The algebraic structure of relative twisted vertex operators

Abstract

Twisted vertex operators based on rational lattices have had many applications in vertex operator algebra theory and conformal field theory. In this paper, "relativized" twisted vertex operators are constructed in a general context based on isometries of rational lattices, and a generalized twisted Jacobi identity is established for them. This result generalizes many previous results. Relatived untwisted vertex operators had been studied in a monograph by the authors. The present paper includes as a special case the proof of the main relations among twisted vertex operators based on even lattices announced some time ago by the second author.

ℤ3symmetry and W3algebra in lattice vertex operator algebras

“…τ 2 -twisted) V L -modules. Basic references to twisted modules for lattice vertex operator algebras are [6], [7] and [25]. The argument here is similar to that in [22, Section 6].…”

“…We usually denote L by √ 2A 2 . We follow Sections 2 and 3 of [7] with L = √ 2A 2 , p = 3, and q = 6. In our case α, β ∈ 2Z for all α, β ∈ L, so that the alternating Z-bilinear map c 0 : L × L → Z/6Z defined by [7, (2.9)] is trivial.…”

“…We follow [7] with L = √ 2A 2 , p = 3, q = 6, and ν = τ . Let h = C ⊗ Z L and extend the Z-bilinear form ·, · on L to h linearly.…”

“…There are exactly two inequivalent irreducible τ i -twisted M -modules M T (τ i ) and W T (τ i ), i = 1, 2. We investigate the irreducible τ i -twisted V L -modules constructed in [7] and obtain M T (τ i ) and W T (τ i ) inside them.…”

“…For basic definitions concerning lattice vertex operator algebras we refer to [7] and [17]. We also recall certain properties of the vertex operator algebra V √ 2A 2 (cf.…”