Equivariant Segal–Stolz–Teichner conjecture

Let $G$ be a symmetry group, let $\nu$ be the gravitational anomaly, and let $k$ be the 't Hooft anomaly, with $\nu\oplus k\in (I_\mathbb{Z}\Omega^\text{spin})^4(BG)$. For a simple simply-connected compact Lie group, the non-gravitational part is identified with $\mathrm{H}^4(BG,\mathbb{Z})\simeq\mathbb{Z}$. Equivariant Segal–Stolz–Teichner conjecture. The equivariant $\mathrm{TMF}$ group $\mathrm{TMF}^{-(\nu\oplus k)}_G(\mathrm{pt})$ is the deformation class of 2d $\mathcal{N}=(0,1)$ supersymmetric theories with anomaly $\nu\oplus k\in (I_\mathbb{Z}\Omega^\text{spin})^4(BG)$. This extends the proposed $\mathrm{TMF}$ classification from theories without symmetry to theories with a symmetry group and is intended to determine the anomaly of the corresponding spacetime theory.