Built on

J. Schwinger, “On the Euclidean structure of relativistic field theory,” Proc. Natl. Acad. Sci. US 44
1960
Earlier work this paper cites.
K. Osterwalder and R. Schrader, “Axioms For Euclidean Green’s Functions,” Commun. Math. Phys. 31
1975
Earlier work this paper cites.
M. Luscher and G. Mack, “Global Conformal Invariance in Quantum Field Theory,” Commun. Math. Phys. 41
1975
Earlier work this paper cites.
G. Mack, “Convergence of Operator Product Expansions on the Vacuum in Conformal Invariant Quantum Field Theory,” Commun. Math. Phys. 53
1977
Earlier work this paper cites.
R. Haag, Local quantum physics: Fields, particles, algebras
1992
Earlier work this paper cites.
H. Osborn and A. C. Petkou, “Implications of conformal invariance in field theories for general dimensions,” Annals Phys. 231
1994
Earlier work this paper cites.
A. Strominger, “Black hole entropy from near horizon microstates,” JHEP 9802
1998
Earlier work this paper cites.
F. A. Dolan and H. Osborn, “Conformal four point functions and the operator product expansion,” Nucl. Phys. B 599
2001
Earlier work this paper cites.
A. Adams, N. Arkani-Hamed, S. Dubovsky, A. Nicolis and R. Rattazzi, “Causality, analyticity and an IR obstruction to UV completion,” JHEP 0610
2006
Earlier work this paper cites.
L. Cornalba, M. S. Costa, J. Penedones and R. Schiappa, “Eikonal Approximation in AdS/CFT: From Shock Waves to Four-Point Functions,” JHEP 0708
2007
Earlier work this paper cites.
L. Cornalba, M. S. Costa, J. Penedones and R. Schiappa, “Eikonal Approximation in AdS/CFT: Conformal Partial Waves and Finite N Four-Point Functions,” Nucl. Phys. B 767
2007
Earlier work this paper cites.
J. P. Bruneton, “On causality and superluminal behavior in classical field theories: Applications to k-essence theories and MOND-like theories of gravity,” Phys. Rev. D 75
2007
Earlier work this paper cites.
M. Brigante, H. Liu, R. C. Myers, S. Shenker and S. Yaida, “The Viscosity Bound and Causality Violation,” Phys. Rev. Lett. 100
Original
2008
Earlier work this paper cites.
R. Rattazzi, V. S. Rychkov, E. Tonni and A. Vichi, “Bounding scalar operator dimensions in 4D CFT,” JHEP 0812
Original
2008
Earlier work this paper cites.
D. M. Hofman and J. Maldacena, “Conformal collider physics: Energy and charge correlations,” JHEP 0805
Original
2008
Earlier work this paper cites.
D. M. Hofman, “Higher Derivative Gravity, Causality and Positivity of Energy in a UV complete QFT,” Nucl. Phys. B 823
Original
2009
Earlier work this paper cites.

Similar

I. Heemskerk, J. Penedones, J. Polchinski and J. Sully, “Holography from Conformal Field Theory,” JHEP 0910
Original
2009
Cited alongside, same era.
G. Mack, “D-dimensional Conformal Field Theories with anomalous dimensions as Dual Resonance Models,” Bulg. J. Phys. 36
Original
2009
Cited alongside, same era.
X. O. Camanho and J. D. Edelstein, “Causality constraints in AdS/CFT from conformal collider physics and Gauss-Bonnet gravity,” JHEP 1004
Original
2010
Cited alongside, same era.
I. Heemskerk and J. Sully, “More Holography from Conformal Field Theory,” JHEP 1009
Original
2010
Cited alongside, same era.
Z. Komargodski and A. Schwimmer, “On Renormalization Group Flows in Four Dimensions,” JHEP 1112

Then

A. L. Fitzpatrick, J. Kaplan, D. Poland and D. Simmons-Duffin, “The Analytic Bootstrap and AdS Superhorizon Locality,” JHEP 1312
Original
2013
Later among the works it cites.
A. L. Fitzpatrick and J. Kaplan, “AdS Field Theory from Conformal Field Theory,” JHEP 1302
Original
2013
Later among the works it cites.
J. Maldacena and A. Zhiboedov, “Constraining Conformal Field Theories with A Higher Spin Symmetry,” J. Phys. A 46
Original
2013
Later among the works it cites.
N. Boulanger, D. Ponomarev, E. D. Skvortsov and M. Taronna, “On the uniqueness of higher-spin symmetries in AdS and CFT,” Int. J. Mod. Phys. A 28
Original
2013
Later among the works it cites.
M. Hogervorst and S. Rychkov, “Radial Coordinates for Conformal Blocks,” Phys. Rev. D 87

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2015

Causality Constraints in Conformal Field Theory

Hartman, Thomas, Jain, Sachin, Kundu, Sandipan

Understand

Causality places nontrivial constraints on QFT in Lorentzian signature, for example fixing the signs of certain terms in the low energy Lagrangian.

In d-dimensional conformal field theory, we show how such constraints are encoded in crossing symmetry of Euclidean correlators, and derive analogous constraints directly from the conformal bootstrap (analytically).
The bootstrap setup is a Lorentzian four-point function corresponding to propagation through a shockwave.
Crossing symmetry fixes the signs of certain log terms that appear in the conformal block expansion, which constrains the interactions of low-lying operators.

Built on

J. Schwinger, “On the Euclidean structure of relativistic field theory,” Proc. Natl. Acad. Sci. US 44
1960
Earlier work this paper cites.
K. Osterwalder and R. Schrader, “Axioms For Euclidean Green’s Functions,” Commun. Math. Phys. 31
1975
Earlier work this paper cites.
M. Luscher and G. Mack, “Global Conformal Invariance in Quantum Field Theory,” Commun. Math. Phys. 41
1975
Earlier work this paper cites.
G. Mack, “Convergence of Operator Product Expansions on the Vacuum in Conformal Invariant Quantum Field Theory,” Commun. Math. Phys. 53
1977
Earlier work this paper cites.
R. Haag, Local quantum physics: Fields, particles, algebras
1992
Earlier work this paper cites.
H. Osborn and A. C. Petkou, “Implications of conformal invariance in field theories for general dimensions,” Annals Phys. 231
1994
Earlier work this paper cites.
A. Strominger, “Black hole entropy from near horizon microstates,” JHEP 9802
1998
Earlier work this paper cites.
F. A. Dolan and H. Osborn, “Conformal four point functions and the operator product expansion,” Nucl. Phys. B 599
2001
Earlier work this paper cites.
A. Adams, N. Arkani-Hamed, S. Dubovsky, A. Nicolis and R. Rattazzi, “Causality, analyticity and an IR obstruction to UV completion,” JHEP 0610
2006
Earlier work this paper cites.
L. Cornalba, M. S. Costa, J. Penedones and R. Schiappa, “Eikonal Approximation in AdS/CFT: From Shock Waves to Four-Point Functions,” JHEP 0708
2007
Earlier work this paper cites.
L. Cornalba, M. S. Costa, J. Penedones and R. Schiappa, “Eikonal Approximation in AdS/CFT: Conformal Partial Waves and Finite N Four-Point Functions,” Nucl. Phys. B 767
2007
Earlier work this paper cites.
J. P. Bruneton, “On causality and superluminal behavior in classical field theories: Applications to k-essence theories and MOND-like theories of gravity,” Phys. Rev. D 75
2007
Earlier work this paper cites.
M. Brigante, H. Liu, R. C. Myers, S. Shenker and S. Yaida, “The Viscosity Bound and Causality Violation,” Phys. Rev. Lett. 100
Original
2008
Earlier work this paper cites.
R. Rattazzi, V. S. Rychkov, E. Tonni and A. Vichi, “Bounding scalar operator dimensions in 4D CFT,” JHEP 0812
Original
2008
Earlier work this paper cites.
D. M. Hofman and J. Maldacena, “Conformal collider physics: Energy and charge correlations,” JHEP 0805
Original
2008
Earlier work this paper cites.
D. M. Hofman, “Higher Derivative Gravity, Causality and Positivity of Energy in a UV complete QFT,” Nucl. Phys. B 823
Original
2009
Earlier work this paper cites.

Similar

I. Heemskerk, J. Penedones, J. Polchinski and J. Sully, “Holography from Conformal Field Theory,” JHEP 0910
Original
2009
Cited alongside, same era.
G. Mack, “D-dimensional Conformal Field Theories with anomalous dimensions as Dual Resonance Models,” Bulg. J. Phys. 36
Original
2009
Cited alongside, same era.
X. O. Camanho and J. D. Edelstein, “Causality constraints in AdS/CFT from conformal collider physics and Gauss-Bonnet gravity,” JHEP 1004
Original
2010
Cited alongside, same era.
I. Heemskerk and J. Sully, “More Holography from Conformal Field Theory,” JHEP 1009
Original
2010
Cited alongside, same era.
Z. Komargodski and A. Schwimmer, “On Renormalization Group Flows in Four Dimensions,” JHEP 1112

Then

A. L. Fitzpatrick, J. Kaplan, D. Poland and D. Simmons-Duffin, “The Analytic Bootstrap and AdS Superhorizon Locality,” JHEP 1312
Original
2013
Later among the works it cites.
A. L. Fitzpatrick and J. Kaplan, “AdS Field Theory from Conformal Field Theory,” JHEP 1302
Original
2013
Later among the works it cites.
J. Maldacena and A. Zhiboedov, “Constraining Conformal Field Theories with A Higher Spin Symmetry,” J. Phys. A 46
Original
2013
Later among the works it cites.
N. Boulanger, D. Ponomarev, E. D. Skvortsov and M. Taronna, “On the uniqueness of higher-spin symmetries in AdS and CFT,” Int. J. Mod. Phys. A 28
Original
2013
Later among the works it cites.
M. Hogervorst and S. Rychkov, “Radial Coordinates for Conformal Blocks,” Phys. Rev. D 87

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…

Original

2011

Cited alongside, same era.

A. L. Fitzpatrick, E. Katz, D. Poland and D. Simmons-Duffin, “Effective Conformal Theory and the Flat-Space Limit of AdS,” JHEP 1107

Original

2011

Cited alongside, same era.

J. Penedones, “Writing CFT correlation functions as AdS scattering amplitudes,” JHEP 1103

Original

2011

Cited alongside, same era.

A. L. Fitzpatrick, J. Kaplan, J. Penedones, S. Raju and B. C. van Rees, “A Natural Language for AdS/CFT Correlators,” JHEP 1111

Original

2011

Cited alongside, same era.

M. Kulaxizi and A. Parnachev, “Energy Flux Positivity and Unitarity in CFTs,” Phys. Rev. Lett. 106

Original

2011

Cited alongside, same era.

S. El-Showk, M. F. Paulos, D. Poland, S. Rychkov, D. Simmons-Duffin and A. Vichi, “Solving the 3D Ising Model with the Conformal Bootstrap,” Phys. Rev. D 86

Original

2012

Cited alongside, same era.

S. El-Showk and K. Papadodimas, “Emergent Spacetime and Holographic CFTs,” JHEP 1210

Original

2012

Cited alongside, same era.

A. L. Fitzpatrick and J. Kaplan, “Analyticity and the Holographic S-Matrix,” JHEP 1210

Original

2012

Cited alongside, same era.

Original

2013