Bootstrapping mixed correlators in the 2D Ising model

Bootstrapping mixed correlators in three dimensional conformal field theories with a $\mathbb Z_2$ global symmetry has previously led to a closed allowed region in ($\Delta_\sigma$, $\Delta_\epsilon$) space surrounding the 3D Ising model. We repeat that analysis in two dimensions. By further assuming a gap in the spin-2 sector, we also find a closed allowed region in ($\Delta_\sigma$, $\Delta_\epsilon$) space surrounding the 2D Ising model.