SYMMETRY-BREAKING IN THE DOUBLE-WELL HERMITIAN MATRIX MODELS

We study symmetry breaking in Z2 symmetric large N matrix models. In the 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 recursion coefficients R(n) and S(n) that all lead to identical free energies and eigenvalue densities. These solutions can be parameterized by an arbitrary 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 with distinct free energies already at the torus level. For the double-well phi4 theory the double scaling string equations are parameterized by a conserved angular momentum parameter in the range 0 less-than-or-equal-to l < infinity and a single arbitrary U(1) phase angle.