Loops versus matrices - The nonperturbative aspects of noncritical string

The nonperturbative aspects of string theory are explored for non-critical string in two distinct formulations, loop equations and matrix models. The effects corresponding to the D-brane in these formulations are especially investigated in detail. It is shown that matrix models can universally yield a definite value of the chemical potential for an instanton while loop equations cannot. This implies that it may not be possible to formulate string theory nonperturbatively solely in terms of closed strings.