The VOSA-to-$\mathrm{TMF}$ class conjecture

Let $\mathbb{V}$ be a holomorphic VOSA of central charge $n/2$ containing an affine algebra $\hat{\mathfrak{g}}_k$. Let $G$ be the simply-connected compact Lie group of type $\mathfrak{g}$, and let $\tau\colon BG\to K(\mathbb{Z},4)$ represent a generator of $H^4(BG;\mathbb{Z})\simeq\mathbb{Z}$. Then

The VOSA-to-$\operatorname{TMF}$ class conjecture. The VOSA should determine a class

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

such that $\Phi([\mathbb{V}])\in \operatorname{KO}^n_G((q))(\mathrm{pt})$ can be computed from the theory of VOSAs. This proposes a mathematical realization of the Stolz–Teichner correspondence for purely left-moving theories, but genuinely equivariant twisted $\operatorname{TMF}$ was not yet adequately developed in the source.