TMF-homology conjecture for boundary conditions of supersymmetric sigma models

Let $X$ be the target of a 3-dimensional $\mathcal{N}=1$ supersymmetric sigma model, and let $X_+$ denote $X$ with a disjoint basepoint. Sigma-model boundary-condition conjecture. The homotopy type of the space of boundary conditions is described by $\operatorname{TMF}\otimes X_+$. This is the homological counterpart of the TMF-cohomological description for nondynamical background fields; it reflects the additional dynamical and Dirichlet boundary conditions in a genuine sigma model.