Instantons, fluxons, and open gauge string theory

We use the exact instanton expansion to illustrate various string characteristics of non-commutative gauge theory in two dimensions. We analyse the spectrum of the model and present some evidence in favour of Hagedorn and fractal behaviours. The decompactication limit of non-commutative torus instantons is shown to map in a very precise way, at both the classical and quantum levels, onto fluxon solutions on the non-commutative plane. The weak-coupling singularities of the usual Gross - Taylor string partition function for QCD on the torus are studied in the instanton representation and its double-scaling limit, appropriate for the mapping onto non-commutative gauge theory, is shown to be a generating function for the volumes of the principal moduli spaces of holo-morphic differentials. The non-commutative deformation of this moduli space geometry is described and appropriate open string interpretations are proposed in terms of the fluxon expansion.