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 a universal formula. We perform some checks of that formula and we compare it with 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.

Figures (2)

• Figure 1: Plot of the holographic (continuous line) and proper (dashed line) beta functions versus the holographic coupling.
• Figure 2: Plot of $8c/N^2$ vs $x$, for different cases. In the case of the flow to N=1 SYM, the canonical $c$ (eq. (\ref{['int']})) is given by the dashed line, and the holographic $c$ (eq. (\ref{['chol']})) is given by the dotted line. Finally, in the case of N=4 Coulomb branch, the canonical $c$-function (eq. (\ref{['cgubs']})) is given by the continuous line.