content_image/348338.jpg content_image/348340.jpg content_image/348348.jpg
<img src='content_image/348338.jpg'>

<img src='content_image/348340.jpg'>

where η$_{µν}$ = diag [ − 1 , 1 , 1 , 1] is the Minkowski metric. 

We will now show that a conformally AdS spacetime, is a solution to the flow upto order N = 4 in α ′ . Also we will prove the following propositions – 

Proposition IV.1 The flow Eq.(1) with β taken upto O ( α ′ $^{4}$) has a solution of the form 

<img src='content_image/348348.jpg'>

with Ω( λ = 0) = Ω$_{0}$ and k is a constant. This is a conformally Anti-deSitter (AdS) space- time, similar to the bulk spacetime in the Randall-Sundrum braneworld model [14]. 

Proposition IV.2 For the solution in Eq.(26) the flow equation upto O ( α ′ $^{N}$) where N ≤ 4 

