Built on

Y.Z. Li, “Holographic studies of the generic massless cubic gravities,” Phys. Rev. D 99
Original
1901
Earlier work this paper cites.
H. Lü and R. Wen, “Holographic ( a , c ) (a,c) -charges and their universal relation in d = 6 d=6 from massless higher-order gravities,” Phys. Rev. D 99
Original
1901
Earlier work this paper cites.
A. Belin, D.M. Hofman and G. Mathys, “Einstein gravity from ANEC correlators,” JHEP 08
Original
1904
Earlier work this paper cites.
M. Kologlu, P. Kravchuk, D. Simmons-Duffin and A. Zhiboedov, “Shocks, superconvergence, and a stringy equivalence principle,” JHEP 11
Original
1904
Earlier work this paper cites.
M. Kologlu, P. Kravchuk, D. Simmons-Duffin and A. Zhiboedov, “The light-ray OPE and conformal colliders,” JHEP 01
Original
1905
Earlier work this paper cites.
P. Bueno, P.A. Cano, J. Moreno and Á. Murcia, “All higher-curvature gravities as Generalized quasi-topological gravities,” JHEP 11
Original
1906
Earlier work this paper cites.
P. Bueno, P.A. Cano and R.A. Hennigar, “(Generalized) quasi-topological gravities at all orders,” Class. Quant. Grav. 37
Original
1909
Earlier work this paper cites.
J. S. R. Chisholm, “Change of variables in quantum field theories,” Nucl. Phys. 26
1961
Earlier work this paper cites.
M.J. Duff, “Observations on conformal anomalies,” Nucl. Phys. B 125
1977
Earlier work this paper cites.
A.B. Zamolodchikov, “Irreversibility of the flux of the renormalization group in a 2D field theory,” JETP Lett. 43
1986
Earlier work this paper cites.
J.L. Cardy, “Is there a c c theorem in four-dimensions?” Phys. Lett. B 215
1988
Earlier work this paper cites.
H. Osborn, “Derivation of a four-dimensional c c theorem,” Phys. Lett. B 222
1989
Earlier work this paper cites.
R.M. Wald, “Black hole entropy is the Noether charge,” Phys. Rev. D 48
1993
Earlier work this paper cites.
M.J. Duff, “Twenty years of the Weyl anomaly,” Class. Quant. Grav. 11
1994
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.
J. Erdmenger and H. Osborn, “Conserved currents and the energy momentum tensor in conformally invariant theories for general dimensions,” Nucl. Phys. B 483
1997
Earlier work this paper cites.
J.M. Maldacena, “The large N N limit of superconformal field theories and supergravity,” Adv. Theor. Math. Phys. 2
1998
Earlier work this paper cites.

Similar

S.S. Gubser, I.R. Klebanov and A.M. Polyakov, “Gauge theory correlators from noncritical string theory,” Phys. Lett. B 428
1998
Cited alongside, same era.
E. Witten, “Anti-de Sitter space and holography,” Adv. Theor. Math. Phys. 2
1998
Cited alongside, same era.
M. Henningson and K. Skenderis, “The Holographic Weyl anomaly,” JHEP 07
1998
Cited alongside, same era.
D.Z. Freedman, S.S. Gubser, K. Pilch and N.P. Warner, “Renormalization group flows from holography supersymmetry and a c c theorem,” Adv. Theor. Math. Phys. 3
1999
Cited alongside, same era.
S. Nojiri and S.D. Odintsov, “On the conformal anomaly from higher derivative gravity in AdS/CFT correspondence,” Int. J. Mod. Phys. A 15
2000
Cited alongside, same era.

Then

X.O. Camanho, J.D. Edelstein, J. Maldacena and A. Zhiboedov, “Causality constraints on corrections to the graviton three-point coupling,” JHEP 02
Original
2016
Later among the works it cites.
P. Bueno and P.A. Cano, “Einsteinian cubic gravity,” Phys. Rev. D 94
Original
2016
Later among the works it cites.
T. Hartman, S. Kundu and A. Tajdini, “Averaged null energy condition from causality,” JHEP 07
Original
2017
Later among the works it cites.
N. Afkhami-Jeddi, T. Hartman, S. Kundu and A. Tajdini, “Einstein gravity 3-point functions from conformal field theory,” JHEP 12
Original
2017
Later among the works it cites.
M.S. Costa, T. Hansen and J. Penedones, “Bounds for OPE coefficients on the Regge trajectory,” JHEP 10

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2021

Hidden Relations of Central Charges and OPEs in Holographic CFT

Li, Yue-Zhou, Lu, H., Ma, Liang

Understand

It is known that the $(a,c)$ central charges in four-dimensional CFTs are linear combinations of the three independent OPE coefficients of the stress-tensor three-point function.

In this paper, we adopt the holographic approach using AdS gravity as an effect field theory and consider higher-order corrections up to and including the cubic Riemann tensor invariants.
We derive the holographic central charges and OPE coefficients and show that they are invariant under the metric field redefinition.
We further discover a hidden relation among the OPE coefficients that two of them can be expressed in terms of the third using differential operators, which are the unit radial vector and the Laplacian of a four-dimensional hyperbolic space whose radial variable is an appropriate length parameter that is invariant under the field redefinition.

Built on

Y.Z. Li, “Holographic studies of the generic massless cubic gravities,” Phys. Rev. D 99
Original
1901
Earlier work this paper cites.
H. Lü and R. Wen, “Holographic ( a , c ) (a,c) -charges and their universal relation in d = 6 d=6 from massless higher-order gravities,” Phys. Rev. D 99
Original
1901
Earlier work this paper cites.
A. Belin, D.M. Hofman and G. Mathys, “Einstein gravity from ANEC correlators,” JHEP 08
Original
1904
Earlier work this paper cites.
M. Kologlu, P. Kravchuk, D. Simmons-Duffin and A. Zhiboedov, “Shocks, superconvergence, and a stringy equivalence principle,” JHEP 11
Original
1904
Earlier work this paper cites.
M. Kologlu, P. Kravchuk, D. Simmons-Duffin and A. Zhiboedov, “The light-ray OPE and conformal colliders,” JHEP 01
Original
1905
Earlier work this paper cites.
P. Bueno, P.A. Cano, J. Moreno and Á. Murcia, “All higher-curvature gravities as Generalized quasi-topological gravities,” JHEP 11
Original
1906
Earlier work this paper cites.
P. Bueno, P.A. Cano and R.A. Hennigar, “(Generalized) quasi-topological gravities at all orders,” Class. Quant. Grav. 37
Original
1909
Earlier work this paper cites.
J. S. R. Chisholm, “Change of variables in quantum field theories,” Nucl. Phys. 26
1961
Earlier work this paper cites.
M.J. Duff, “Observations on conformal anomalies,” Nucl. Phys. B 125
1977
Earlier work this paper cites.
A.B. Zamolodchikov, “Irreversibility of the flux of the renormalization group in a 2D field theory,” JETP Lett. 43
1986
Earlier work this paper cites.
J.L. Cardy, “Is there a c c theorem in four-dimensions?” Phys. Lett. B 215
1988
Earlier work this paper cites.
H. Osborn, “Derivation of a four-dimensional c c theorem,” Phys. Lett. B 222
1989
Earlier work this paper cites.
R.M. Wald, “Black hole entropy is the Noether charge,” Phys. Rev. D 48
1993
Earlier work this paper cites.
M.J. Duff, “Twenty years of the Weyl anomaly,” Class. Quant. Grav. 11
1994
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.
J. Erdmenger and H. Osborn, “Conserved currents and the energy momentum tensor in conformally invariant theories for general dimensions,” Nucl. Phys. B 483
1997
Earlier work this paper cites.
J.M. Maldacena, “The large N N limit of superconformal field theories and supergravity,” Adv. Theor. Math. Phys. 2
1998
Earlier work this paper cites.

Similar

S.S. Gubser, I.R. Klebanov and A.M. Polyakov, “Gauge theory correlators from noncritical string theory,” Phys. Lett. B 428
1998
Cited alongside, same era.
E. Witten, “Anti-de Sitter space and holography,” Adv. Theor. Math. Phys. 2
1998
Cited alongside, same era.
M. Henningson and K. Skenderis, “The Holographic Weyl anomaly,” JHEP 07
1998
Cited alongside, same era.
D.Z. Freedman, S.S. Gubser, K. Pilch and N.P. Warner, “Renormalization group flows from holography supersymmetry and a c c theorem,” Adv. Theor. Math. Phys. 3
1999
Cited alongside, same era.
S. Nojiri and S.D. Odintsov, “On the conformal anomaly from higher derivative gravity in AdS/CFT correspondence,” Int. J. Mod. Phys. A 15
2000
Cited alongside, same era.