Hidden relations of central charges and OPEs in holographic CFT

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

doi:10.1007/JHEP11(2021)135

Hidden relations of central charges and OPEs in holographic CFT

Yue-Zhou Li
(
- Tianjin U. and
- McGill U.
)
,
H. Lu
(
- Tianjin U. and
- PCFT, Hefei
)
,
Liang Ma
(
- Tianjin U.
)

Aug 11, 2021

31 pages

Published in:

JHEP 11 (2021) 135

Published: Nov 18, 2021

e-Print:

2108.05384 [hep-th]

DOI:

10.1007/JHEP11(2021)135

Report number:

USTC-ICTS/PCFT-21-33

View in:

reference search9 citations

Citations per year

Abstract: (Springer)

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. Furthermore, we prove that the consequential relation c = 1/3ℓ

_{eff}

∂a/∂ℓ

_{eff}

and its higher-dimensional generalization are valid for massless AdS gravity constructed from the most general Riemann tensor invariants.

Note:

Latex, 1 figure, 31 pages, typos corrected, a reference added, a technique issue clarified, to appear in JHEP

AdS-CFT Correspondence
Gauge-gravity correspondence
Classical Theories of Gravity
Conformal Field Theory
tensor: Riemann
gravitation: anti-de Sitter
field theory: conformal
dimension: 4
tensor: energy-momentum
operator: differential

References(53)

Figures(0)

Observations on Conformal Anomalies

M.J. Duff
(
- Queen Mary, U. of London
)

- Nucl.Phys.B 125 (1977) 334-348
•
DOI:
- 10.1016/0550-3213(77)90410-2

[2]

Twenty years of the Weyl anomaly

M.J. Duff
(
- Texas A-M
)

- Class.Quant.Grav. 11 (1994) 1387-1404,
- Salamfest 1993:0552-576
•
e-Print:
- hep-th/9308075
•
DOI:
- 10.1088/0264-9381/11/6/004

[3]

Irreversibility of the Flux of the Renormalization Group in a 2D Field Theory

A.B. Zamolodchikov
(
- Moscow, ITEP
)

- JETP Lett. 43 (1986) 730-732,
- Pisma Zh.Eksp.Teor.Fiz. 43 (1986) 565-567

Is There a c Theorem in Four-Dimensions?

John L. Cardy
(
- UC, Santa Barbara
)

- Phys.Lett.B 215 (1988) 749-752
•
DOI:
- 10.1016/0370-2693(88)90054-8

On Renormalization Group Flows in Four Dimensions

Zohar Komargodski
(
- Weizmann Inst. and
- Princeton, Inst. Advanced Study
)
,
Adam Schwimmer
(
- Weizmann Inst.
)

- JHEP 12 (2011) 099
•
e-Print:
- 1107.3987
•
DOI:
- 10.1007/JHEP12(2011)099

[6]

Implications of conformal invariance in field theories for general dimensions

H. Osborn
(
- Cambridge U.
)
,
A.C. Petkou
(
- Cambridge U.
)

- Annals Phys. 231 (1994) 311-362
•
e-Print:
- hep-th/9307010
•
DOI:
- 10.1006/aphy.1994.1045

[7]

Conserved currents and the energy momentum tensor in conformally invariant theories for general dimensions

J. Erdmenger
(
- Cambridge U.
)
,
H. Osborn
(
- Cambridge U.
)

- Nucl.Phys.B 483 (1997) 431-474
•
e-Print:
- hep-th/9605009
•
DOI:
- 10.1016/S0550-3213(96)00545-7

[8]

Conformal collider physics: Energy and charge correlations

- JHEP 05 (2008) 012
•
e-Print:
- 0803.1467
•
DOI:
- 10.1088/1126-6708/2008/05/012

[9]

A Proof of the Conformal Collider Bounds

Diego M. Hofman
(
- Amsterdam U.
)
,
Daliang Li
(
- Johns Hopkins U.
)
,
David Meltzer
(
- Yale U.
)
,
David Poland
(
- Yale U. and
- Princeton, Inst. Advanced Study
)
,
Fernando Rejon-Barrera
(
- Amsterdam U.
)

- JHEP 06 (2016) 111
•
e-Print:
- 1603.03771
•
DOI:
- 10.1007/JHEP06(2016)111

[10]

Averaged Null Energy Condition from Causality

- JHEP 07 (2017) 066
•
e-Print:
- 1610.05308
•
DOI:
- 10.1007/JHEP07(2017)066

[11]

Holography from Conformal Field Theory

Idse Heemskerk
(
- UC, Santa Barbara
)
,
Joao Penedones
(
- Santa Barbara, KITP
)
,
Joseph Polchinski
(
- Santa Barbara, KITP
)
,
James Sully
(
- UC, Santa Barbara
)

- JHEP 10 (2009) 079
•
e-Print:
- 0907.0151
•
DOI:
- 10.1088/1126-6708/2009/10/079

[12]

The Large N limit of superconformal field theories and supergravity

Juan Martin Maldacena
(
- Harvard U.
)

- Int.J.Theor.Phys. 38 (1999) 1113-1133 (reprint),
- Adv.Theor.Math.Phys. 2 (1998) 231-252
•
e-Print:
- hep-th/9711200
•
DOI:
- 10.4310/ATMP.1998.v2.n2.a1