W3 Constructions on Affine Lie Algebras

Abstract

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.

9 pages

Cited by in corpus (5)

• W-symmetry in Conformal Field Theory
• Irrational Conformal Field Theory
• The Complete Spectrum of the $W_N$ String
• Automorphisms of W-Algebras and Extended Rational Conformal Field Theories
• W-Strings from Affine Lie Algebras