Non-critical string field theory for 2d quantum gravity coupled to (p,q)--conformal fields

TL;DR

This paper introduces a non-critical string field theory framework for two-dimensional quantum gravity coupled with ($p$,$q$) conformal fields, utilizing $W_p$ algebra generators to formulate the Hamiltonian and Schwinger-Dyson equations.

Contribution

It develops a novel non-critical string field theory for 2D quantum gravity coupled to ($p$,$q$) conformal fields using $W_p$ algebra, linking the Hamiltonian to algebra generators.

Findings

Hamiltonian described by $W_p$ algebra generators

Schwinger-Dyson equations equivalent to vacuum conditions

Framework applicable to ($p$,$q$) conformal field couplings

Abstract

We propose a non-critical string field theory for $2d$ quantum gravity coupled to ($p$,$q$) conformal fields. The Hamiltonian is described by the generators of the $W_p$ algebra, and the Schwinger-Dyson equation is equivalent to a vacuum condition imposed on the generators of $W_p$ algebra.