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

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.

70 pages, LaTeX, typographical errors are corrected, to be published in Phys. Rev. D

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Cited by in corpus (6)

• Collective String Field Theory of Matrix Models in the BMN Limit
• T-duality of ZZ-brane
• Boundary fields and renormalization group flow in the two-matrix model
• T-Duality Transformation and Universal Structure of Non-Critical String Field Theory
• Interaction of boundaries with heterogeneous matter states in matrix models
• Loop Equations for + and - Loops in c = 1/2 Non-Critical String Theory