  We numerically study the crossing symmetry constraints in 4D CFTs, using
previously introduced algorithms based on semidefinite programming. We study
bounds on OPE coefficients of tensor operators as a function of their scaling
dimension and extend previous studies of bounds on OPE coefficients of
conserved vector currents to the product groups SO(N)xSO(M). We also analyze
the bounds on the OPE coefficients of the conserved vector currents associated
with the groups SO(N), SU(N) and SO(N)xSO(M) under the assumption that in the
singlet channel no scalar operator has dimension less than four, namely that
the CFT has no relevant deformations. This is motivated by applications in the
context of composite Higgs models, where the strongly coupled sector is assumed
to be a spontaneously broken CFT with a global symmetry.
