Unitary vertex operator algebras

Abstract

Unitary vertex operator algebras are introduced and studied. It is proved that most well-known rational vertex operator algebras are unitary. The classification of unitary vertex operator algebras with central charge c ≤ 1 is also discussed.

Classification of unitary vertex subalgebras and conformal subnets for rank-one lattice chiral CFT models

“…From (22) we deduce that the lowest z-power in equation (47) is g 2 > 0. Thus we can restrict our attention just to B and therefore to equation (48) because −g 2 + 4 ≤ 0.…”

“…By [22,Theorem 4.12], V L 2N has a structure of unitary VOA with PCT operator θ. Note also that all unitary structures on a simple VOA are equivalent up to unitary isomorphism (see [10, p. 38]).…”

“…A unitary subalgebra of V L 2N is M (1) ⊗ C C1 (which we indicate just with M (1)) with vacuum vector Ω ⊗ 1, conformal vector ν ⊗ 1 and PCT operator θ| M (1) . More in general, this is a well-know unitary VOA with central charge 1, called the Heisenberg or current VOA (see [22,Section 4.3]).…”

Some exceptional extensions of Virasoro vertex operator algebras

“…Then any modular invariant of Virasoro vertex operator algebra L(c p,q , 0) is equal to one of the following modular invariants: [16]. Recall that when p = m + 3 and q = m + 2, the Virasoro vertex operator algebra L(c m , 0) := L(c p,q , 0) is unitary [15]. The following results about exceptional extensions of unitary Virasoro vertex operator algebras have been obtained in [16].…”

“…It is well-known that the central charges of rational Virasoro vertex operator algebras belong to a discrete set (see the formula (3.1)), and there is an important subclass of rational Virasoro vertex operator algebras which are unitary vertex operator algebras [15]. Connections between unitary vertex operator algebras and conformal nets have been studied recently in [7].…”