Non-perturbative RR Potentials in the c=1 Matrix Model

We use the \hat c=1 matrix model to compute the potential energy V(C) for(the zero mode of) the RR scalar in two-dimensional type 0B string theory. Thepotential is induced by turning on a background RR flux, which in the matrixmodel corresponds to unequal Fermi levels for the two types of fermions.Perturbatively, this leads to a linear runaway potential, but non-perturbativeeffects stabilize the potential, and we find the exact expressionV(C)=\frac{1}{2\pi}\int da\arccos [\cos(C)/\sqrt{1+e^{-2\pi a}}]. We alsocompute the finite-temperature partition function of the 0B theory in thepresence of flux. The perturbative expansion is T-dual to the analogous resultin type 0A theory, but non-perturbative effects (which depend on C) do notrespect naive R\to 1/R duality. The model can also be used to study scatteringamplitudes in background RR fluxes.Comment: 38 pages, 4 figure