String Field Theory in the Temporal Gauge

TL;DR

This paper constructs the string field Hamiltonian for specific noncritical string theories in the temporal gauge, connecting matrix models, conformal field theory, and continuum equations, and discusses potential generalizations.

Contribution

It introduces a continuum approach to derive the string field Hamiltonian for $c<1$ string theories in the temporal gauge, linking discrete models with continuum physics.

Findings

Derived the string field Hamiltonian from continuum Schwinger-Dyson equations.

Connected boundary conformal field theory with matrix models.

Confirmed consistency with known noncritical string theory results.

Abstract

We construct the string field Hamiltonian for $c=1-\frac{6}{m(m+1)}$ string theory in the temporal gauge. In order to do so, we first examine the Schwinger-Dyson equations of the matrix chain models and propose the continuum version of them. Results of boundary conformal field theory are useful in making a connection between the discrete and continuum pictures. The $W$ constraints are derived from the continuum Schwinger-Dyson equations. We also check that these equations are consistent with other known results about noncritical string theory. The string field Hamiltonian is easily obtained from the continuum Schwinger-Dyson equations. It looks similar to Kaku-Kikkawa's Hamiltonian and may readily be generalized to $c>1$ cases.