The Worldsheet Conformal Field Theory of the Fractional Superstring

TL;DR

This paper systematically analyzes the worldsheet conformal field theories of fractional superstrings, clarifying their structure, statistics, and the role of twist currents, revealing they are isomorphic to free boson and fermion theories.

Contribution

It provides a detailed mapping of the post-projection worldsheet theories for fractional superstrings, including their algebraic properties and the role of twist currents.

Findings

Post-projection theories are isomorphic to free bosons and fermions.

Explicit expressions for the twist current in terms of primary fields.

Determined the spacetime statistics of the surviving states.

Abstract

Two of the important unresolved issues concerning fractional superstrings have been the appearance of new massive sectors whose spacetime 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 spacetime statistics properties of the surviving states.