Permutation orbifolds of vertex operator superalgebra and associative algebras

2023/10/01 by Dong, Chongying, Xu, Feng, Yu, Nina
#17B69 #FOS: Mathematics #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.2310.00579

Abstract

Let V be a vertex operator superalgebra and g=(1 2 ⋯ k) be a k-cycle which is viewed as an automorphism of the tensor product vertex operator superalgebra V^{⊗ k}. In this paper, we construct an explicit isomorphism from A_g(V^{⊗ k}) to A(V) if k is odd and to A_σ(V) if k is even where σ is the canonical automorphism of V of order 2 determined by the superspace structure of V. These recover previous results by Barron and Barron-Werf that there is a one-to-one correspondence between irreducible g-twisted V^{⊗ k}-modules and irreducible V-modules (resp. irreducible σ-twisted V-modules) when k is odd (resp. even). This explicit isomorphism is expected to be useful in our further study on the Zhu algebra of fixed point subalgebra.

Related

• Permutation orbifolds and associative algebras
• Twisted modules for tensor product vertex operator superalgebras and permutation automorphisms of odd order
• Permutation-twisted modules for even order cycles acting on tensor product vertex operator superalgebras
• Fusion products of twisted modules in permutation orbifolds
• Super orbifold theory