N = 4 SUPERCONFORMAL COSET THEORIES

Starting from the N = 1 superconformal coset (GKO) construction we derive the conditions under which superconformal symmetry extends to an N = 4 superconformal symmetry. The generic N = 4 superconformal algebra in coset models is the one having D(2, 1; α) as projective subalgebra. A large class of models satisfying these conditions are of the form W ⊗ SU(2) ⊗ U(1) with W a Wolf symmetric space. Decoupling of the U(1) current yields N = 4 superconformal theories on the odd-dimensional W ⊗ SU(2) coset where the N = 4 algebra is now of the Bershadsky-Knizhnik type, i.e. quadratically non-linearly generated. © 1990.