Truncatable bootstrap equations in algebraic form and critical surface exponents

Understand

We describe examples of drastic truncations of conformal bootstrap equations encoding much more information than that obtained by a direct numerical approach.

• A three-term truncation of the four point function of a free scalar in any space dimensions provides algebraic identities among conformal block derivatives which generate the exact spectrum of the infinitely many primary operators contributing to it.
• In boundary conformal field theories, we point out that the appearance of free parameters in the solutions of bootstrap equations is not an artifact of truncations, rather it reflects a physical property of permeable conformal interfaces which are described by the same equations.
• Surface transitions correspond to isolated points in the parameter space.