REVIEW 2 major objections 5 minor 4 cited by
Conformal 3-point functions and the Lorentzian OPE in momentum space
T0 review · 2 major / 5 minor · reviewed 2026-08-14 · deepseek-v4-flash
Pith's one-line read This paper establishes that momentum-space Wightman 3-point functions in conformal field theory are Appell F4 double hypergeometric series, with the physical solution and normalization selected by the Lorentzian operator product expansion.
desk verdict The scalar Wightman 3-point function is a genuinely useful closed-form result; the spin and time-ordered extensions are plausible but less complete. read the letter →
The pith
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
The reading
What carries the argument
The load-bearing object is the momentum-space OPE coefficient $\widetilde C_{12O}(p,q)$, the formal Fourier transform of the position-space OPE coefficient, which is analytic in $q$ around $q=0$ and thereby turns OPE limits into boundary conditions. The conformal Ward identities for special conformal transformations become a pair of second-order partial differential equations in the two variables $z_f=p_f^2/p_0^2$ and $z_i=p_i^2/p_0^2$; their general solution is a linear combination of four Appell $F_4$ functions. Appell's $F_4$ is the double hypergeometric series $\sum_{n,m}\frac{(a)_{n+m}(b)_{n+m}}{n!m!(c_f)_n(c_i)_m}z_f^n z_i^m$. The OPE boundary conditions select exactly one of the four solutions in the scalar case (and in the spin-$\ell$ case via a recursion), and the transformation formula (38) analytically continues the selected solution past the light cone $p_0^2=0$.
What would settle it
Evaluate the direct Fourier transform of the position-space Wightman 3-point function (the integral in appendix B) at a generic configuration with time-like $p_0$ and compare it with eq. (47); any mismatch in the branch cut at $p_0^2=0$ or in the coefficient relation (44) would refute the central claim.
Extended reading notes
Core claim
The discovery is that the Lorentzian OPE supplies a boundary condition that fixes the solution of the conformal Ward identities: among the four Appell $F_4$ solutions, only one respects the light-cone and zero-momentum OPE limits. For three scalars the Wightman function is therefore $$\langle\!\langle\phi_f(p_f)\phi_0(p_0)\phi_i(p_i)\rangle\!\rangle = \tilde\lambda_{f0i}\,\Theta(-p_f)\Theta(p_i)\,\frac{(-$p_f^{2}$)^{\Delta_f-d/2}(-$p_i^{2}$)^{\Delta_i-d/2}}{($p_0^{2}$)^{(\Delta_i+\Delta_f-\Delta_0)/2}}\, F_{\Delta_f\Delta_0\Delta_i}\left(\frac{$p_f^{2}$}{$p_0^{2}$},\frac{$p_i^{2}$}{$p_0^{2}$}\right),$$ valid in the region where the $F_4$ series converges, with eq. (47) covering all kinematic regions by analytic continuation. For two scalars and one traceless symmetric tensor of spin $\ell$, the same Appell structure survives: a recursion in the polarization vector determines all tensor structures from one $F_4$, and the coefficient is fixed by matching the position-space OPE. The paper further shows that partially time-ordered and fully time-ordered correlators are the other solutions of the same differential system with different boundary conditions, and that in fully spacelike kinematics the time-ordered function reproduces the known Euclidean expression.
Load-bearing premise
The load-bearing assumption is that the Fourier-transformed OPE coefficient is analytic in the total momentum $q$ near $q=0$, so the zero-momentum and light-cone limits select a single solution with no correction series; if that analyticity fails, the Appell $F_4$ form and its normalization no longer follow.
Editorial extensions
If this is right
- Any scalar 3-point Wightman function in a Lorentzian CFT, in any $d\ge 2$ and any scaling dimensions above the unitarity bound, can be evaluated as a convergent double hypergeometric series instead of a numerical Bessel integral.
- The same closed form covers two scalars plus one traceless symmetric tensor of arbitrary spin, bringing conserved currents and the stress tensor within reach.
- Time-ordered correlators are the remaining solutions of the same differential system; in fully spacelike kinematics the fully time-ordered function coincides with the known Euclidean expression.
- At double-trace dimensions the hypergeometric series terminates and the 3-point function factorizes into products of 2-point functions, as in generalized free field theory.
- In $d=2$ the Appell function factorizes into ordinary hypergeometric functions, reproducing the holomorphic factorization of the position-space correlator.
Reading between the lines
- The analyticity of the momentum-space OPE coefficient could serve as a defining condition for bootstrapping higher-point Lorentzian momentum-space correlators without explicit Fourier transforms; the paper only demonstrates the single-term 3-point case.
- The unresolved partially time-ordered function with both momenta time-like suggests that OPE boundary data are incomplete there; imposing the known generalized-free-field factorization might select the missing term.
- Because the result is analytic in the spacetime dimension $d$, the closed form can be continued to $d=3$ and $d=4$ and compared with inflationary or cosmological correlators, a connection the paper does not draw.
Signed reviews
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. This paper derives closed-form expressions for Lorentzian momentum-space 3-point Wightman functions in conformal field theory. Instead of direct Fourier transformation, the author uses conformal Ward identities and OPE boundary conditions. For three scalars, the main result is Eq. (37): the Wightman function equals a product of power laws times an Appell F4 double hypergeometric series, with Eq. (47) providing a continuation covering all kinematic regions. Section 3 extends the result to two scalars plus one traceless symmetric tensor of arbitrary spin, and Section 4 discusses time-ordered and partially time-ordered correlators. Appendix B checks the scalar formula against direct Fourier transforms in two OPE limits and reports numerical checks.
Significance. If correct, the result is a genuine improvement: it replaces a complicated Bessel-function integral for the scalar 3-point function with a simple hypergeometric expression, and it demonstrates that the momentum-space OPE, together with conformal Ward identities, can fix the full kinematic dependence without fitted parameters. The extension to traceless symmetric tensors and the discussion of time-ordered products are useful and mostly clearly presented. The analytic checks in Appendix B, the two-dimensional holomorphic factorization, and the generalized-free-field limits are well chosen and strengthen the paper. However, the selection of the unique solution and the continuation coefficients rests on an unproven analyticity assumption for the exact momentum-space OPE coefficient, and the time-like continuation region lacks direct verification in the manuscript.
major comments (2)
- [Sec. 2.2, Eq. (21); Sec. 2.4, Eqs. (35), (43), (44)] The uniqueness of the solution in Eq. (35) and the normalization of the time-like continuation coefficients in Eq. (44) both rely on the claim that the momentum-space OPE coefficient ~C_{12O}(p,q) is analytic in q around q=0. This is asserted from the formal expansion in Eq. (21), but the paper itself states in Sec. 2.2 that this definition is "purely formal so far" and that convergence is an open problem. The exact Fourier transform of the OPE coefficient could contain non-analytic or non-perturbative corrections in q; if so, the light-cone asymptotics in Eq. (29) and the cancellation of non-analytic terms near p_f -> 0 in Eq. (43) receive uncontrolled contributions. This is load-bearing because it determines both which of the four Ward-identity solutions is physical and the value of the continuation coefficients. I request either a proof of the needed analyticity at the level of the exact Fourier transform, or a direct numerical check of Eqs. (41)/(47) against the integral in Eq. (108) for time-like p0 with representative dimensions and a quantified agreement.
- [Appendix B, Eqs. (108), (113), (119), (127)] The analytic checks in Appendix B cover the simultaneous light-cone limit with space-like p0 and the pf -> 0 OPE limit, but no analytic check is shown for the time-like-p0 branch where Eq. (44) is essential. The text says that numerical checks were performed, but gives no comparison data, parameter ranges, or tolerances, so the continuation region is effectively unverified in the manuscript. This matters because the singular point p0^2 = 0 and the cancellation in Eq. (43) are exactly where the analyticity assumption is used. Please extend Appendix B with explicit numerical comparisons for p0^2 < 0, for example by evaluating Eq. (113) on a scan over p_f^2/p_i^2 and scaling dimensions and comparing with Eq. (47).
minor comments (5)
- [Abstract and Sec. 4.1] The abstract says that time-ordered and partially time-ordered products are constructed, but Sec. 4.1 explicitly leaves the case of time-like p1 and p2 as an open problem. Please reword the abstract and the discussion in Sec. 4.1 to state precisely which configurations are constructed.
- [Sec. 3.1] The sentence "The only type of spin representations allowed by conformal symmetry are are traceless symmetric tensors" contains a duplicated "are" and should be corrected.
- [Appendix A, first sentence] The text says that there are d(d+1)/2 generators of SO(d,2), but SO(d,2) has (d+2)(d+1)/2 generators; this appears to be a typo and should be fixed.
- [Eq. (47)] It would help the reader to state explicitly the branch or i-epsilon prescription used for each power of p^2 in the three-term continuation formula, since the reality of the Wightman function and the branch structure at p0^2 = 0 are otherwise hard to verify.
- [Appendix B] The numerical comparison is described only verbally; a figure or table with representative momenta, scaling dimensions, and relative errors would make the claimed verification reproducible and would substantially strengthen confidence in the result.
Circularity Check
No circularity: the Appell F4 closed form is derived from Ward identities plus OPE boundary conditions, with no fitted parameters and no load-bearing self-citation.
full rationale
The paper's derivation chain is self-contained rather than circular. The Poincare- and scale-covariant ansatz (15) is combined with the special-conformal Ward identities (32), whose general solution is a four-parameter space of Appell F4 combinations (35). The Lorentzian OPE limits (22)-(28) supply boundary conditions that select the single consistent solution and fix its overall coefficient through eqs. (24), (44)-(46). This is a genuine constraint-and-selection problem: the OPE limits provide only asymptotic power behavior, not the full double hypergeometric function, so the final result is not equivalent to its inputs by construction. No parameter is fitted to the target 3-point function; the normalization is the physical OPE coefficient lambda, which is external input. The analytic continuation to time-like p0 in section 2.4 is fixed by demanding cancellation of non-analytic terms in the pf -> 0 OPE limit, and the resulting expression is checked against direct Fourier transforms in appendix B. The paper explicitly notes that the momentum-space OPE is 'purely formal so far' and that its convergence in higher dimensions 'remains open'; that is an admitted assumption and a correctness risk, but it is not a circular reduction, because the assumed OPE boundary conditions do not already contain the claimed closed-form result. Self-citations such as refs. [42], [44], and [64] appear in contextual remarks or for standard two-point functions and known formalism, but the central claim does not reduce to any of them. No circular step of any of the enumerated kinds can be quoted, so the appropriate finding is no significant circularity.
Assumptions & free parameters
assumptions (5)
- domain assumption The Lorentzian OPE can be applied in momentum space to a 3-point Wightman function and the coefficient ~C(p,q) is analytic in q around q=0.
- standard math The special conformal Ward identity (31) applies to momentum-space operators and its four Appell F4 solutions exhaust the solution space.
- domain assumption Wightman functions are analytic in scaling dimensions, so the OPE-selected solution extends through the special integer dimensions Delta = d/2 + n.
- domain assumption Unitarity bounds Delta >= (d-2)/2 and the standard positivity structure of momentum eigenstates hold.
- domain assumption For the spin case, the ansatz (56) with l+1 polarization functions spans all Poincare and scale invariants, and the recursion (59) from the transverse Ward identity is complete.
Cite this review
Pith. "Pith review of Conformal 3-point functions and the Lorentzian OPE in momentum space." pith.science (2026). https://pith.science/paper/BL5AETGX
@misc{pith2026190900878,
author = {Pith},
title = {Pith review of: Conformal 3-point functions and the Lorentzian OPE in momentum space},
year = {2026},
howpublished = {\url{https://pith.science/paper/BL5AETGX}},
note = {Machine review of arXiv:1909.00878}
}
abstract
In conformal field theory in Minkowski momentum space, the 3-point correlation functions of local operators are completely fixed by symmetry. Using Ward identities together with the existence of a Lorentzian operator product expansion (OPE), we show that the Wightman function of three scalar operators is a double hypergeometric series of the Appell $F_4$ type. We extend this simple closed-form expression to the case of two scalar operators and one traceless symmetric tensor with arbitrary spin. Time-ordered and partially-time-ordered products are constructed in a similar fashion and their relation with the Wightman function is discussed.
Figures
Forward citations
Cited by 4 Pith papers
-
Geometry of Kinematic Flow
The wavefunction coefficients of conformally coupled scalars in power-law cosmologies obey differential equations whose basis functions can be arranged on hypercubes and zonotopes, with a single merger rule generating...
-
Effective dynamics of open 2D CFTs
The momentum-space thermal four-point response function of scalar primaries in an arbitrary 2D CFT is expressed as an infinite sum over global conformal blocks of Meijer G-functions.
-
An Ode to the Penrose and Witten transforms in Twistor space for 3D CFT
The authors show that the infinity twistor must be added to twistor-space invariants to describe general primary operators in 3D CFTs, and they derive the corresponding Penrose, Witten, and super-Penrose transforms.
-
Lectures on the Spinor and Twistor Formalism in 3D Conformal Field Theory
Lecture notes recapping off-shell spinor helicity, twistor, and super-twistor methods for 3d CFT correlators, with 55 exercises and no substantial new research result.
Reference graph
Works this paper leans on
-
[1]
Conformal symmetry of critical fluctuations,
A. M. Polyakov, “Conformal symmetry of critical fluctuations,” JETP Lett. 12 (1970) 381–383. [Pisma Zh. Eksp. Teor. Fiz.12,538(1970)]
work page 1970
-
[2]
Conformal symmetry and three-point functio ns,
E. J. Schreier, “Conformal symmetry and three-point functio ns,” Phys. Rev. D3 (1971) 980–988
work page 1971
-
[3]
Implications of conformal invarian ce in field theories for general dimensions,
H. Osborn and A. C. Petkou, “Implications of conformal invarian ce in field theories for general dimensions,” Annals Phys. 231 (1994) 311–362 , arXiv:hep-th/9307010 [hep-th]
arXiv 1994
-
[4]
J. Erdmenger and H. Osborn, “Conserved currents and the en ergy momentum tensor in conformally invariant theories for general dimensions,” Nucl. Phys. B483 (1997) 431–474 , arXiv:hep-th/9605009 [hep-th]
arXiv 1997
-
[5]
A Note on CFT Correlators in Th ree Dimensions,
S. Giombi, S. Prakash, and X. Yin, “A Note on CFT Correlators in Th ree Dimensions,” JHEP 07 (2013) 105 , arXiv:1104.4317 [hep-th]
arXiv 2013
-
[6]
Spinnin g Conformal Correlators,
M. S. Costa, J. Penedones, D. Poland, and S. Rychkov, “Spinnin g Conformal Correlators,” JHEP 11 (2011) 071 , arXiv:1107.3554 [hep-th]
arXiv 2011
-
[7]
Constraining Conformal Field Th eories with A Higher Spin Symmetry,
J. Maldacena and A. Zhiboedov, “Constraining Conformal Field Th eories with A Higher Spin Symmetry,” J. Phys. A46 (2013) 214011 , arXiv:1112.1016 [hep-th]
arXiv 2013
-
[8]
A note on three-point functions of conserved c urrents,
A. Zhiboedov, “A note on three-point functions of conserved c urrents,” arXiv:1206.6370 [hep-th]
Show all 68 references
-
[9]
General Three-Point Functions in 4D CFT,
E. Elkhidir, D. Karateev, and M. Serone, “General Three-Point Functions in 4D CFT,” JHEP 01 (2015) 133 , arXiv:1412.1796 [hep-th]
2015 arXiv
-
[10]
Conformal two-point c orrelation functions from the operator product expansion,
J.-F. Fortin, V. Prilepina, and W. Skiba, “Conformal two-point c orrelation functions from the operator product expansion,” JHEP 04 (2020) 114 , arXiv:1906.12349 [hep-th]
2020 arXiv
-
[11]
Conformal Three-Poin t Correlation Functions from the Operator Product Expansion,
J.-F. Fortin, V. Prilepina, and W. Skiba, “Conformal Three-Poin t Correlation Functions from the Operator Product Expansion,” arXiv:1907.08599 [hep-th]
1907 arXiv
-
[12]
Weight Shif ting Operators and Conformal Blocks,
D. Karateev, P. Kravchuk, and D. Simmons-Duffin, “Weight Shif ting Operators and Conformal Blocks,” JHEP 02 (2018) 081 , arXiv:1706.07813 [hep-th]
2018 arXiv
-
[13]
Harmonic A nalysis and Mean Field Theory,
D. Karateev, P. Kravchuk, and D. Simmons-Duffin, “Harmonic A nalysis and Mean Field Theory,” JHEP 10 (2019) 217 , arXiv:1809.05111 [hep-th]
2019 arXiv
-
[14]
OPE C onvergence in Conformal Field Theory,
D. Pappadopulo, S. Rychkov, J. Espin, and R. Rattazzi, “OPE C onvergence in Conformal Field Theory,” Phys. Rev. D86 (2012) 105043 , arXiv:1208.6449 [hep-th]
2012 arXiv
-
[15]
Radial Coordinates for Conf ormal Blocks,
M. Hogervorst and S. Rychkov, “Radial Coordinates for Conf ormal Blocks,” Phys. Rev. D87 (2013) 106004 , arXiv:1303.1111 [hep-th] . 31
2013 arXiv
-
[16]
Remarks on the Convergence Pr operties of the Conformal Block Expansion,
S. Rychkov and P. Yvernay, “Remarks on the Convergence Pr operties of the Conformal Block Expansion,” Phys. Lett. B753 (2016) 682–686 , arXiv:1510.08486 [hep-th]
2016 arXiv
-
[17]
Analytic Euclidean Boot strap,
B. Mukhametzhanov and A. Zhiboedov, “Analytic Euclidean Boot strap,” JHEP 10 (2019) 270 , arXiv:1808.03212 [hep-th]
2019 arXiv
-
[18]
Bounding sc alar operator dimensions in 4D CFT,
R. Rattazzi, V. S. Rychkov, E. Tonni, and A. Vichi, “Bounding sc alar operator dimensions in 4D CFT,” JHEP 12 (2008) 031 , arXiv:0807.0004 [hep-th]
2008 arXiv
-
[19]
Rychkov, EPFL Lectures on Conformal Field Theory in D ≥ 3 Dimensions
S. Rychkov, EPFL Lectures on Conformal Field Theory in D ≥ 3 Dimensions . SpringerBriefs in Physics, 2016. arXiv:1601.05000 [hep-th]
2016 arXiv
-
[20]
The Conformal Bootstrap,
D. Simmons-Duffin, “The Conformal Bootstrap,” in Proceedings, Theoretical Advanced Study Institute in Elementary Particle Physics: N ew Frontiers in Fields and Strings (TASI 2015): Boulder, CO, USA, June 1-26, 2015 , pp. 1–74. 2017. arXiv:1602.07982 [hep-th]
2015 arXiv
-
[21]
The Conformal Bootstra p: Theory, Numerical Techniques, and Applications,
D. Poland, S. Rychkov, and A. Vichi, “The Conformal Bootstra p: Theory, Numerical Techniques, and Applications,” Rev. Mod. Phys. 91 no. 1, (2019) 15002 , arXiv:1805.04405 [hep-th] . [Rev. Mod. Phys.91,015002(2019)]
2019 arXiv
-
[22]
Lorentzian CFT 3-point functio ns in momentum space,
T. Bautista and H. Godazgar, “Lorentzian CFT 3-point functio ns in momentum space,” JHEP 01 (2020) 142 , arXiv:1908.04733 [hep-th]
2020 arXiv
-
[23]
Solving the Conformal Constraints for Scalar Operators in Momentum Space and the Evalu ation of Feynman’s Master Integrals,
C. Coriano, L. Delle Rose, E. Mottola, and M. Serino, “Solving the Conformal Constraints for Scalar Operators in Momentum Space and the Evalu ation of Feynman’s Master Integrals,” JHEP 07 (2013) 011 , arXiv:1304.6944 [hep-th]
2013 arXiv
-
[24]
Implications of co nformal invariance in momentum space,
A. Bzowski, P. McFadden, and K. Skenderis, “Implications of co nformal invariance in momentum space,” JHEP 03 (2014) 111 , arXiv:1304.7760 [hep-th]
2014 arXiv
-
[25]
Scalar 3-point fu nctions in CFT: renormalisation, beta functions and anomalies,
A. Bzowski, P. McFadden, and K. Skenderis, “Scalar 3-point fu nctions in CFT: renormalisation, beta functions and anomalies,” JHEP 03 (2016) 066 , arXiv:1510.08442 [hep-th]
2016 arXiv
-
[26]
TTT in CFT: Trace Iden tities and the Conformal Anomaly Effective Action,
C. Coriano, M. M. Maglio, and E. Mottola, “TTT in CFT: Trace Iden tities and the Conformal Anomaly Effective Action,” Nucl. Phys. B942 (2019) 303–328 , arXiv:1703.08860 [hep-th]
2019 arXiv
-
[27]
Renormalised 3-p oint functions of stress tensors and conserved currents in CFT,
A. Bzowski, P. McFadden, and K. Skenderis, “Renormalised 3-p oint functions of stress tensors and conserved currents in CFT,” JHEP 11 (2018) 153 , arXiv:1711.09105 [hep-th]
2018 arXiv
-
[28]
Momentum space approach to crossing symmetric CFT correlators,
H. Isono, T. Noumi, and G. Shiu, “Momentum space approach to crossing symmetric CFT correlators,” JHEP 07 (2018) 136 , arXiv:1805.11107 [hep-th]
2018 arXiv
-
[29]
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,” JHEP 11 (2018) 159 , arXiv:1805.12100 [hep-th] . 32
2018 arXiv
-
[30]
The general 3-graviton vertex ( T T T) of conformal field theories in momentum space in d = 4,
C. Corian` o and M. M. Maglio, “The general 3-graviton vertex ( T T T) of conformal field theories in momentum space in d = 4,” Nucl. Phys. B937 (2018) 56–134 , arXiv:1808.10221 [hep-th]
2018 arXiv
-
[31]
Momentum space confor mal three-point functions of conserved currents and a general spinning operato r,
H. Isono, T. Noumi, and T. Takeuchi, “Momentum space confor mal three-point functions of conserved currents and a general spinning operato r,” JHEP 05 (2019) 057 , arXiv:1903.01110 [hep-th]
2019 arXiv
-
[32]
Momentum space approach to crossing symmetric CFT correlators. Part II. General spacetime dimension ,
H. Isono, T. Noumi, and G. Shiu, “Momentum space approach to crossing symmetric CFT correlators. Part II. General spacetime dimension ,” JHEP 10 (2019) 183 , arXiv:1908.04572 [hep-th]
2019 arXiv
-
[33]
On graviton non-Gaussianit ies during inflation,
J. M. Maldacena and G. L. Pimentel, “On graviton non-Gaussianit ies during inflation,” JHEP 09 (2011) 045 , arXiv:1104.2846 [hep-th]
2011 arXiv
-
[34]
Conformal consistency relations for single-field inflation,
P. Creminelli, J. Nore˜ na, and M. Simonovi´ c, “Conformal consistency relations for single-field inflation,” JCAP 1207 (2012) 052 , arXiv:1203.4595 [hep-th]
2012 arXiv
-
[35]
Constraints from Conf ormal Symmetry on the Three Point Scalar Correlator in Inflation,
N. Kundu, A. Shukla, and S. P. Trivedi, “Constraints from Conf ormal Symmetry on the Three Point Scalar Correlator in Inflation,” JHEP 04 (2015) 061 , arXiv:1410.2606 [hep-th]
2015 arXiv
-
[36]
Cosmological Collider Physic s,
N. Arkani-Hamed and J. Maldacena, “Cosmological Collider Physic s,” arXiv:1503.08043 [hep-th]
-
[37]
Ward Identities for Sca le and Special Conformal Transformations in Inflation,
N. Kundu, A. Shukla, and S. P. Trivedi, “Ward Identities for Sca le and Special Conformal Transformations in Inflation,” JHEP 01 (2016) 046 , arXiv:1507.06017 [hep-th]
2016 arXiv
-
[38]
Symmetry constraints in inflation, α-vacua, and the three point function,
A. Shukla, S. P. Trivedi, and V. Vishal, “Symmetry constraints in inflation, α-vacua, and the three point function,” JHEP 12 (2016) 102 , arXiv:1607.08636 [hep-th]
2016 arXiv
-
[39]
The Cosmological Bootstrap: Inflationary Correlators from Symmetries and Singula rities,
N. Arkani-Hamed, D. Baumann, H. Lee, and G. L. Pimentel, “The Cosmological Bootstrap: Inflationary Correlators from Symmetries and Singula rities,” arXiv:1811.00024 [hep-th]
-
[40]
A Mellin Space Approach to Cosmological Correlators ,
C. Sleight, “A Mellin Space Approach to Cosmological Correlators ,” JHEP 01 (2020) 090 , arXiv:1906.12302 [hep-th]
2020 arXiv
-
[41]
Bootstrapping Inflationary Corre lators in Mellin Space,
C. Sleight and M. Taronna, “Bootstrapping Inflationary Corre lators in Mellin Space,” JHEP 02 (2020) 098 , arXiv:1907.01143 [hep-th]
2020 arXiv
-
[42]
Scale Anomalies, States, and Ra tes in Conformal Field Theory,
M. Gillioz, X. Lu, and M. A. Luty, “Scale Anomalies, States, and Ra tes in Conformal Field Theory,” JHEP 04 (2017) 171 , arXiv:1612.07800 [hep-th]
2017 arXiv
-
[43]
Graviton Scattering and a Sum R ule for the c Anomaly in 4D CFT,
M. Gillioz, X. Lu, and M. A. Luty, “Graviton Scattering and a Sum R ule for the c Anomaly in 4D CFT,” JHEP 09 (2018) 025 , arXiv:1801.05807 [hep-th]
2018 arXiv
-
[44]
Momentum-space conformal blocks on the light cone,
M. Gillioz, “Momentum-space conformal blocks on the light cone,” JHEP 10 (2018) 125 , arXiv:1807.07003 [hep-th] . 33
2018 arXiv
-
[45]
From correlation functions to event shapes,
A. V. Belitsky, S. Hohenegger, G. P. Korchemsky, E. Sokatch ev, and A. Zhiboedov, “From correlation functions to event shapes,” Nucl. Phys. B884 (2014) 305–343 , arXiv:1309.0769 [hep-th]
2014 arXiv
-
[46]
Light-ray operators in co nformal field theory,
P. Kravchuk and D. Simmons-Duffin, “Light-ray operators in co nformal field theory,” JHEP 11 (2018) 102 , arXiv:1805.00098 [hep-th] . [,236(2018)]
2018 arXiv
-
[47]
Shocks, Superconvergence, and a Stringy Equivalence Principle,
M. Kologlu, P. Kravchuk, D. Simmons-Duffin, and A. Zhiboedov, “ Shocks, Superconvergence, and a Stringy Equivalence Principle,” arXiv:1904.05905 [hep-th]
1904 arXiv
-
[48]
The light-ray OPE and conformal colliders,
M. Kologlu, P. Kravchuk, D. Simmons-Duffin, and A. Zhiboedov, “ The light-ray OPE and conformal colliders,” arXiv:1905.01311 [hep-th]
1905 arXiv
-
[49]
Conformal collider physics: En ergy and charge correlations,
D. M. Hofman and J. Maldacena, “Conformal collider physics: En ergy and charge correlations,” JHEP 05 (2008) 012 , arXiv:0803.1467 [hep-th]
2008 arXiv
-
[50]
Bounds on OPE Co efficients from Interference Effects in the Conformal Collider,
C. Cordova, J. Maldacena, and G. J. Turiaci, “Bounds on OPE Co efficients from Interference Effects in the Conformal Collider,” JHEP 11 (2017) 032 , arXiv:1710.03199 [hep-th]
2017 arXiv
-
[51]
Universal Bounds on Operator Dimens ions from the Average Null Energy Condition,
C. Cordova and K. Diab, “Universal Bounds on Operator Dimens ions from the Average Null Energy Condition,” JHEP 02 (2018) 131 , arXiv:1712.01089 [hep-th]
2018 arXiv
-
[52]
Constraints o n parity violating conformal field theories in d = 3,
S. D. Chowdhury, J. R. David, and S. Prakash, “Constraints o n parity violating conformal field theories in d = 3,” JHEP 11 (2017) 171 , arXiv:1707.03007 [hep-th]
2017 arXiv
-
[53]
Shoc kwaves from the Operator Product Expansion,
N. Afkhami-Jeddi, T. Hartman, S. Kundu, and A. Tajdini, “Shoc kwaves from the Operator Product Expansion,” JHEP 03 (2019) 201 , arXiv:1709.03597 [hep-th]
2019 arXiv
-
[54]
A Conformal Collide r for Holographic CFTs,
N. Afkhami-Jeddi, S. Kundu, and A. Tajdini, “A Conformal Collide r for Holographic CFTs,” JHEP 10 (2018) 156 , arXiv:1805.07393 [hep-th]
2018 arXiv
-
[55]
Higher Spin ANEC and the Space of CFTs,
D. Meltzer, “Higher Spin ANEC and the Space of CFTs,” JHEP 07 (2019) 001 , arXiv:1811.01913 [hep-th]
2019 arXiv
-
[56]
Einstein gravity from AN EC correlators,
A. Belin, D. M. Hofman, and G. Mathys, “Einstein gravity from AN EC correlators,” JHEP 08 (2019) 032 , arXiv:1904.05892 [hep-th]
2019 arXiv
-
[57]
Higher Derivative Gravity, Causality and Positivit y of Energy in a UV complete QFT,
D. M. Hofman, “Higher Derivative Gravity, Causality and Positivit y of Energy in a UV complete QFT,” Nucl. Phys. B823 (2009) 174–194 , arXiv:0907.1625 [hep-th]
2009 arXiv
-
[58]
Averaged Null Energy C ondition from Causality,
T. Hartman, S. Kundu, and A. Tajdini, “Averaged Null Energy C ondition from Causality,” JHEP 07 (2017) 066 , arXiv:1610.05308 [hep-th]
2017 arXiv
-
[59]
Light-ray Operators and the BM S Algebra,
C. C´ ordova and S.-H. Shao, “Light-ray Operators and the BM S Algebra,” Phys. Rev. D98 no. 12, (2018) 125015 , arXiv:1810.05706 [hep-th] . 34
2018 arXiv
-
[60]
A Conformal Tru ncation Framework for Infinite-Volume Dynamics,
E. Katz, Z. U. Khandker, and M. T. Walters, “A Conformal Tru ncation Framework for Infinite-Volume Dynamics,” JHEP 07 (2016) 140 , arXiv:1604.01766 [hep-th]
2016 arXiv
-
[61]
Lightcone effective Hamiltonians and RG flows,
A. L. Fitzpatrick, J. Kaplan, E. Katz, L. G. Vitale, and M. T. Walt ers, “Lightcone effective Hamiltonians and RG flows,” JHEP 08 (2018) 120 , arXiv:1803.10793 [hep-th]
2018 arXiv
-
[62]
Recursion relation for general 3d blocks,
R. S. Erramilli, L. V. Iliesiu, and P. Kravchuk, “Recursion relation for general 3d blocks,” JHEP 12 (2019) 116 , arXiv:1907.11247 [hep-th]
2019 arXiv
-
[63]
Convergence of Operator Product Expansions on t he Vacuum in Conformal Invariant Quantum Field Theory,
G. Mack, “Convergence of Operator Product Expansions on t he Vacuum in Conformal Invariant Quantum Field Theory,” Commun. Math. Phys. 53 (1977) 155
1977
-
[64]
Convergent Mo mentum-Space OPE and Bootstrap Equations in Conformal Field Theory,
M. Gillioz, X. Lu, M. A. Luty, and G. Mikaberidze, “Convergent Mo mentum-Space OPE and Bootstrap Equations in Conformal Field Theory,” JHEP 03 (2020) 102 , arXiv:1912.05550 [hep-th]
2020 arXiv
-
[65]
NIST Digital Library of Mathematical Functions
“ NIST Digital Library of Mathematical Functions .” Http://dlmf.nist.gov/, release 1.0.23 of 2019-06-15. http://dlmf.nist.gov/. F. W. J. Olver, A. B. Olde Daalhuis, D. W. Lozier, B. I. Schneider, R. F. Boisvert, C. W. Clark, B. R. Miller and B. V. Saunders, eds
2019
-
[66]
Projectors, Shadows, and Conformal Blo cks,
D. Simmons-Duffin, “Projectors, Shadows, and Conformal Blo cks,” JHEP 04 (2014) 146 , arXiv:1204.3894 [hep-th]
2014 arXiv
-
[67]
Conformal Partial Waves: Furthe r Mathematical Results,
F. A. Dolan and H. Osborn, “Conformal Partial Waves: Furthe r Mathematical Results,” arXiv:1108.6194 [hep-th]
-
[68]
Pro jectors and seed conformal blocks for traceless mixed-symmetry tensors,
M. S. Costa, T. Hansen, J. Penedones, and E. Trevisani, “Pro jectors and seed conformal blocks for traceless mixed-symmetry tensors,” JHEP 07 (2016) 018 , arXiv:1603.05551 [hep-th] . 35
2016 arXiv
Reviewed August 14, 2026 · model on record in the stance chip above.
Discussion (0). Continue with ORCID to comment.