A note on the holographic beta and C functions

D. Anselmi; L. Girardello; M. Porrati; A. Zaffaroni

doi:10.1016/S0370-2693(00)00472-X

A note on the holographic beta and C functions

D. Anselmi, L. Girardello, M. Porrati, A. Zaffaroni

Research output: Contribution to journal › Article › peer-review

Abstract

The holographic RG flow in AdS/CFT correspondence naturally defines a holographic scheme in which the central charge c and the beta function are related by the formula ċ = -2cβ(a)β(b)G(ab), where G(ab) is the metric of the kinetic term of the supergravity scalars. In particular, the metric in the space of couplings is f(ab) = 2cG(ab). We perform some checks of that result and we compare it with the quantum field theory expectations. We discuss alternative definitions of the c-function. In particular, we compare, for a particular supersymmetric flow, the holographic c-function with the central charge computed directly from the two-point function of the stress-energy tensor. (C) 2000 Elsevier Science B.V.

Original language	English (US)
Pages (from-to)	346-352
Number of pages	7
Journal	Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics
Volume	481
Issue number	2-4
DOIs	https://doi.org/10.1016/S0370-2693(00)00472-X
State	Published - May 25 2000

ASJC Scopus subject areas

Nuclear and High Energy Physics

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@article{7e5daa140da6499aa7efb93878e32075,

title = "A note on the holographic beta and C functions",

abstract = "The holographic RG flow in AdS/CFT correspondence naturally defines a holographic scheme in which the central charge c and the beta function are related by the formula ċ = -2cβ(a)β(b)G(ab), where G(ab) is the metric of the kinetic term of the supergravity scalars. In particular, the metric in the space of couplings is f(ab) = 2cG(ab). We perform some checks of that result and we compare it with the quantum field theory expectations. We discuss alternative definitions of the c-function. In particular, we compare, for a particular supersymmetric flow, the holographic c-function with the central charge computed directly from the two-point function of the stress-energy tensor. (C) 2000 Elsevier Science B.V.",

author = "D. Anselmi and L. Girardello and M. Porrati and A. Zaffaroni",

note = "Funding Information: We would like to thank D.Z. Freedman, M. Petrini and A. Starinets for useful discussions. L.G. and A.Z. are partially supported by INFN and MURST, and by the European Commission TMR program ERBFMRX-CT96-0045, wherein they are associated to the University of Torino. M.P. is supported in part by NSF grant no. PHY-9722083. ",

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doi = "10.1016/S0370-2693(00)00472-X",

language = "English (US)",

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TY - JOUR

T1 - A note on the holographic beta and C functions

AU - Anselmi, D.

AU - Girardello, L.

AU - Porrati, M.

AU - Zaffaroni, A.

N1 - Funding Information: We would like to thank D.Z. Freedman, M. Petrini and A. Starinets for useful discussions. L.G. and A.Z. are partially supported by INFN and MURST, and by the European Commission TMR program ERBFMRX-CT96-0045, wherein they are associated to the University of Torino. M.P. is supported in part by NSF grant no. PHY-9722083.

PY - 2000/5/25

Y1 - 2000/5/25

N2 - The holographic RG flow in AdS/CFT correspondence naturally defines a holographic scheme in which the central charge c and the beta function are related by the formula ċ = -2cβ(a)β(b)G(ab), where G(ab) is the metric of the kinetic term of the supergravity scalars. In particular, the metric in the space of couplings is f(ab) = 2cG(ab). We perform some checks of that result and we compare it with the quantum field theory expectations. We discuss alternative definitions of the c-function. In particular, we compare, for a particular supersymmetric flow, the holographic c-function with the central charge computed directly from the two-point function of the stress-energy tensor. (C) 2000 Elsevier Science B.V.

AB - The holographic RG flow in AdS/CFT correspondence naturally defines a holographic scheme in which the central charge c and the beta function are related by the formula ċ = -2cβ(a)β(b)G(ab), where G(ab) is the metric of the kinetic term of the supergravity scalars. In particular, the metric in the space of couplings is f(ab) = 2cG(ab). We perform some checks of that result and we compare it with the quantum field theory expectations. We discuss alternative definitions of the c-function. In particular, we compare, for a particular supersymmetric flow, the holographic c-function with the central charge computed directly from the two-point function of the stress-energy tensor. (C) 2000 Elsevier Science B.V.

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JO - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics

JF - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics

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