W - Infinity Ward Identities and Correlation Functions in the C = 1 Matrix Model

⋆ e-mail: [email protected], [email protected], [email protected]. † Supported by DOE grant DE-FG02-90ER40542. ‡ e-mail: [email protected]. § On leave from Tata Institute of Fundamental Research, Bombay 400 005, India. ¶ Address after January 1,1992 : Tata Institute of Fundamental Research, Bombay 400 005, India. We explore consequences of W -infinity symmetry in the fermionic field theory of the c = 1 matrix model. We derive exact Ward identities relating correlation functions of the bilocal operator. These identities can be expressed as equations satisfied by the effective action of a three dimensional theory and contain nonperturbative information about the model. We use these identities to calculate the two point function of the bilocal operator in the double scaling limit. We extract the operator whose two point correlator has a single pole at an (imaginary) integer value of the energy. We then rewrite theW -infinity charges in terms of operators in the matrix model and use this derive constraints satisfied by the partition function of the matrix model with a general time dependent potential.