A study of holographic renormalization group (RG) flows is discussed in the framework of supergravity and string theories. Some RG flow solutions are found in N = 4 Chern-Simons gauged supergravity in three dimensions. The resulting solutions describe vev flows, driven by a vacuum expectation value (vev) of a relevant operator or a vev of a marginal operator, in a dual two dimensional eld theory. In the minimal six dimensional supergravity, RG
flow solutions, describing two dimensional vev flows driven by a vev of a marginal operator, in the presence of Yang-Mills instantons are found...
