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

This paper reports on the one-matrix model at the kth multicritical point which 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 Ln. 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 Li (O ≤ i ≤ k - 2) can be identified with a set of gauge symmetries of the corresponding string field theory