Flux-vacua in two dimensional string theory

We analyze the two dimensional type 0 theory with background RR-fluxes. Boththe 0A and the 0B theory have two distinct fluxes $q$ and $\tilde q$. We studythese two theories at finite temperature (compactified on a Euclidean circle ofradius $R$) as a function of the fluxes, the tachyon condensate $\mu$ and theradius $R$. Surprisingly, the dependence on $q$, $\tilde q$ and $\mu$ is rathersimple. The partition function is the absolute value square of a holomorphicfunction of $y=|q|+|\tilde q| + i \sqrt{2\alpha'} \mu$ (up to a simple butinteresting correction). As expected, the 0A and the 0B answers are related byT-duality. Our answers are derived using the exact matrix models description ofthese systems and are interpreted in the low energy spacetime Lagrangian.Comment: 41 pages, 4 figures, harvmac.te