Conformal Bootstrap

Exclusion plots, islands, and the exact 3D Ising CFT from crossing symmetry + unitarity

Parameters

3D Ising Result

Δσ = 0.5181489(10) Δε = 1.412625(10) c/c_free = 0.94685(15)
Kos-Poland-Simmons-Duffin (2016): Bootstrap islands isolate the 3D Ising CFT to a tiny region in parameter space — to 8 decimal places, using only crossing symmetry and unitarity.

Method

Σ_O λ²_O F_{Δ,l}(z) = 0
If a linear functional α satisfies α[F_{Δ,l}] ≥ 0 for all allowed (Δ,l), and α[F_{0,0}] < 0, then no consistent CFT exists for that external Δ.
SDPB: semidefinite programming
The allowed region shrinks as n_max increases. The island surrounding the 3D Ising point emerges from the intersection of allowed regions.