Matrix Models of 2D String Theory in Non--trivial Backgrounds

After a brief review of critical string theory in trivial backgrounds we begin with introduction to strings in non--trivial backgrounds and noncritical string theory. In particular, we relate the latter to critical string theory in a linear dilaton background. We then show how a black hole background arises from 2D string theory and discuss some of its properties. A time--dependant tachyon background is constructed by perturbing the CFT describing string theory in a linear dilaton background. It is then explained that the T--dual of this theory with one non--vanishing tachyon coupling, which is a sine-Liouville CFT, is seemingly equivalent to the exact CFT describing the Euclidean black hole background. Subsequently, we launch into a review of some important facts concerning random matrix models and matrix quantum mechanics (MQM), culminating in an MQM model of 2D string theory in a dynamic tachyon background. We then solve this theory explicitly in the tree level approximation for the case of two non--vanishing tachyon couplings, which generalises the case of sine-Liouville CFT previously considered in the literature.