Central Charge Reduction and Spacetime Statistics in the Fractional Superstring

Fractional superstrings in the tensor-product formulation experience ``internal projections'' which reduce their effective central charges. Simple expressions for the characters of the resulting effective worldsheet theory are found. All states in the effective theory can be consistently assigned definite spacetime statistics. The projection to the effective theory is shown to be described by the action of a dimension-three current in the original tensor-product theory.Comment: 11 pages (LaTeX), CLNS 92/1168, McGill/92-41 (minor typos corrected

New Jacobi-Like Identities for Z_k Parafermion Characters

We state and prove various new identities involving the Z_K parafermion characters (or level-K string functions) for the cases K=4, K=8, and K=16. These identities fall into three classes: identities in the first class are generalizations of the famous Jacobi theta-function identity (which is the K=2 special case), identities in another class relate the level K>2 characters to the Dedekind eta-function, and identities in a third class relate the K>2 characters to the Jacobi theta-functions. These identities play a crucial role in the interpretation of fractional superstring spectra by indicating spacetime supersymmetry and aiding in the identification of the spacetime spin and statistics of fractional superstring states.Comment: 72 pages (or 78/2 = 39 pages in reduced format

N=2 structures on solvable Lie algebras: the c=9 classification

Let G be a finite-dimensional Lie algebra (not necessarily semisimple). It is known that if G is self-dual (that is, if it possesses an invariant metric) then there is a canonical N=1 superconformal algebra associated to its N=1 affinization---that is, it admits an N=1 (affine) Sugawara construction. Under certain additional hypotheses, this N=1 structure admits an N=2 extension. If this is the case, G is said to possess an N=2 structure. It is also known that an N=2 structure on a self-dual Lie algebra G is equivalent to a vector space decomposition G = G_+ \oplus G_- where G_\pm are isotropic Lie subalgebras. In other words, N=2 structures on G are in one-to-one correspondence with Manin triples (G,G_+,G_-). In this paper we exploit this correspondence to obtain a classification of the c=9 N=2 structures on self-dual solvable Lie algebras. In the process we also give some simple proofs for a variety of Lie algebraic results concerning self-dual Lie algebras admitting symplectic or K\"ahler structures.Comment: 49 pages in 2 columns (=25 physical pages), (uufiles-gz-9)'d .dvi file (uses AMSFonts 2.1+). Revision: Added 1 reference, corrected typos, added some more materia

Gravitino condensation in fivebrane backgrounds

We calculate the tension of the D3-brane in the fivebrane background which is described by the exactly solvable SU(2)_k x U(1) world-sheet conformal field theory with large Kac-Moody level k. The D3-brane tension is extracted from the amplitude of one closed string exchange between two parallel D3-branes, and the amplitude is calculated by utilizing the open-closed string duality. The tension of the D3-brane in the background does not coincide with the one in the flat space-time even in the flat space-time limit: k -> infinity. The finite curvature effect should vanish in the flat space-time limit and only the topological effect can remain. Therefore, the deviation indicates the condensation of gravitino and/or dilatino which has been expected in the fivebrane background as a gravitational instanton.Comment: 16 pages, 1 figur