Free field realizations of $N=1$ SUSY affine vertex algebras

Abstract

We construct Wakimoto-type free field realizations of $N=1$ SUSY affine vertex algebras associated with basic classical Lie superalgebras. Using the superfield formalism, we obtain a SUSY analogue of the Wakimoto realization in terms of $\beta\gamma$--$bc$ systems and boson--fermion systems (or SUSY Heisenberg vertex algebras). We also construct screening operators for the free field realizations. A distinctive feature of the SUSY setting is that, unlike the ordinary Wakimoto realization, the injectivity of the free field homomorphism depends on the level. We prove that the homomorphism is injective for nondegenerate $\kappa$, whereas at $\kappa=0$ it fails to be injective. Thus, the SUSY Wakimoto realization exhibits a degeneration at $\kappa=0$ that has no direct counterpart in the ordinary affine case.