The affine VOSA class conjecture

Let $\mathbb{V}$ be a unitary self-dual VOSA of central charge $c=n/2$ containing the affine Lie VOA $\mathfrak{g}_k$, and let $G$ be the corresponding compact simply-connected group. Let $\mathbb{W}$ be the canonically $\mathbb{Z}/2$-twisted module, and let $\tau\colon BG\to K(\mathbb{Z},4)$ represent the generator of $H^4(BG;\mathbb{Z})\simeq\mathbb{Z}$. The affine VOSA class conjecture. There is a class

$$[\mathbb{V}]\in \operatorname{TMF}^{n+k\tau}_G(\mathrm{pt})$$

such that

$$\Phi([\mathbb{V}])=\eta(q)^{-n}[\mathbb{W}]\in \operatorname{KO}^n_G((q))(\mathrm{pt}).$$

This is the precise equivariant refinement of the proposed correspondence between self-dual VOSAs and $\operatorname{TMF}$ classes; its genuinely equivariant twisted theory was not adequately developed in the source.