Abstract
We propose a random matrix model as a representation for D = 1 open strings. We show that the model with one flavor of boundary fields is equivalent to N fermions with spin in a central potential that also includes a long-range ferromagnetic interaction between the fermions that falls off as 1/(rij)2. We also generalize this theory to contain an arbitrary number of flavors. For an appropriate choice of the matrix model potential the ground state of the system can be found. Using this potential, we calculate the free energy in the double scaling limit and show that the free energy expansion has the expected form for a theory of open and closed strings if the boundary field mass and couplings have a logarithmic divergence. We then examine the critical properties of this theory and show that the length of the boundary around a hole remains finite, even near the critical point. We also argue that unlike critical string theory or a D = 0 theory, the open string coupling constant is a free parameter.
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