Virasoro constraints on the matrix-model partition function and string field theory

Abstract

The one-matrix model at the kth multicritical point is known to describe the (2, 2k-1) minimal model coupled to gravity, and the partition function of this model is known to obey a set of Virasoro constraints generated by a set of differential operators L_n. Working at the tree level of string theory, and using the Feigin-Fuchs description of the (2, 2k-1) minimal model, we show that the Virasoro constraints generated by L_i (0≤i≤k-2) can be identified with a set of gauge symmetries of the corresponding string field theory.