Bimodues associated to twisted modules of vertex operator algebras and fusion rules

Yiyi Zhu

doi:10.1142/S1005386726000076

paper

Bimodues associated to twisted modules of vertex operator algebras and fusion rules

arXiv:2204.00238 · doi:10.1142/S1005386726000076

Abstract

Let $V$ be a vertex operator algebra, $T \in N$ and $(M^{k}, Y_{M^{k}})$ for $k = 1, 2, 3$ be a $g_{k}$ -twisted module, where $g_{k}$ are commuting automorphisms of $V$ such that $g_{k}^{T} = 1$ for $k = 1, 2, 3$ and $g_{3} = g_{1} g_{2}$ . Suppose $I (\cdot, z)$ is an intertwining operator of type $(a r r a y c M^{3} M^{1} M^{2} a r r a y)$ . We construct an $A_{g_{1} g_{2}} (V)$ - $A_{g_{2}} (V)$ -bimodule $A_{g_{1} g_{2}, g_{2}} (M^{1})$ which determines the action of $M^{1}$ from the bottom level of $M^{2}$ to the bottom level of $M^{3}$ and explored its connections with fusion rules.

arXiv comment26 pages