Spontaneous supersymmetry breaking and instanton sum in 2D type IIA superstring theory
We consider a double-well supersymmetric matrix model and its interpretation as a nonperturbative definition of two-dimensional type IIA superstring theory. The interpretation is confirmed by direct comparison of symmetries and amplitudes in both sides of the matrix model and the IIA superstring theory. Next, we obtain the full nonperturbative free energy of the matrix model in terms of the Tracy-Widom distribution in random matrix theory. Its weak coupling expansion implies spontaneous supersymmetry breaking due to instantons, and strong coupling behavior suggests the existence of a well-defined S-dual theory. Furthermore, from the expression of the free energy, we see a smooth connection between a non-supersymmetric string theory and the IIA superstring theory.