Stochastic Hamiltonian for Non-Critical String Field Theories from Double-Scaled Matrix Models

TL;DR

This paper derives explicit stochastic Hamiltonians for non-critical string field theories from matrix models across various central charges, exploring their algebraic structures and potential for background-independent formulations.

Contribution

It provides explicit forms of stochastic Hamiltonians for multiple non-critical string theories directly from matrix models, including their algebraic properties and universality features.

Findings

Derived Hamiltonians for $c=0$, $k=3$, and $c=1/2$ cases.

Analyzed the associated Schwinger-Dyson operator algebras.

Identified universal structures potentially aiding background-independent string theory.

Abstract

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 $W_3$ 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.