Structure constants of the fractional supersymmetry chiral algebras

Abstract

The fractional supersymmetry chiral algebras, A (K) , in two-dimensional conformal field theory are extended Virasoro algebras with fractional spin currents J (K) . We show that associativity and closure of A (K) determines its structure constants in the case that the Virasoro algebra is extended by precisely one current.We compute the structure constants of the A (K) algebras explicitly and we show that correlators of J (K) 's satisfy non-Abelian braiding relations.

Aspects of fractional superstrings

“…(2.25) and the triality of SO (8). [17,29] W 4 is similarly the difference between a D 4 ⊗D 4 ⊗D 4 ⊗D 4 MIPF and a simple current invariant of D 4 ⊗ D 4 ⊗ D 4 ⊗ D 4 .…”

“…Last, we derive a linear (rather than quadratic) relationship between the required conformal anomaly and the conformal dimension of the supercurrent ghost.K+2 is the central charge for one dimension, and λ K is a constant. [8] The relationship between critical dimension, D, and the level, K, of the parafermion CFT may be shown to be D = 2 + 16 K , (1.8)for K = 2, 4, 8, 16, and ∞. (The K = 2 theory is the standard Type II superstring theory with its partition function expressed in terms of string functions rather than theta-functions, which implies a set of identities between these two classes of functions.)…”

Low-lying states of the six-dimensional fractional superstring

“…The non-split or tensored algebras have non-abelian braiding properties and do not, in general, satisfy any particular relation between λ and c. In principle, though, if the exact form of the (non-abelian) braiding of the currents were known, one could solve the associativity conditions to find new relations between λ and c. (For an example of this approach, see refs. [10,11]. )…”

“…The first is that the complexity of these theories increases considerably with increasing K. Although the world-sheet fractional supersymmetry algebra is non-local, the Z 4 parafermion fields that appear in the K = 4 FSS can be simply represented by free bosons, which enables the calculations to be simplified tremendously. This is not the case in the K = 8 and K = 16 theories [10,11]. Furthermore, a close examination shows that the appropriate world-sheet fractional supersymmetry algebra for the K = 8 theory contains two spin-13/5 currents in addition to the spin-6/5 current [11], which further complicate the analysis.…”

Chiral gauged Wess-Zumino-Witten theories and coset models in conformal field theory

“…This fractional supercurrent extends the Virasoro algebra [18] : G (k) (z) and the stress energy-momentum tensor T (z) form a non-local fractional superconformal algebra [19], which is the basis for fractional superstring [11]. …”