Stochastic Hamiltonians for noncritical string field theories from double-scaled matrix models.

We present detailed discussions on the stochastic Hamiltonians for non-critical string field theories on the basis of matrix models. Beginning from the simplest c = 0 case, we derive the explicit forms of the Hamiltonians for the higher critical case k = 3 (which corresponds to c = −22/5) and for the case c = 1/2, directly from the double-scaled matrix models. In particular, for the two-matrix case, we do not put any restrictions on the spin configurations of the string fields. The properties of the resulting infinite algebras of Schwinger-Dyson operators associated with the Hamiltonians and the derivation of the Virasoro and W3 algebras therefrom are also investigated. Our results suggest certain universal structure of the stochastic Hamiltonians, which might be useful for an attempt towards a background independent string field theory. E-mail: [email protected] E-mail: [email protected]