11 problems

Strong graded locality theorem. Every nice holomorphic VOSA $V$ with central charge $c\leq 24$ is strongly graded-local. In particular, it gives rise to a holomorphic graded-local…

Let $V\!B^{\natural}$ denote the shorter moonshine module, also called the Baby Monster SVOA. A self-dual unitary rational SVOA is called “very nice” in the sense used in the sourc…

Rationality conjecture. The vertex operator superalgebra $V_{c_{p,q}}$ is rational. Moreover, the minimal series modules $L_{c,h_{r,s}}$, with $0<r<p$, $0<s<q$, and…

Hoehn's shorter moonshine $VB^\natural$ uniqueness conjecture. The VOSA $VB^\natural$ is the unique nice holomorphic VOSA with central charge

Let $\mathcal{A}$ be an irreducible graded-local conformal net, meaning a graded-local conformal net satisfying the irreducibility condition. Converse conformal-net conjecture. For…

A fake copy is a nice, self-dual vertex operator superalgebra of central charge $24$ with vanishing weight-$1$ spaces both in the superalgebra and in its canonically twisted module…

Let $\textbf{P}$ be the category of modules over the vertex operator superalgebra $\mathsf{B}_{0\vert 1} \brac{2,4}$. The Grothendieck fusion product is intended to define a ring s…

Let $V$ be a vertex operator superalgebra and let $k$ be a positive even integer. The cyclic permutation $(1\;2\;\cdots\;k)$ acts on the tensor product vertex operator superalgebra…

Let $V_{fer}$ denote the free fermion vertex operator superalgebra, let $k$ be an even positive integer, and let $V_{\mathbb{Z}\alpha}$ be the rank-one lattice vertex operator supe…

Let $V$) be a vertex operator superalgebra and let $k$ be an even positive integer. Consider weak, weak admissible, ordinary, parity-stable, and parity-unstable modules for the cyc…

Let $V$ be a vertex operator superalgebra, let $k$ be even, and let $g=(1\;2\;\cdots\;k)$ act by permuting the tensor factors of $V^{\otimes k}$. A parity-twisted $V$-module is a m…