Conformal subalgebras of lattice vertex algebras

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In this paper we classify, under certain restrictions, all homogeneous conformal subalgebras L of a lattice vertex superalgebra VΛ corresponding to an integer lattice Λ. We require that L is graded by an almost finite root system Δ⊂ Λ and that L is stable under the action of the Heisenberg conformal algebra H⊂ VΛ. We also describe the root systems of these subalgebras. The key ingredient of this classification is an infinite type conformal algebra K obtained by the Tits-Kantor-Koeher construction from a certain Jordan conformal triple system J. We realize a central extension K of K inside the fermionic vertex superalgebra V, thus extending the bozon-fermion correspondence.