Bootstrapping mixed correlators in the 3D Ising model

We study the conformal bootstrap for systems of correlators involving nonidentical operators. The constraints of crossing symmetry and unitarity for such mixed correlators can be phrased in the language of semidefinite programming. We apply this formalism to the simplest system of mixed correlators in 3D CFTs with a Z(2) global symmetry. For the leading Z(2) - odd operator sigma and Z(2) - even operator is an element of, we obtain numerical constraints on the allowed dimensions (Delta(sigma), Delta(is an element of)) assuming that sigma and is an element of are the only relevant scalars in the theory. These constraints yield a small closed region in (Delta(sigma), Delta(is an element of)) space compatible with the known values in the 3D Ising CFT.