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This Lagrangian has general covariance with respect to a-v co-ordinate transformations on the world sheet and therefore leads to the existence of constraint equations among canonical variables. These constraints are equivalent to Virasoro's on-shell subsidiary conditions. I t is now of great interests whether such arguments can be extended to interacting strings. ADEMOLLO et al. (7) considered the interaction with an external photonlike field. In this note we discuss the interaction with an external scalar field r Our approach is based on the geometrical meaning of (1). We suppose that, owing to the presence of an external field r the geometry of the world sheet is distorted from the free case. We assume that the distorted geometry is described by the metric tensor (~ whose relation to the free metric G is

It is demonstrated that the quautum theory of gravity can be a zero- slope limit of the generalized Virasoro model where the Regge intercept is fixed at two. The quautum theory of gravity is taken to mean Gupta-Feynman's perturbation on the flat background. The correspondence for the graviton Compton scattering is demonstrated by direct calculations. (LBS)

Recently, there has been some interes t in the question of how the Veneziano model (1) can be made consistent wi th current algebra off-mass-shell predict ions (2), while we are asking whether i t is compat ible wi th the model of eh i ra l -symmetry breaking (a). In a =-K coupled system, MCKAY and others (a) succeeded in construct ing mult ip leterm Veneziano ampli tude, consistent with all the PCAC and charge algebra constraints, while i t is inconsistent wi th the model of ehi ra l -symmetry breaking (~). CSIKOR (5), on the other hand, has suggested tha t we m a t be get r id of the difficulty b y using a correct off-mass-shell ampl i tude (~'~). The purpose of this note is to demonstra te t ha t the Csikor-type ampl i tude with a single satel l i te te rm is sufficient to sat isfy al l the off-mass-shell constraints by current algebra, while i t is s t i l l compat ible wi th the model of G~LL-MA~ and others (3). The two-part icle off-mass-shell ampl i tude is defined by