In typical examples of the AdS/CFT correspondence, the world-sheet theory with holes in the presence of D-branes is assumed to be equivalent in a low-energy limit to a world-sheet theory without holes for a different background such as $AdS_5 ¥times S^5$. In the case of the bosonic string, we claim under the assumption of this equivalence that open string field theory on $N$ coincident D-branes can be used to provide a nonperturbative definition of closed string theory based on the fact that the $1/N$ expansion of correlation functions of gauge-invariant operators reproduces the world-sheet theory with holes where the moduli space of Riemann surfaces is precisely covered.