LOOPS AND UNORIENTED STRINGS

We derive and analyze Schwinger-Dyson equations for Dyson's Coulomb gas at arbitrary temperature. This system interpolates between theories of oriented and unoriented strings. The Schwinger-Dyson equations can be formulated as Virasoro constraints constructed from a boson with a temperature-dependent background charge. We describe a geometric interpretation of these equations, calculate correlation functions perturbatively in 1/N and discuss a high-low temperature duality exhibited by the Coulomb gas. We also interpret the double scaling continuum limit of the loop equations.