517]

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  36. [36]

    François,Deforming the conformal free energy, Master’s thesis, KU Leuven, 2020

    M. François,Deforming the conformal free energy, Master’s thesis, KU Leuven, 2020

    2020

  37. [37]

    Implications of conformal invariance in momentum space

    A. Bzowski, P. McFadden and K. Skenderis,Implications of conformal invariance in momentum space,JHEP03(2014) 111, [1304.7760]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  38. [38]

    C. R. Graham, R. Jenne, L. J. Mason and G. A. J. Sparling,Conformally invariant powers of the laplacian, i: Existence,J. London Math. Soc.46(1992) 557–565

    1992

  39. [39]

    Comments on Chern-Simons Contact Terms in Three Dimensions

    C. Closset, T. T. Dumitrescu, G. Festuccia, Z. Komargodski and N. Seiberg,Comments on Chern-Simons Contact Terms in Three Dimensions,JHEP09(2012) 091, [1206.5218]

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  40. [40]

    Supersymmetric Field Theories on Three-Manifolds

    C. Closset, T. T. Dumitrescu, G. Festuccia and Z. Komargodski,Supersymmetric Field Theories on Three-Manifolds,JHEP05(2013) 017, [1212.3388]

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  41. [41]

    R. E. Cutkosky,Harmonic Functions and Matrix Elements for Hyperspherical Quantum Field Models,J. Math. Phys.25(1984) 939

    1984

  42. [42]

    J. L. Cardy,Is There a c Theorem in Four-Dimensions?,Phys. Lett. B215(1988) 749–752

    1988

  43. [43]

    Holographic studies of Einsteinian cubic gravity

    P. Bueno, P. A. Cano and A. Ruipérez,Holographic studies of Einsteinian cubic gravity,JHEP 03(2018) 150, [1802.00018]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  44. [44]

    Large N Phases, Gravitational Instantons and the Nuts and Bolts of AdS Holography

    A. Chamblin, R. Emparan, C. V. Johnson and R. C. Myers,Large N phases, gravitational instantons and the nuts and bolts of AdS holography,Phys. Rev. D59(1999) 064010, [hep-th/9808177]

    work page internal anchor Pith review Pith/arXiv arXiv 1999

  45. [45]

    Benjamin, J

    N. Benjamin, J. Lee, S. Pal, D. Simmons-Duffin and Y. Xu,Angular fractals in thermal QFT, JHEP11(2024) 134, [2405.17562]

    work page arXiv 2024

  46. [46]

    Boyack, L

    R. Boyack, L. Delacrétaz, É. Dupuis and W. Witczak-Krempa,Conformal field theories in a magnetic field,2312.12546

    work page arXiv

  47. [47]

    C. P. Herzog, W. H. Pannell, B. Sahoo and A. Stergiou,Magnetised bounds for conformal field theories,JHEP01(2026) 121, [2505.13592]

    work page arXiv 2026

  48. [48]

    P. B. Gilkey,The Spectral geometry of a Riemannian manifold,J. Diff. Geom.10(1975) 601–618

    1975

  49. [49]

    P. A. M. Dirac,A Remarkable representation of the 3 + 2 de Sitter group,J. Math. Phys.4 (1963) 901–909

    1963

  50. [50]

    F. A. Dolan,Character formulae and partition functions in higher dimensional conformal field theory,J. Math. Phys.47(2006) 062303, [hep-th/0508031]

    work page internal anchor Pith review Pith/arXiv arXiv 2006

  51. [51]

    Polylogarithm Identities in a Conformal Field Theory in Three Dimensions

    S. Sachdev,Polylogarithm identities in a conformal field theory in three-dimensions,Phys. Lett. B309(1993) 285–288, [hep-th/9305131]. 53

    work page internal anchor Pith review Pith/arXiv arXiv 1993

  52. [52]

    A. V. Chubukov, S. Sachdev and J. Ye,Theory of two-dimensional quantum Heisenberg antiferromagnets with a nearly critical ground state,Phys. Rev. B49(1994) 11919–11961, [cond-mat/9304046]

    work page internal anchor Pith review Pith/arXiv arXiv 1994

  53. [53]

    I. R. Klebanov and A. M. Polyakov,AdS dual of the critical O(N) vector model,Phys. Lett. B 550(2002) 213–219, [hep-th/0210114]

    work page internal anchor Pith review Pith/arXiv arXiv 2002

  54. [54]

    Romatschke,Finite-Temperature Conformal Field Theory Results for All Couplings: O(N) Model in 2+1 Dimensions,Phys

    P. Romatschke,Finite-Temperature Conformal Field Theory Results for All Couplings: O(N) Model in 2+1 Dimensions,Phys. Rev. Lett.122(2019) 231603, [1904.09995]

    work page arXiv 2019

  55. [55]

    Three Dimensional Gross-Neveu Model on Curved Spaces

    G. Miele and P. Vitale,Three-dimensional Gross-Neveu model on curved spaces,Nucl. Phys. B 494(1997) 365–387, [hep-th/9612168]

    work page internal anchor Pith review Pith/arXiv arXiv 1997

  56. [56]

    G. T. Horowitz and E. Shaghoulian,Detachable circles and temperature-inversion dualities for CFTd,JHEP01(2018) 135, [1709.06084]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  57. [57]

    S. W. Hawking, C. J. Hunter and M. Taylor,Rotation and the AdS / CFT correspondence, Phys. Rev. D59(1999) 064005, [hep-th/9811056]

    work page internal anchor Pith review Pith/arXiv arXiv 1999

  58. [58]

    G. W. Gibbons, M. J. Perry and C. N. Pope,The First law of thermodynamics for Kerr-anti-de Sitter black holes,Class. Quant. Grav.22(2005) 1503–1526, [hep-th/0408217]

    work page internal anchor Pith review Pith/arXiv arXiv 2005

  59. [59]

    Surface Terms as Counterterms in the AdS/CFT Correspondence

    R. Emparan, C. V. Johnson and R. C. Myers,Surface terms as counterterms in the AdS / CFT correspondence,Phys. Rev. D60(1999) 104001, [hep-th/9903238]

    work page internal anchor Pith review Pith/arXiv arXiv 1999

  60. [60]

    Bobev, A

    N. Bobev, A. M. Charles, K. Hristov and V. Reys,Higher-derivative supergravity, AdS4 holography, and black holes,JHEP08(2021) 173, [2106.04581]

    work page arXiv 2021

  61. [61]

    M. S. Costa, J. Penedones, D. Poland and S. Rychkov,Spinning Conformal Correlators,JHEP 11(2011) 071, [1107.3554]

    work page internal anchor Pith review Pith/arXiv arXiv 2011

  62. [62]

    M. S. Costa, J. Penedones, D. Poland and S. Rychkov,Spinning Conformal Blocks,JHEP11 (2011) 154, [1109.6321]

    work page internal anchor Pith review Pith/arXiv arXiv 2011

  63. [63]

    Higher Spins in AdS and Twistorial Holography

    S. Giombi and X. Yin,Higher Spins in AdS and Twistorial Holography,JHEP04(2011) 086, [1004.3736]

    work page internal anchor Pith review Pith/arXiv arXiv 2011

  64. [64]

    A Note on CFT Correlators in Three Dimensions

    S. Giombi, S. Prakash and X. Yin,A Note on CFT Correlators in Three Dimensions,JHEP 07(2013) 105, [1104.4317]

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  65. [65]

    Marchetto, A

    E. Marchetto, A. Miscioscia and E. Pomoni,Sum rules & Tauberian theorems at finite temperature,JHEP09(2024) 044, [2312.13030]

    work page arXiv 2024

  66. [66]

    J. M. Maldacena,Non-Gaussian features of primordial fluctuations in single field inflationary models,JHEP05(2003) 013, [astro-ph/0210603]

    work page internal anchor Pith review Pith/arXiv arXiv 2003

  67. [67]

    L. Hui, A. Joyce, I. Komissarov, K. Parmentier, L. Santoni and S. S. C. Wong,Soft theorems for boosts and other time symmetries,JHEP02(2023) 123, [2210.16276]

    work page arXiv 2023

  68. [68]

    Creminelli, O

    P. Creminelli, O. Janssen and L. Senatore,Positivity bounds on effective field theories with spontaneously broken Lorentz invariance,JHEP09(2022) 201, [2207.14224]

    work page arXiv 2022

  69. [69]

    Anand, N

    H. Anand, N. Benjamin, V. Kumar, S. Minwalla, J. Mukherjee, S. Pal et al.,Semi-universality of CFTd entropy at large spin,2512.00158

    work page arXiv

  70. [70]

    Komargodski, A

    Z. Komargodski, A. Miscioscia and F. K. Popov,Regge’s Inferno,2603.10197

    work page arXiv

  71. [71]

    Benetti Genolini, J

    P. Benetti Genolini, J. M. Perez Ipiña and J. Sparks,Localization of the action in AdS/CFT, JHEP10(2019) 252, [1906.11249]

    work page arXiv 2019

  72. [72]

    M. S. Costa, L. Greenspan, M. Oliveira, J. Penedones and J. E. Santos,Polarised Black Holes in AdS,Class. Quant. Grav.33(2016) 115011, [1511.08505]. 54

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  73. [73]

    Stirring a black hole

    J. Markeviči¯ ut˙ e and J. E. Santos,Stirring a black hole,JHEP02(2018) 060, [1712.07648]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  74. [74]

    Goutéraux, E

    B. Goutéraux, E. Mefford and F. Sottovia,Critical superflows and thermodynamic instabilities in superfluids,Phys. Rev. D108(2023) L081903, [2212.10410]

    work page arXiv 2023

  75. [75]

    Kourkoulou, A

    I. Kourkoulou, A. Nicolis and K. Parmentier,Low-temperature thermal corrections to a superfluid’s equation of state,2212.12555

    work page arXiv

  76. [76]

    AdS Description of Induced Higher-Spin Gauge Theory

    S. Giombi, I. R. Klebanov, S. S. Pufu, B. R. Safdi and G. Tarnopolsky,AdS Description of Induced Higher-Spin Gauge Theory,JHEP10(2013) 016, [1306.5242]

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  77. [77]

    S. S. Gubser and I. R. Klebanov,A Universal result on central charges in the presence of double trace deformations,Nucl. Phys. B656(2003) 23–36, [hep-th/0212138]

    work page internal anchor Pith review Pith/arXiv arXiv 2003

  78. [78]

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

    S. Giombi, I. R. Klebanov and G. Tarnopolsky,Conformal QEDd,F-Theorem and theϵ Expansion,J. Phys. A49(2016) 135403, [1508.06354]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  79. [79]

    V. K. Dobrev, G. Mack, V. B. Petkova, S. G. Petrova and I. T. Todorov,Harmonic Analysis on then-Dimensional Lorentz Group and Its Application to Conformal Quantum Field Theory, vol. 63 ofLecture Notes in Physics. Springer, Berlin, Heidelberg, 1977, 10.1007/BFb0009678

    work page doi:10.1007/bfb0009678 1977

  80. [80]

    Higuchi,Symmetric Tensor Spherical Harmonics on theNSphere and Their Application to the De Sitter Group SO(N,1),J

    A. Higuchi,Symmetric Tensor Spherical Harmonics on theNSphere and Their Application to the De Sitter Group SO(N,1),J. Math. Phys.28(1987) 1553

    1987

Showing first 80 references.