Q-Systems and Extensions of Completely Unitary Vertex Operator Algebras

Abstract Complete unitarity is a natural condition on CFT-type regular vertex operator algebra (VOA), which ensures that its modular tensor category (MTC) unitary. In this paper we show any unitary (conformal) extension $U$ of completely VOA $V$ Our method to relate with Q-system $A_U$ in the $C^*$-tensor $\textrm{Rep}^{\textrm{u}}(V)$ $V$-modules. We also update main result [ 30] cases by showing $\textrm{Rep}^{\textrm{u}}(U)$ $U$-modules equivalent $\textrm{Rep}^{\textrm{u}}(A_U)$ $A_U$-modules as MTCs. As an application, obtain infinitely many new (regular and) VOAs including all $c<1$ VOAs. latter are one-to-one correspondence (irreducible) conformal nets same central charge $c$, classification given 29].