Abstract
We study the continuum properties of the Hermitian one-matrix model defined by a cubic potential with imaginary coupling, using the orthogonal polynomials and loop-equation approaches. The model is well defined mathematically and has a continuum limit which cannot be naively interpreted as pure gravity since each term of the sum over surfaces is not positive-definite. Nevertheless, the model may be considered as an analytic continuation of the standard matrix-model formulation of gravity. We study in detail the conditions under which the analytic continuation may be performed. In particular, the specific heat is found to obey a Painlevé equation. Although we find a solution that is compatible, as far as global stability is concerned, with the one proposed by David, it is not completely clear that the two solutions are the same.
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