arXiv subjects
Publications and source records attributed to A. Deckmyn.
For a generic $\Ww$ algebra, we give an algorithmic procedure for factoring out all fields of dimension $1/2$, both bosonic and fermionic, and some fields of dimension $1$. This generalizes and makes more explicit the Goddard-Schwimmer theorem for free fermions. We also show how the induced gravity theory for the original $\Ww$ algebra containing the free fields relates to the theory where the fields are factored out.
We use an argument of Romans showing that every Virasoro construction leads to realizations of $W_3$, to construct $W_3$ realizations on arbitrary affine Lie algebras. Solutions are presented for generic values of the level as well as for specific values of the level but with arbitrary parameters. We give a detailed discussion of the $\aff{su}(2)_\ell$-case. Finally, we discuss possible applications of these realizations to the construction of $W$-strings.