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We present an analytic expression of the nonperturbative free energy of adouble-well supersymmetric matrix model in its double scaling limit, whichcorresponds to two-dimensional type IIA superstring theory on a nontrivialRamond-Ramond background. To this end we draw upon the wisdom of random matrixtheory developed by Tracy and Widom, which expresses the largest eigenvaluedistribution of unitary ensembles in terms of a Painleve II transcendent.Regularity of the result at any value of the string coupling constant showsthat the third-order phase transition between a supersymmetry-preserving phaseand a supersymmetry-broken phase, previously found at the planar level, becomesa smooth crossover in the double scaling limit. Accordingly, the supersymmetryis always broken spontaneously as its order parameter stays nonzero for thewhole region of the coupling constant. Coincidence of the result with theunitary one-matrix model suggests that one-dimensional type 0 string theoriespartially correspond to the type IIA superstring theory. Our formulationnaturally allows for introduction of an instanton chemical potential, andreveals the presence of a novel phase transition, possibly interpreted ascondensation of instantons.

Tracy-Widom distribution as instanton sum of 2D IIA superstrings