Equivariant Stolz–Teichner conjecture for field theories and equivariant TMF

Let $G$ be a compact Lie group acting on a manifold $X$, let $X{/{\!/}^{\nabla}}G$ denote the quotient stack encoding the action with connection data, and let $[\ell]\in H^4(BG;\mathbb{Z})$ be a level. Write ${\sf QFT}^{\ell}_{2|1}(X{/{\!/}^{\nabla}}G)$ for the category of $[?]$-twisted 2|1-dimensional field theories and ${\rm TMF}^{\ell}_G(X)$ for $[?]$-twisted $G$-equivariant TMF. Equivariant Stolz–Teichner conjecture. There is a cocycle map

$${\sf QFT}^{\ell}_{2|1}(X{/{\!/}^{\nabla}}G)\longrightarrow {\rm TMF}^{\ell}_G(X)$$

valued in $[?]$-twisted $G$-equivariant TMF of $X$; moreover, families of $G$-equivariant string manifolds admit an analogous commuting triangle. This is a proposed equivariant refinement of the Stolz–Teichner picture, but the paper notes that the relevant higher-categorical field-theory definitions form a non-unique collection and that variations remain open.