Regularity of fixed-point vertex operator subalgebras

Understand

We show that if $T$ is a simple non-negatively graded regular vertex operator algebra with a nonsingular invariant bilinear form and $\sigma$ is a finite order automorphism of $T$, then the fixed-point vertex operator subalgebra $T^\sigma$ is also regular.

• This yields regularity for fixed point vertex operator subalgebras under the action of any finite solvable group.
• As an application, we obtain an $SL_2(\mathbb{Z})$-compatibility between twisted twining characters for commuting finite order automorphisms of holomorphic vertex operator algebras.
• This resolves one of the principal claims in the Generalized Moonshine conjecture.