Cyclic Permutations in Kazama-Suzuki String Models

Moddings by cyclic permutation symmetries are performed in 4-dimensional strings, built up from N=2 coset models of the type $CP_m=SU(m+1)/SU(m)\times U(1)$. For some exemplifying cases, the massless chiral and antichiral states of $E_6$ are computed. The extent of the equivalence between different conformal invariant theories which possess equal chiral rings is analyzed.Comment: 26 pages, LaTex fil

Decimation-in-Frequency Fast Fourier Transforms for the Symmetric Group

In this thesis, we present a new class of algorithms that determine fast Fourier transforms for a given finite group G. These algorithms use eigenspace projections determined by a chain of subgroups of G, and rely on a path algebraic approach to the representation theory of finite groups developed by Ram (26). Applying this framework to the symmetric group, Sn, yields a class of fast Fourier transforms that we conjecture to run in O(n2n!) time. We also discuss several future directions for this research

Non-Hermitian Symmetric N=2 Coset Models, Poincare Polynomials, and String Compactification

The field identification problem, including fixed point resolution, is solved for the non-hermitian symmetric $N=2$ superconformal coset theories. Thereby these models are finally identified as well-defined modular invariant CFTs. As an application, the theories are used as subtheories in tensor products with $c=9$, which in turn are taken as the inner sector of heterotic superstring compactifications. All string theories of this type are classified, and the chiral ring as well as the number of massless generations and anti-generations are computed with the help of the extended Poincare polynomial. Several equivalences between a priori different non-hermitian cosets show up; in particular there is a level-rank duality for an infinite series based on $C$ type Lie algebras. Further, some general results for generic $N=2$ cosets are proven: a simple formula for the number of identification currents is found, and it is shown that the set of Ramond ground states of any $N=2$ coset model is invariant under charge conjugation.Comment: 44 pages, LATEX, HD-THEP-93-