Non–Perturbative String Equations for Type 0A

Well–defined non–perturbative formulations of the physics of string theories, sometimes with D–branes present, were identified over a decade ago, from careful study of double scaled matrix models. Following recent work which recasts some of those early results in the context of type 0 string theory, a study is made of a much larger family of models, which are proposed as type 0A models of the entire superconformal minimal series coupled to supergravity. This gives many further examples of important physical phenomena, including non–perturbative descriptions of geometrical transitions between D–branes and fluxes, tachyon condensation, and holography. In particular, features of a large family of non–perturbatively stable string equations are studied, and results are extracted which pertain to type 0A string theory, with D–branes and fluxes, in this large class of backgrounds. For the entire construction to work, large parts of the spectrum of the supergravitationally dressed superconformal minimal models and that of the gravitationally dressed bosonic conformal minimal models must coincide, and it is shown how this happens. The example of the super–dressed tricritical Ising model is studied in some detail. On leave from the Centre for Particle Theory, Department of Mathematical Sciences, University of Durham, Durham DH1 3LE, England. Address for correspondence.