SYMMETRY-BREAKING IN THE DOUBLE-WELL HERMITIAN MATRIX MODELS

We study symmetry breaking in Z2 symmetric large N matrix models. In t he planar approximation for both the symmetric double-well phi4 model and the symmetric Penner model, we find there is an infinite family of broken symmetry solutions characterized by different sets of recursio n coefficients R(n) and S(n) that all lead to identical free energies and eigenvalue densities. These solutions can be parameterized by an a rbitrary angle theta(x), for each value of x = n/N < 1. In the double scaling limit, this class reduces to a smaller family of solutions wit h distinct free energies already at the torus level. For the double-we ll phi4 theory the double scaling string equations are parameterized b y a conserved angular momentum parameter in the range 0 less-than-or-e qual-to l < infinity and a single arbitrary U(1) phase angle.