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 c = -2c beta(a)beta(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. All rights reserved
Anselmi, D., Girardello, L., Porrati, M., Zaffaroni, A. (2000). A note on the holographic beta and C functions. PHYSICS LETTERS. SECTION B, 481(2-4), 346-352 [10.1016/S0370-2693(00)00472-X].
A note on the holographic beta and C functions
GIRARDELLO, LUCIANO;ZAFFARONI, ALBERTO
2000
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 c = -2c beta(a)beta(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. All rights reserved
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