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

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