MATRIX MODELS AND ONE-DIMENSIONAL OPEN STRING THEORY

We propose a random matrix model as a representation for D = 1 open st rings. We show that the model with one flavor of boundary fields is eq uivalent to N fermions with spin in a central potential that also incl udes a long-range ferromagnetic interaction between the fermions that falls off as 1/(r(ij))2. We also generalize this theory to contain an arbitrary number of flavors. For an appropriate choice of the matrix m odel potential the ground state of the system can be found. Using this potential, we calculate the free energy in the double scaling limit a nd show that the free energy expansion has the expected form for a the ory of open and closed strings if the boundary field mass and coupling s have a logarithmic divergence. We then examine the critical properti es of this theory and show that the length of the boundary around a ho le remains finite, even near the critical point. We also argue that un like critical string theory or a D = 0 theory, the open string couplin g constant is a free parameter.