Minimal superstring theories

In this thesis we study the (2, 4m) series of Type OA minimal superstring theories, which are intimately related to the KdV integrable hierarchy. Chapters 1 to 3 constitute a comprehensive review of the relevant background material, including noncritical string theory, matrix models and integrable systems. In Chapter 4 we generalise the (2， 4m) theories so as to include unoriented worldsheet contributions in the partition sum. This generalisation is tested against a known result in the literature. Chapter 5 explores the D-branes of the theories in more detail and, by studying the Bäcklund transformation of the KdV hierarchy, gives conclusive evidence that the parameter speculated to control the number of zz branes in the theory is indeed quantised. The FZZT brane partition function is studied, and it is shown that the effects of the boundary cosmological constant arise only in certain predictable forms. Chapter 6 examines the string theory interpretation of the negative KdV hierarchy, which naively relates to supercritical string theories living in greater than ten dimensions. The models are seen to have some non-trivial characteristic properties, indicating that they do indeed describe valid string theories, but it is unclear whether said theories are actually supercritical.