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Solving (1, q) KdV gravity

1991 
Abstract In this paper we explicitly compute the correlation functions of the (1, q ) series of the KdV hierarchy i.e. models with q − 1 primary fields. We also find from algebraic considerations a ghost number conservation law for the (1, q ) models. All the results in this paper follow from the algebraic properties of the KdV hierarchy without using any extraneous information from a field theory interpretation. We find the interesting result that some correlation functions vanish even when they conserve ghost number. This is an indication for further selection rules.
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