Built on

A. L. Fitzpatrick and K.-W. Huang, “Universal Lowest-Twist in CFTs from Holography,” JHEP
Original
1903
Earlier work this paper cites.
A. Belin, D. M. Hofman, and G. Mathys, “Einstein gravity from ANEC correlators,” JHEP
Original
1904
Earlier work this paper cites.
M. Kologlu, P. Kravchuk, D. Simmons-Duffin, and A. Zhiboedov, “Shocks, Superconvergence, and a Stringy Equivalence Principle,” arXiv:1904.05905 [hep-th]
Original
1904
Earlier work this paper cites.
M. Kologlu, P. Kravchuk, D. Simmons-Duffin, and A. Zhiboedov, “The light-ray OPE and conformal colliders,” arXiv:1905.01311 [hep-th]
Original
1905
Earlier work this paper cites.
Y.-Z. Li, Z.-F. Mai, and H. Lü, “Holographic OPE Coefficients from AdS Black Holes with Matters,” JHEP
Original
1905
Earlier work this paper cites.
K.-W. Huang, “Stress-tensor commutators in conformal field theories near the lightcone,” Phys. Rev. D
Original
1907
Earlier work this paper cites.
M. Kulaxizi, G. S. Ng, and A. Parnachev, “Subleading Eikonal, AdS/CFT and Double Stress Tensors,” arXiv:1907.00867 [hep-th]
Original
1907
Earlier work this paper cites.
A. L. Fitzpatrick, K.-W. Huang, and D. Li, “Probing universalities in d > 2 d>2 CFTs: from black holes to shockwaves,” JHEP
Original
1907
Earlier work this paper cites.
R. Karlsson, M. Kulaxizi, A. Parnachev, and P. Tadić, “Leading Multi-Stress Tensors and Conformal Bootstrap,” JHEP
Original
1909
Earlier work this paper cites.
Y.-Z. Li, “Heavy-light Bootstrap from Lorentzian Inversion Formula,” JHEP
Original
1910
Earlier work this paper cites.
J. Schwinger, “Field theory commutators,” Phys. Rev. Lett
1959
Earlier work this paper cites.
J. S. Schwinger, “NonAbelian gauge fields. Relativistic invariance,” Phys. Rev
1962
Earlier work this paper cites.
M. Gell-Mann, “Symmetries of baryons and mesons,” Phys. Rev
1962
Earlier work this paper cites.
J. Schwinger, “Commutation relations and conservation laws,” Phys. Rev
1963
Earlier work this paper cites.
S. Deser and D. Boulware, “Stress-Tensor Commutators and Schwinger Terms,” J. Math. Phys
1967
Earlier work this paper cites.
H. Sugawara, “A field theory of currents,” Phys. Rev
1968
Earlier work this paper cites.

Similar

R. A. Brandt, “Approach to equal-time commutators in quantum field theory,” Phys. Rev
1968
Cited alongside, same era.
J. Trubatch, “Stress-tensor commutation relations,” Nuovo Cim. A
1970
Cited alongside, same era.
H. Osborn and A. Petkou, “Implications of conformal invariance in field theories for general dimensions,” Annals Phys
1994
Cited alongside, same era.
K.-W. Huang, “A Lightcone Commutator and Stress-Tensor Exchange in d > 2 d>2 CFTs,” arXiv:2002.00110 [hep-th]
Original
2002
Cited alongside, same era.
R. Karlsson, M. Kulaxizi, A. Parnachev, and P. Tadić, “Stress tensor sector of conformal correlators operators in the Regge limit,” JHEP
Original
2002
Cited alongside, same era.

Then

D. Simmons-Duffin, “Tasi lectures on the conformal bootstrap,” 2016
2016
Later among the works it cites.
B. Czech, L. Lamprou, S. McCandlish, B. Mosk, and J. Sully, “A stereoscopic look into the bulk,” Journal of High Energy Physics
2016
Later among the works it cites.
J. de Boer, F. M. Haehl, M. P. Heller, and R. C. Myers, “Entanglement, holography and causal diamonds,” Journal of High Energy Physics
2016
Later among the works it cites.
T. Hartman, S. Kundu, and A. Tajdini, “Averaged Null Energy Condition from Causality,” JHEP
Original
2017
Later among the works it cites.
C. Cordova, J. Maldacena, and G. J. Turiaci, “Bounds on OPE Coefficients from Interference Effects in the Conformal Collider,” JHEP
Original
2017
Later among the works it cites.

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2020

On Local and Integrated Stress-Tensor Commutators

Besken, Mert, de Boer, Jan, Mathys, Grégoire

Understand

We discuss some general aspects of commutators of local operators in Lorentzian CFTs, which can be obtained from a suitable analytic continuation of the Euclidean operator product expansion (OPE).

Commutators only make sense as distributions, and care has to be taken to extract the right distribution from the OPE.
We provide explicit computations in two and four-dimensional CFTs, focusing mainly on commutators of components of the stress-tensor.
We rederive several familiar results, such as the canonical commutation relations of free field theory, the local form of the Poincar\'e algebra, and the Virasoro algebra of two-dimensional CFT.

Built on

A. L. Fitzpatrick and K.-W. Huang, “Universal Lowest-Twist in CFTs from Holography,” JHEP
Original
1903
Earlier work this paper cites.
A. Belin, D. M. Hofman, and G. Mathys, “Einstein gravity from ANEC correlators,” JHEP
Original
1904
Earlier work this paper cites.
M. Kologlu, P. Kravchuk, D. Simmons-Duffin, and A. Zhiboedov, “Shocks, Superconvergence, and a Stringy Equivalence Principle,” arXiv:1904.05905 [hep-th]
Original
1904
Earlier work this paper cites.
M. Kologlu, P. Kravchuk, D. Simmons-Duffin, and A. Zhiboedov, “The light-ray OPE and conformal colliders,” arXiv:1905.01311 [hep-th]
Original
1905
Earlier work this paper cites.
Y.-Z. Li, Z.-F. Mai, and H. Lü, “Holographic OPE Coefficients from AdS Black Holes with Matters,” JHEP
Original
1905
Earlier work this paper cites.
K.-W. Huang, “Stress-tensor commutators in conformal field theories near the lightcone,” Phys. Rev. D
Original
1907
Earlier work this paper cites.
M. Kulaxizi, G. S. Ng, and A. Parnachev, “Subleading Eikonal, AdS/CFT and Double Stress Tensors,” arXiv:1907.00867 [hep-th]
Original
1907
Earlier work this paper cites.
A. L. Fitzpatrick, K.-W. Huang, and D. Li, “Probing universalities in d > 2 d>2 CFTs: from black holes to shockwaves,” JHEP
Original
1907
Earlier work this paper cites.
R. Karlsson, M. Kulaxizi, A. Parnachev, and P. Tadić, “Leading Multi-Stress Tensors and Conformal Bootstrap,” JHEP
Original
1909
Earlier work this paper cites.
Y.-Z. Li, “Heavy-light Bootstrap from Lorentzian Inversion Formula,” JHEP
Original
1910
Earlier work this paper cites.
J. Schwinger, “Field theory commutators,” Phys. Rev. Lett
1959
Earlier work this paper cites.
J. S. Schwinger, “NonAbelian gauge fields. Relativistic invariance,” Phys. Rev
1962
Earlier work this paper cites.
M. Gell-Mann, “Symmetries of baryons and mesons,” Phys. Rev
1962
Earlier work this paper cites.
J. Schwinger, “Commutation relations and conservation laws,” Phys. Rev
1963
Earlier work this paper cites.
S. Deser and D. Boulware, “Stress-Tensor Commutators and Schwinger Terms,” J. Math. Phys
1967
Earlier work this paper cites.
H. Sugawara, “A field theory of currents,” Phys. Rev
1968
Earlier work this paper cites.

Similar

R. A. Brandt, “Approach to equal-time commutators in quantum field theory,” Phys. Rev
1968
Cited alongside, same era.
J. Trubatch, “Stress-tensor commutation relations,” Nuovo Cim. A
1970
Cited alongside, same era.
H. Osborn and A. Petkou, “Implications of conformal invariance in field theories for general dimensions,” Annals Phys
1994
Cited alongside, same era.
K.-W. Huang, “A Lightcone Commutator and Stress-Tensor Exchange in d > 2 d>2 CFTs,” arXiv:2002.00110 [hep-th]
Original
2002
Cited alongside, same era.
R. Karlsson, M. Kulaxizi, A. Parnachev, and P. Tadić, “Stress tensor sector of conformal correlators operators in the Regge limit,” JHEP
Original
2002
Cited alongside, same era.

Then

D. Simmons-Duffin, “Tasi lectures on the conformal bootstrap,” 2016
2016
Later among the works it cites.
B. Czech, L. Lamprou, S. McCandlish, B. Mosk, and J. Sully, “A stereoscopic look into the bulk,” Journal of High Energy Physics
2016
Later among the works it cites.
J. de Boer, F. M. Haehl, M. P. Heller, and R. C. Myers, “Entanglement, holography and causal diamonds,” Journal of High Energy Physics
2016
Later among the works it cites.
T. Hartman, S. Kundu, and A. Tajdini, “Averaged Null Energy Condition from Causality,” JHEP
Original
2017
Later among the works it cites.
C. Cordova, J. Maldacena, and G. J. Turiaci, “Bounds on OPE Coefficients from Interference Effects in the Conformal Collider,” JHEP
Original
2017
Later among the works it cites.

Beyond the bibliography

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

Open on alphaXiv

alphaXiv is searching for related work…

V. Braun, G. Korchemsky, and D. Müller, “The Uses of conformal symmetry in QCD,” Prog. Part. Nucl. Phys

2003

Cited alongside, same era.

Y.-Z. Li and H.-Y. Zhang, “More on heavy-light bootstrap up to double-stress-tensor,” JHEP

Original

2004

Cited alongside, same era.

A. L. Fitzpatrick, K.-W. Huang, D. Meltzer, E. Perlmutter, and D. Simmons-Duffin, “Model-dependence of minimal-twist OPEs in d > 2 d>2 holographic CFTs,” JHEP

Original

2007

Cited alongside, same era.

D. M. Hofman and J. Maldacena, “Conformal collider physics: Energy and charge correlations,” JHEP

Original

2008

Cited alongside, same era.

C.-H. Chang, M. Kologlu, P. Kravchuk, D. Simmons-Duffin, and A. Zhiboedov, “Transverse spin in the light-ray OPE,” arXiv:2010.04726 [hep-th]

Original

2010

Cited alongside, same era.

A. Belin, D. M. Hofman, G. Mathys, and M. T. Walters, “On the stress tensor light-ray operator algebra,” arXiv:2011.13862 [hep-th]

Original

2011

Cited alongside, same era.

D. Simmons-Duffin, “Projectors, shadows, and conformal blocks,” Journal of High Energy Physics

2014

Cited alongside, same era.

H. Casini, E. Teste, and G. Torroba, “Markov Property of the Conformal Field Theory Vacuum and the a Theorem,” Phys. Rev. Lett

Original

2017