  AdS/CFT duality is a conjectured dual correspondence between the large $N$
limit of Conformal Field Theory (CFT) in $d$-dimensions and the supergravity
(SUGRA) in $d+1$-dimensional Anti de Sitter (AdS) space. By using this
conjecture, we can study various properties of large $N$ CFT by simple
calculations in SUGRA. Recently much attention has been paid to the
Renormalization Group (RG) flow viewed from the SUGRA side. Such RG flow in CFT
is known to be characterized by the c-function which connects CFTs with
different central charges. Therefore, we are interested in deriving this
c-function from SUGRA with the help of AdS/CFT correspondence. To derive the
c-function, we calculate the conformal anomaly (CA) in SUGRA, since it is
closely related to the central charge. In this thesis, we discuss the various
aspects of CA from AdS/CFT duality, especially for the cases of SUGRA in 3 and
5-dimensions which correspond to 2 and 4-dimensional CFTs, respectively. It is
known that the bosonic part of SUGRA with scalar (dilaton) and arbitrary scalar
potential describes the special RG flows in dual quantum field theory. So we
calculate dilaton-dependent CA from dilatonic gravity with arbitrary potential.
After that, we propose candidates of c-functions from such dilatonic gravity
and investigate the properties of them.
