STRING BETA FUNCTION EQUATIONS FROM THE c = 1 MATRIX MODEL

We derive the σ-model tachyon β-function equation of 2-dimensional string theory, in the background of flat space and linear dilaton, working entirely within the c = 1 matrix model. The tachyon β-function equation is satisfied by a nonlocal and nonlinear combination of the (massless) scalar field of the matrix model. We discuss the possibility of describing the ‘discrete states’ as well as other possible gravitational and higher tensor backgrounds of 2-dimensional string theory within the c = 1 matrix model. We also comment on the realization of the W -infinity symmetry of the matrix model in the string theory. The present work reinforces the viewpoint that a nonlocal (and nonlinear) transform is required to extract the space-time physics of 2-dimensional string theory from the c = 1 matrix model. On leave from Theoretical Physics Group, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay 400 005, India. e-mail: [email protected] e-mail: [email protected] e-mail: [email protected]