Isolated solutions in the 3d conformal bootstrap (3d Ising model)

Determine whether the solution space of the three-dimensional conformal bootstrap equations contains isolated points, specifically establish that the 3d Ising model corresponds to an isolated solution (the numerically observed “island” shrinks to a point).

Background

By analogy, the paper shows hyperbolic bootstrap equations have isolated solutions (e.g., uniqueness in certain regimes). The authors contrast this with conformal bootstrap: in 2d, isolated solutions (like the 2d Ising model) are known, but in 3d this is still an open question.

They suggest that proving isolated solutions in 3d would require results analogous to their converse theorem for hyperbolic bootstrap, underscoring both the difficulty and importance of the problem in conformal field theory.