ONE-LOOP CORRELATION-FUNCTIONS IN THE MODEL OF NONCRITICAL FERMIONIC STRINGS

In the model of noncritical fermionic strings, the David-Distler-Kawai ansatz is used to study one-loop n-point (n less than or equal to 4) correlation functions for the vertex operators of massless bosonic sta tes. The action functional of the model is the sum of super-liouville action functional for the conformal mode and the action functional of d scalar supermultiplets. It is assumed that the total cosmological te rm is equal to zero. The amplitudes are calculated as the residues at the pole of the correlation function that corresponds to the conservat ion of Liouville momentum in the form Sigma beta(i) = Q(1 - h), where Q = root(9-d)/2 and h is the genus of the world sheet. In the one-loop approximation, the amplitudes can be obtained in the modular-invarian t form, provided that the coefficients appearing in the sum over spin structures depend on moduli. In this case, the modular measure is defi ned up to a modular-invariant factor. This arbitrariness can be used t o represent one-point correlation functions in the same functional for m as for strings of critical dimension.