Differential operator realizations of superalgebras and free field representations of corresponding current algebras

Abstract

Based on the particular orderings introduced for the positive roots of finite-dimensional basic Lie superalgebras, we construct the explicit differential operator representations of the osp ( 2 r | 2 n ) and osp ( 2 r + 1 | 2 n ) superalgebras and the explicit free field realizations of the corresponding current superalgebras osp ( 2 r | 2 n ) k and osp ( 2 r + 1 | 2 n ) k at an arbitrary level k. The free field representations of the corresponding energy–momentum tensors and screening currents of the first kind are also presented.