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On the holographic renormalization group

Jan de Boer
(
- Utrecht U. and
- Leiden U.
)
,
Erik P. Verlinde
(
- Princeton U.
)
,
Herman L. Verlinde
(
- Princeton U. and
- Amsterdam U.
)

Dec, 1999

15 pages

Published in:

JHEP 08 (2000) 003

e-Print:

hep-th/9912012 [hep-th]

DOI:

10.1088/1126-6708/2000/08/003

Report number:

PUPT-1898,
ITFA-99-39,
SPIN-1999-29

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Abstract:

We propose a direct correspondence between the classical evolution equations of 5-d supergravity and the renormalization group (RG) equations of the dual 4-d large

N

gauge theory. Using standard Hamilton-Jacobi theory, we derive first order flow equations for the classical supergravity action

S

, that take the usual form of the Callan-Symanzik equations, including the corrections due to the conformal anomaly. This result gives direct support for the identification of

S

with the quantum effective action of the gauge theory. In addition we find interesting new relations between the beta-functions and the counterterms that affect the 4-d cosmological and Newton constant.

supergravity
dimension: 5
gauge field theory: SU(N)
dimension: 4
expansion 1/N
renormalization group: transformation
renormalization group: beta function
anomaly: conformal
effective action
cosmological constant

References(20)

Figures(0)

The Large $N$ limit of superconformal field theories and supergravity

Juan Martin Maldacena
(
- Harvard U.
)

- Int.J.Theor.Phys. 38 (1999) 1113-1133 (reprint),
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S.S. Gubser
(
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)
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Igor R. Klebanov
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)
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Alexander M. Polyakov
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)

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Edward Witten
(
- Princeton, Inst. Advanced Study
)

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•
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e-Print:
- hep-th/9805114

A Remark on the AdS / CFT correspondence and the renormalization group flow

Emil T. Akhmedov
(
- Moscow, ITEP
)

- Phys.Lett.B 442 (1998) 152-158
•
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•
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Enrique Alvarez
(
- CERN and
- Madrid, Autonoma U.
)
,
Cesar Gomez
(
- CERN and
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)

- Nucl.Phys.B 541 (1999) 441-460
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D.Z. Freedman
(
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)
,
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(
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)
,
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(
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)
,
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(
- Southern California U. and
- CERN
)

- JHEP 07 (2000) 038
•
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•
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L. Girardello
(
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)
,
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(
- Imperial Coll., London
)
,
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(
- New York U.
)
,
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(
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- INFN, Milan
)

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•
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L. Girardello
(
- CERN and
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)
,
M. Petrini
(
- Imperial Coll., London
)
,
M. Porrati
(
- CERN and
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)
,
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(
- CERN
)

- JHEP 12 (1998) 022
•
e-Print:
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•
DOI:
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S. Ferrara
(
- CERN
)
,
M. Porrati
(
- CERN and
- New York U.
)

- Phys.Lett.B 458 (1999) 43-52
•
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•
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Vijay Balasubramanian
(
- Harvard U. and
- Santa Barbara, KITP
)
,
Per Kraus
(
- Chicago U., EFI
)

- Phys.Rev.Lett. 83 (1999) 3605-3608
•
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- hep-th/9903190
•
DOI:
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Gravitational stability and renormalization group flow

Kostas Skenderis
(
- Utrecht U.
)
,
Paul K. Townsend
(
- Cambridge U., DAMTP
)

- Phys.Lett.B 468 (1999) 46-51
•
e-Print:
- hep-th/9909070
•
DOI:
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O. DeWolfe
(
- MIT, LNS
)
,
D.Z. Freedman
(
- MIT, LNS and
- MIT
)
,
S.S. Gubser
(
- Harvard U.
)
,
A. Karch
(
- MIT, LNS
)

- Phys.Rev.D 62 (2000) 046008
•
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- hep-th/9909134
•
DOI:
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Klaus Behrndt
(
- Caltech
)
,
Mirjam Cvetic
(
- Pennsylvania U. and
- Santa Barbara, KITP
)

- Phys.Lett.B 475 (2000) 253-260
•
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•
DOI:
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Ulrich Ellwanger
(
- Orsay, LPT
)

- Phys.Lett.B 473 (2000) 233-240
•
e-Print:
- hep-th/9909103
•
DOI:
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Renormalization and Effective Lagrangians

Joseph Polchinski
(
- Harvard U.
)

- Nucl.Phys.B 231 (1984) 269-295
•
DOI:
- 10.1016/0550-3213(84)90287-6

Holography and compactification

Herman L. Verlinde
(
- Princeton U. and
- Amsterdam U.
)

- Nucl.Phys.B 580 (2000) 264-274
•
e-Print:
- hep-th/9906182
•
DOI:
- 10.1016/S0550-3213(00)00224-8

A Large mass hierarchy from a small extra dimension

Lisa Randall
(
- Princeton U. and
- MIT
)
,
Raman Sundrum
(
- Boston U.
)

- Phys.Rev.Lett. 83 (1999) 3370-3373
•
e-Print:
- hep-ph/9905221
•
DOI:
- 10.1103/PhysRevLett.83.3370

An Alternative to compactification

Lisa Randall
(
- Princeton U. and
- MIT, LNS
)
,
Raman Sundrum
(
- Boston U.
)

- Phys.Rev.Lett. 83 (1999) 4690-4693
•
e-Print:
- hep-th/9906064
•
DOI:
- 10.1103/PhysRevLett.83.4690

The Holographic Weyl anomaly

M. Henningson
(
- CERN
)
,
K. Skenderis
(
- Leuven U.
)

- JHEP 07 (1998) 023
•
e-Print:
- hep-th/9806087
•
DOI:
- 10.1088/1126-6708/1998/07/023