Speaker
Nat Levine
Description
Extremal solutions and functionals play an important role in the conformal bootstrap. One may wonder if it is possible to rigorously prove that they exist, and to deduce their properties. This is a question about what happens when numerics have fully converged, i.e. at Lambda=infinity. In the simplest setting of OPE maximisation in 1d CFT, we prove that extremal solutions exist using the Fenchel-Rockafellar theorem. These are interacting, unitary, exact solutions of the crossing equation that maximise an OPE coefficient. This approach may have interesting implications for (i) whether 3d Ising can be an extremal solution and (ii) potential 'hybrid' bootstrap approaches.