Logarithmic vertex algebras related to sp(4)

Abstract

We present several results and conjectures pertaining to parafermion vertex algebra and related logarithmic vertex algebras. Starting from the tensor product of two copies of the singlet vertex algebra M(2), we consider various subalgebras that appear in its decomposition including N −1 (sl(2)) and its Z 2 -fixed point algebra, and the S 2 -symmetric orbifold of the singlet vertex algebra M(2). In particular, we show that N −1 (sl( 2)) has an extension to a W -algebra of type (2,3,4,5,6,7,8). Finally we state some conjectures about singlet and triplet type W -algebras of type sp(4) and their characters.