  We study d=2 0A string theory perturbed by tachyon momentum modes in
backgrounds with non-trivial tachyon condensate and Ramond-Ramond (RR) flux. In
the matrix model description, we uncover a complexified Toda lattice hierarchy
constrained by a pair of novel holomorphic string equations. We solve these
constraints in the classical limit for general RR flux and tachyon condensate.
Due to the non-holomorphic nature of the tachyon perturbations, the
transcendental equations which we derive for the string susceptibility are
manifestly non-holomorphic. We explore the phase structure and critical
behavior of the theory.
