Coset Constructions of Logarithmic (1, p) Models

One of the best understood families of logarithmic onformal field theories consists of the (1, p) models (p= 2,3) of central charge (Formula presented). This family includes the theories corresponding to the (Formula presented) and the triplet (Formula presented), as well as the ubiquitous symplectic fermions theory. In this work, these algebras are realised through a coset construction. The (Formula presented) algebra of level k was introduced by Feigin and Semikhatov as a (conjectured) quantum hamiltonian reduction of (Formula presented), generalising the Bershadsky-Polyakov algebra (Formula presented). Inspired by work of Adamović for p= 3, vertex algebras (Formula presented) are constructed as subalgebras of the kernel of certain screening charges acting on a rank 2 lattice vertex algebra of indefinite signature. It is shown that for p≤ 5, the algebra (Formula presented) is a quotient of (Formula presented) at level (Formula presented) and that the known part of the operator product algebra of the latter algebra is consistent with this holding for p> 5 as well. The tripletalgebra (Formula presented) is then realised as a coset inside the full kernel of the screening operator, while the singletalgebra (Formula presented) is similarly realised inside (Formula presented). As an application, and to illustrate these results, the coset character decompositions are explicitly worked out for p = 2 and 3.