From loops to fields in 2D quantum gravity

This paper discusses a target space field theory of macroscopic loops W(ell...) in two-dimensional gravity. The propagator left-angle W(ell 1)W(ell 2)right-angle and topology-changing amplitudes left-angle W(ell 1)W(ell 2)W(ell)right-angle (string interactions) are considered as off-shell Euclidean Green's functions in this field theory. In the course of the analysis, the authors identify a new set of operators in the c = 1 system and interpret them in two-dimensional gravity. The authors also identify an infinite set of new conserved charges in the c = 1 system which are associated with the special states in the theory. The analysis also shows that the eigenvalue coordinate of the matrix model and a zero mode of the Liouville field are not functionally related but are conjugate variables in an integral transform