Status of Fractional Superstrings

We argue why it is important to search beyond the superstring for consistent string theories that have space-time supersymmetry with critical space-time dimensions less than 10. We give a lengthy introduction on the motivation and approach. We discuss briefly some promising possibilities, namely, fractional superstrings. More specifically, we consider the K = 4, or spin-4/3 fractional superstring, which has a 3-dimensional flat Minkowski space-time representation with bosons and fermions in its spectrum. Its central charge of 5 is less than the critical value of 10. The no-ghost theorem for the bosonic sector is proved, using the recently constructed Kac determinants. We summarize the present status and point out some open questions. Talk at the conference “Strings 93”, Berkeley, May 23-29, 1993.