The worldsheet conformal field theory of the fractional superstring

• Published in: Nuclear physics. B 1994-01, Vol.413 (1), p.103-161
• Main Author: Dienes, Keith R.
• Format: Article
• Language: English
• Subjects: Conformal field theory, algebraic structures; Exact sciences and technology; General theory of fields and particles; Physics; The physics of elementary particles and fields; Theory of fundamental strings
• ISSN: 0550-3213; 1873-1562
• DOI: 10.1016/0550-3213(94)90616-5

Two of the important unresolved issues concerning fractional superstrings have been the appearance of new massive sectors whose space-time statistics properties are unclear, and the appearance of new types of “internal projections” which alter or deform the worldsheet conformal field theory in a highly non-trivial manner. In this paper we provide a systematic analysis of these two connected issues, and explicitly map out the effective post-projection worldsheet theories for each of the fractional-superstring sectors. In this way we determine their central charges, highest weights, fusion rules, and characters, and find that these theories are isomorphic to those of free worldsheet bosons and fermions. We also analyze the recently-discovered parafermionic “twist current” which has been shown to play an important role in reorganizing the fractional-superstring Fock space, and find that this current can be expressed directly in terms of the primary fields of the post-projection theory. This thereby enables us to deduce some of the space-time statistics properties of the surviving states.