Aspects of Fractional Superstrings*

We investigate some issues relating to recently proposed fractional superstring theories with Dcritical < 10. Using the factorization approach of Gepner and Qiu, we systematically rederive the partition functions of the K = 4, 8, and 16 theories and examine their spacetime supersymmetry. Generalized GSO projection operators for the K = 4 model are found. Uniqueness of the twist field, φ K/4 K/4, as source of spacetime fermions is demonstrated. Last, we derive a linear (rather than quadratic) relationship between the required conformal anomaly and the conformal dimension of the supercurrent ghost. *Work supported in part by the U.S. Department of Energy under Contract no. DEAC-03-81ER40050. †[email protected] ‡[email protected] Section 1: Introduction In the last few years, several generalizations of standard (supersymmetric) string theory have been proposed. One of them uses the (fractional spin) parafermions introduced from the perspective of 2-D conformal field theory (CFT) by Zamolodchikov and Fateev in 1985 and further developed by Gepner and Qiu. In a series of papers, possible new string theories with local parafermionic world sheet currents (of fractional conformal spin) giving critical dimensions D = 6, 4, 3, and 2 have been proposed. At the heart of these new “fractional superstrings” are ZZK parafermion conformal field theories (PCFT’s) with central charge c = 2(K−1) K+2 . (Equivalently, these are SU(2)K/U(1) conformal field theories.) The (integer) level-K PCFT contains a set of unitary primary fields φm, where 0 ≤ j, |m| ≤ K/2; j, m ∈ ZZ/2, and j −m = 0 (mod 1), which have the identifications φm = φ j m+K = φ K 2 −j m− 2 . (1.1) In the range |m| ≤ j, the conformal dimension is h(φm) = j(j+1) K+2 − m 2 K . At a given level the fusion rules are φ1 m2 × φ j2 m2 = r